Subgroups — C₆₇×#61729 #30740980

Order 17152.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3351	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3348	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3344	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3310	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3190	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	#555×C₆₇	C₂²	1	1	yes	characteristic
25	#554×C₆₇	C₂²	1	1	yes	characteristic
26	#553×C₆₇	—	2	1	no	—
27	#553×C₆₇	C₂²	1	1	yes	characteristic
28	#553×C₆₇	C₂²	1	1	yes	characteristic
29	#552×C₆₇	—	2	1	no	—
30	#552×C₆₇	—	2	1	no	—
31	#552×C₆₇	—	2	1	no	—
32	#552×C₆₇	—	2	1	no	—
33	#552×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	C₂²	1	2	yes	complemented
36	#552×C₆₇	C₂²	1	2	yes	complemented
37	#550×C₆₇	C₂²	1	1	yes	characteristic
38	#546×C₆₇	—	2	1	no	—
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	1	yes	characteristic
41	#546×C₆₇	C₂²	1	1	yes	characteristic
42	D₄²×C₆₇	—	2	1	no	—
43	D₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#540×C₆₇	—	2	1	no	—
45	#538×C₆₇	—	2	1	no	—
46	#538×C₆₇	—	2	1	no	—
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	#529×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#126×C₆₇	—	2	1	no	—
50	C₂×#125×C₆₇	—	2	1	no	—
51	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#525×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#123×C₆₇	—	2	1	no	—
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
59	#518×C₆₇	—	2	1	no	—
60	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#117×C₆₇	—	2	1	no	—
63	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#490×C₆₇	C₂²	1	2	yes	complemented
68	#488×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#485×C₆₇	C₂²	1	2	yes	complemented
71	#485×C₆₇	C₂²	1	2	yes	complemented
72	#484×C₆₇	C₂²	1	2	yes	complemented
73	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#483×C₆₇	C₂²	1	2	yes	complemented
76	#483×C₆₇	C₂²	1	2	yes	complemented
77	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#482×C₆₇	C₂²	1	2	yes	complemented
80	#482×C₆₇	C₂²	1	2	yes	complemented
81	#481×C₆₇	C₂²	1	1	yes	characteristic
82	#481×C₆₇	C₂²	1	1	yes	characteristic
83	#481×C₆₇	C₂²	1	2	yes	complemented
84	#481×C₆₇	C₂²	1	2	yes	complemented
85	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#480×C₆₇	C₂²	1	1	yes	characteristic
90	#480×C₆₇	C₂²	1	2	yes	complemented
91	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#479×C₆₇	C₂²	1	2	yes	complemented
94	#479×C₆₇	C₂²	1	2	yes	complemented
95	#478×C₆₇	C₂²	1	2	yes	complemented
96	#478×C₆₇	C₂²	1	2	yes	complemented
97	#478×C₆₇	C₂²	1	2	yes	complemented
98	#475×C₆₇	C₂²	1	2	yes	complemented
99	#470×C₆₇	C₂²	1	2	yes	complemented
100	#468×C₆₇	C₂²	1	2	yes	complemented
101	#468×C₆₇	C₂²	1	2	yes	complemented
102	#468×C₆₇	C₂²	1	2	yes	complemented
103	#467×C₆₇	C₂²	1	2	yes	complemented
104	#465×C₆₇	C₂²	1	2	yes	complemented
105	#465×C₆₇	C₂²	1	2	yes	complemented
106	#465×C₆₇	C₂²	1	2	yes	complemented
107	#464×C₆₇	C₂²	1	2	yes	complemented
108	#460×C₆₇	C₂²	1	2	yes	complemented
109	#452×C₆₇	C₂²	1	2	yes	complemented
110	#452×C₆₇	C₂²	1	2	yes	complemented
111	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#450×C₆₇	C₂²	1	2	yes	complemented
113	#450×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	1	yes	characteristic
115	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#441×C₆₇	C₂²	1	2	yes	complemented
118	#440×C₆₇	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
121	#436×C₆₇	C₂²	1	2	yes	complemented
122	#435×C₆₇	C₂²	1	2	yes	—
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
125	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#428×C₆₇	C₂²	1	2	yes	complemented
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#427×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
131	#418×C₆₇	C₂²	1	2	yes	complemented
132	#417×C₆₇	C₂²	1	2	yes	complemented
133	#416×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	—	2	1	no	—
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	—	2	1	no	—
146	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
147	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₆₇	—	2	1	no	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	#127×C₆₇	—	2	1	no	—
162	#127×C₆₇	C₂³	1	1	yes	characteristic
163	#126×C₆₇	—	2	1	no	—
164	#126×C₆₇	—	2	1	no	—
165	#126×C₆₇	—	2	2	no	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	1	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	C₂³	1	2	yes	—
178	#125×C₆₇	C₂³	1	2	yes	—
179	#125×C₆₇	C₂³	1	1	yes	characteristic
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	C₂³	1	1	yes	characteristic
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	1	no	—
189	#123×C₆₇	—	2	1	no	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	1	no	—
192	#123×C₆₇	—	2	1	no	—
193	#123×C₆₇	—	2	1	no	—
194	#123×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	1	no	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	no	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
204	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	1	no	—
214	#121×C₆₇	—	2	1	no	—
215	#121×C₆₇	—	2	1	no	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	1	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	C₂³	1	1	yes	characteristic
222	#121×C₆₇	C₂³	1	1	yes	characteristic
223	#121×C₆₇	C₂³	1	1	yes	characteristic
224	#121×C₆₇	C₂³	1	1	yes	characteristic
225	#121×C₆₇	C₂³	1	1	yes	characteristic
226	#121×C₆₇	C₂³	1	1	yes	characteristic
227	#121×C₆₇	C₂³	1	1	yes	characteristic
228	#121×C₆₇	C₂³	1	1	yes	characteristic
229	#121×C₆₇	C₂³	1	1	yes	characteristic
230	#120×C₆₇	—	2	1	no	—
231	#120×C₆₇	—	2	1	no	—
232	#120×C₆₇	—	2	1	no	—
233	#120×C₆₇	—	2	1	no	—
234	#120×C₆₇	—	2	1	no	—
235	#120×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	—	2	1	no	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	1	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
252	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
253	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
255	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	#117×C₆₇	—	2	1	no	—
263	#117×C₆₇	—	2	1	no	—
264	#117×C₆₇	—	2	1	no	—
265	#117×C₆₇	—	2	2	no	—
266	#117×C₆₇	—	2	2	no	—
267	#117×C₆₇	—	2	2	no	—
268	#117×C₆₇	—	2	2	no	—
269	#117×C₆₇	—	2	1	no	—
270	#117×C₆₇	C₂³	1	2	yes	—
271	#117×C₆₇	C₂³	1	2	yes	—
272	#117×C₆₇	C₂³	1	1	yes	characteristic
273	#117×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
280	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
281	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
291	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
292	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
293	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	#107×C₆₇	C₂³	1	2	yes	—
303	#107×C₆₇	C₂³	1	2	yes	—
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#106×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	#106×C₆₇	C₂³	1	2	yes	—
313	#106×C₆₇	C₂³	1	2	yes	—
314	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	#103×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#102×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
340	#97×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	C₂⁴×C₆₇	—	2	1	no	—
344	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
345	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
346	#41×C₆₇	—	4	2	no	—
347	#41×C₆₇	—	4	2	no	—
348	#41×C₆₇	—	8	2	no	—
349	C₂×Q₈×C₆₇	—	2	1	no	—
350	C₂×Q₈×C₆₇	—	2	1	no	—
351	C₂×Q₈×C₆₇	—	4	2	no	—
352	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₇	—	2	1	no	—
355	C₂×D₄×C₆₇	—	2	1	no	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	1	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	1	no	—
366	C₂×D₄×C₆₇	—	2	1	no	—
367	C₂×D₄×C₆₇	—	2	1	no	—
368	C₂×D₄×C₆₇	—	2	1	no	—
369	C₂×D₄×C₆₇	—	4	2	no	—
370	C₂×D₄×C₆₇	—	4	2	no	—
371	C₂×D₄×C₆₇	—	4	2	no	—
372	C₂×D₄×C₆₇	—	4	4	no	—
373	C₂×D₄×C₆₇	—	8	2	no	—
374	C₂×D₄×C₆₇	—	8	2	no	—
375	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
379	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	1	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	2	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	—	2	1	no	—
390	C₂²×C₄×C₆₇	—	2	1	no	—
391	C₂²×C₄×C₆₇	—	2	1	no	—
392	C₂²×C₄×C₆₇	—	2	1	no	—
393	C₂²×C₄×C₆₇	—	2	1	no	—
394	C₂²×C₄×C₆₇	—	2	1	no	—
395	C₂²×C₄×C₆₇	—	4	2	no	—
396	C₂²×C₄×C₆₇	—	4	2	no	—
397	C₂²×C₄×C₆₇	—	4	4	no	—
398	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	Q₁₆×C₆₇	—	4	2	no	—
412	SD₁₆×C₆₇	—	4	2	no	—
413	SD₁₆×C₆₇	—	4	2	no	—
414	SD₁₆×C₆₇	—	4	2	no	—
415	M₁₆×C₆₇	—	4	2	no	—
416	M₁₆×C₆₇	—	4	2	no	—
417	C₂×C₈×C₆₇	—	4	2	no	—
418	C₂×C₈×C₆₇	—	4	2	no	—
419	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
420	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
421	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
422	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	2	no	—
426	C₄⋊C₄×C₆₇	—	2	2	no	—
427	C₄⋊C₄×C₆₇	—	2	2	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	2	no	—
431	C₄⋊C₄×C₆₇	—	2	2	no	—
432	C₄⋊C₄×C₆₇	—	2	2	no	—
433	C₄⋊C₄×C₆₇	—	2	2	no	—
434	C₄⋊C₄×C₆₇	—	2	2	no	—
435	C₄⋊C₄×C₆₇	—	2	2	no	—
436	C₄⋊C₄×C₆₇	—	2	2	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	—	2	1	no	—
446	C₄⋊C₄×C₆₇	—	2	1	no	—
447	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
452	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
453	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	1	no	—
477	C₂²⋊C₄×C₆₇	—	2	1	no	—
478	C₂²⋊C₄×C₆₇	—	2	1	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	—	2	1	no	—
482	C₂²⋊C₄×C₆₇	—	2	1	no	—
483	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₇	—	2	2	no	—
492	C₄²×C₆₇	—	2	2	no	—
493	C₄²×C₆₇	—	2	2	no	—
494	C₄²×C₆₇	—	2	2	no	—
495	C₄²×C₆₇	—	2	1	no	—
496	C₄²×C₆₇	—	2	1	no	—
497	C₄²×C₆₇	—	2	1	no	—
498	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂³×C₆₇	—	2	2	no	—
503	C₂³×C₆₇	—	2	2	no	—
504	C₂³×C₆₇	—	2	2	no	—
505	C₂³×C₆₇	—	2	1	no	—
506	C₂³×C₆₇	—	2	1	no	—
507	C₂³×C₆₇	—	2	1	no	—
508	C₂³×C₆₇	—	4	1	no	—
509	C₂³×C₆₇	—	4	1	no	—
510	C₂³×C₆₇	—	4	1	no	—
511	C₂³×C₆₇	—	4	2	no	—
512	C₂³×C₆₇	—	4	2	no	—
513	C₂³×C₆₇	—	8	1	no	—
514	C₂³×C₆₇	—	8	1	no	—
515	C₂³×C₆₇	—	8	1	no	—
516	C₂³×C₆₇	—	8	1	no	—
517	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
518	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
519	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
522	Q₈×C₆₇	—	2	2	no	—
523	Q₈×C₆₇	—	2	2	no	—
524	Q₈×C₆₇	—	2	2	no	—
525	Q₈×C₆₇	—	4	2	no	—
526	Q₈×C₆₇	—	8	1	no	—
527	D₄×C₆₇	—	2	2	no	—
528	D₄×C₆₇	—	2	2	no	—
529	D₄×C₆₇	—	2	2	no	—
530	D₄×C₆₇	—	2	2	no	—
531	D₄×C₆₇	—	2	2	no	—
532	D₄×C₆₇	—	4	1	no	—
533	D₄×C₆₇	—	4	1	no	—
534	D₄×C₆₇	—	4	2	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	4	2	no	—
538	D₄×C₆₇	—	4	2	no	—
539	D₄×C₆₇	—	4	2	no	—
540	D₄×C₆₇	—	8	1	no	—
541	D₄×C₆₇	—	8	1	no	—
542	D₄×C₆₇	—	8	1	no	—
543	D₄×C₆₇	—	8	1	no	—
544	D₄×C₆₇	—	8	1	no	—
545	D₄×C₆₇	—	8	1	no	—
546	D₄×C₆₇	—	8	1	no	—
547	D₄×C₆₇	—	8	1	no	—
548	D₄×C₆₇	—	8	1	no	—
549	C₂×C₄×C₆₇	—	2	2	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	2	no	—
552	C₂×C₄×C₆₇	—	2	2	no	—
553	C₂×C₄×C₆₇	—	2	2	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	2	no	—
558	C₂×C₄×C₆₇	—	2	2	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	4	1	no	—
565	C₂×C₄×C₆₇	—	4	1	no	—
566	C₂×C₄×C₆₇	—	4	1	no	—
567	C₂×C₄×C₆₇	—	4	1	no	—
568	C₂×C₄×C₆₇	—	4	1	no	—
569	C₂×C₄×C₆₇	—	4	1	no	—
570	C₂×C₄×C₆₇	—	4	1	no	—
571	C₂×C₄×C₆₇	—	4	2	no	—
572	C₂×C₄×C₆₇	—	4	2	no	—
573	C₂×C₄×C₆₇	—	4	2	no	—
574	C₂×C₄×C₆₇	—	4	4	no	—
575	C₂×C₄×C₆₇	—	4	2	no	—
576	C₂×C₄×C₆₇	—	4	4	no	—
577	C₂×C₄×C₆₇	—	4	2	no	—
578	C₂×C₄×C₆₇	—	8	1	no	—
579	C₂×C₄×C₆₇	—	8	1	no	—
580	C₂×C₄×C₆₇	—	8	1	no	—
581	C₂×C₄×C₆₇	—	8	1	no	—
582	C₂×C₄×C₆₇	—	8	1	no	—
583	C₂×C₄×C₆₇	—	8	1	no	—
584	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
587	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
594	C₈×C₆₇	—	2	2	no	—
595	C₈×C₆₇	—	2	2	no	—
596	C₈×C₆₇	—	2	2	no	—
597	C₈×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	1	no	—
599	C₂²×C₆₇	—	2	1	no	—
600	C₂²×C₆₇	—	2	1	no	—
601	C₂²×C₆₇	—	2	1	no	—
602	C₂²×C₆₇	—	2	1	no	—
603	C₂²×C₆₇	—	2	1	no	—
604	C₂²×C₆₇	—	2	1	no	—
605	C₂²×C₆₇	—	2	1	no	—
606	C₂²×C₆₇	—	2	1	no	—
607	C₂²×C₆₇	—	2	1	no	—
608	C₂²×C₆₇	—	2	1	no	—
609	C₂²×C₆₇	—	2	1	no	—
610	C₂²×C₆₇	—	2	1	no	—
611	C₂²×C₆₇	—	4	4	no	—
612	C₂²×C₆₇	—	4	1	no	—
613	C₂²×C₆₇	—	4	1	no	—
614	C₂²×C₆₇	—	4	1	no	—
615	C₂²×C₆₇	—	4	1	no	—
616	C₂²×C₆₇	—	4	1	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	1	no	—
619	C₂²×C₆₇	—	4	1	no	—
620	C₂²×C₆₇	—	4	1	no	—
621	C₂²×C₆₇	—	8	2	no	—
622	C₂²×C₆₇	—	16	2	no	—
623	C₂²×C₆₇	—	16	2	no	—
624	C₂²×C₆₇	#575	1	2	yes	—
625	C₂²×C₆₇	#577	1	2	yes	—
626	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
627	C₄×C₆₇	—	2	1	no	—
628	C₄×C₆₇	—	2	1	no	—
629	C₄×C₆₇	—	2	1	no	—
630	C₄×C₆₇	—	2	1	no	—
631	C₄×C₆₇	—	2	1	no	—
632	C₄×C₆₇	—	2	1	no	—
633	C₄×C₆₇	—	2	1	no	—
634	C₄×C₆₇	—	2	1	no	—
635	C₄×C₆₇	—	2	1	no	—
636	C₄×C₆₇	—	4	2	no	—
637	C₄×C₆₇	—	4	1	no	—
638	C₄×C₆₇	—	4	2	no	—
639	C₄×C₆₇	—	4	2	no	—
640	C₄×C₆₇	—	4	1	no	—
641	C₄×C₆₇	—	4	2	no	—
642	C₄×C₆₇	—	4	1	no	—
643	C₄×C₆₇	—	4	1	no	—
644	C₄×C₆₇	—	4	1	no	—
645	C₄×C₆₇	#585	1	2	yes	—
646	#61729	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
647	C₂×C₆₇	—	2	2	no	—
648	C₂×C₆₇	—	2	2	no	—
649	C₂×C₆₇	—	4	1	no	—
650	C₂×C₆₇	—	4	1	no	—
651	C₂×C₆₇	—	4	1	no	—
652	C₂×C₆₇	—	8	1	no	—
653	C₂×C₆₇	—	8	1	no	—
654	C₂×C₆₇	—	8	1	no	—
655	C₂×C₆₇	#3485	1	1	yes	characteristic
656	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
657	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
658	#3519	C₂×C₆₇	1	1	yes	characteristic
659	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
660	#3351	C₂×C₆₇	1	2	yes	complemented
661	#3348	C₂×C₆₇	1	2	yes	complemented
662	#3344	C₂×C₆₇	1	2	yes	complemented
663	#3337	C₂×C₆₇	1	2	yes	complemented
664	#3323	C₂×C₆₇	1	2	yes	complemented
665	#3317	C₂×C₆₇	1	2	yes	complemented
666	#3310	C₂×C₆₇	1	2	yes	complemented
667	#3296	C₂×C₆₇	1	2	yes	complemented
668	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#3232	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
672	#3190	C₂×C₆₇	1	1	yes	characteristic, complemented
673	#3187	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#3103	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#3094	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
678	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
679	C₂×#481	C₂×C₆₇	1	1	yes	characteristic, complemented
680	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
681	C₆₇	#61729	1	1	yes	characteristic, direct product factor, Sylow
682	#555	C₂²×C₆₇	1	1	yes	characteristic
683	#554	C₂²×C₆₇	1	1	yes	characteristic
684	#553	—	2	1	no	—
685	#553	C₂²×C₆₇	1	1	yes	characteristic
686	#553	C₂²×C₆₇	1	1	yes	characteristic
687	#552	—	2	1	no	—
688	#552	—	2	1	no	—
689	#552	—	2	1	no	—
690	#552	—	2	1	no	—
691	#552	C₂²×C₆₇	1	2	yes	—
692	#552	C₂²×C₆₇	1	2	yes	complemented
693	#552	C₂²×C₆₇	1	2	yes	complemented
694	#552	C₂²×C₆₇	1	2	yes	complemented
695	#550	C₂²×C₆₇	1	1	yes	characteristic
696	#546	—	2	1	no	—
697	#546	—	2	1	no	—
698	#546	C₂²×C₆₇	1	1	yes	characteristic
699	#546	C₂²×C₆₇	1	1	yes	characteristic
700	D₄²	—	2	1	no	—
701	D₄²	C₂²×C₆₇	1	1	yes	characteristic
702	#540	—	2	1	no	—
703	#538	—	2	1	no	—
704	#538	—	2	1	no	—
705	#532	C₂²×C₆₇	1	1	yes	characteristic
706	#529	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#126	—	2	1	no	—
708	C₂×#125	—	2	1	no	—
709	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#525	C₂²×C₆₇	1	1	yes	characteristic
711	#525	C₂²×C₆₇	1	1	yes	characteristic
712	C₂×#123	—	2	1	no	—
713	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
717	#518	—	2	1	no	—
718	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×#117	—	2	1	no	—
721	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
723	#501	C₂²×C₆₇	1	2	yes	complemented
724	#499	C₂²×C₆₇	1	2	yes	complemented
725	#490	C₂²×C₆₇	1	2	yes	complemented
726	#488	C₂²×C₆₇	1	2	yes	complemented
727	#485	C₂²×C₆₇	1	2	yes	complemented
728	#485	C₂²×C₆₇	1	2	yes	complemented
729	#485	C₂²×C₆₇	1	2	yes	complemented
730	#484	C₂²×C₆₇	1	2	yes	complemented
731	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#483	C₂²×C₆₇	1	2	yes	complemented
734	#483	C₂²×C₆₇	1	2	yes	complemented
735	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	#482	C₂²×C₆₇	1	2	yes	complemented
737	#482	C₂²×C₆₇	1	2	yes	complemented
738	#482	C₂²×C₆₇	1	2	yes	complemented
739	#481	C₂²×C₆₇	1	1	yes	characteristic
740	#481	C₂²×C₆₇	1	1	yes	characteristic
741	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
742	#481	C₂²×C₆₇	1	2	yes	complemented
743	#481	C₂²×C₆₇	1	2	yes	complemented
744	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
747	#480	C₂²×C₆₇	1	1	yes	characteristic
748	#480	C₂²×C₆₇	1	2	yes	complemented
749	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
751	#479	C₂²×C₆₇	1	2	yes	complemented
752	#479	C₂²×C₆₇	1	2	yes	complemented
753	#478	C₂²×C₆₇	1	2	yes	complemented
754	#478	C₂²×C₆₇	1	2	yes	complemented
755	#478	C₂²×C₆₇	1	2	yes	complemented
756	#475	C₂²×C₆₇	1	2	yes	complemented
757	#470	C₂²×C₆₇	1	2	yes	complemented
758	#468	C₂²×C₆₇	1	2	yes	complemented
759	#468	C₂²×C₆₇	1	2	yes	complemented
760	#468	C₂²×C₆₇	1	2	yes	complemented
761	#467	C₂²×C₆₇	1	2	yes	complemented
762	#465	C₂²×C₆₇	1	2	yes	complemented
763	#465	C₂²×C₆₇	1	2	yes	complemented
764	#465	C₂²×C₆₇	1	2	yes	complemented
765	#464	C₂²×C₆₇	1	2	yes	complemented
766	#460	C₂²×C₆₇	1	2	yes	complemented
767	#452	C₂²×C₆₇	1	2	yes	complemented
768	#452	C₂²×C₆₇	1	2	yes	complemented
769	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	#450	C₂²×C₆₇	1	2	yes	complemented
771	#450	C₂²×C₆₇	1	2	yes	complemented
772	#448	C₂²×C₆₇	1	1	yes	characteristic
773	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
774	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	#441	C₂²×C₆₇	1	2	yes	complemented
776	#440	C₂²×C₆₇	1	2	yes	complemented
777	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
778	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
779	#436	C₂²×C₆₇	1	2	yes	complemented
780	#435	C₂²×C₆₇	1	2	yes	—
781	#435	C₂²×C₆₇	1	2	yes	complemented
782	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
783	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
785	#428	C₂²×C₆₇	1	2	yes	complemented
786	#428	C₂²×C₆₇	1	2	yes	complemented
787	#427	C₂²×C₆₇	1	2	yes	complemented
788	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
789	#418	C₂²×C₆₇	1	2	yes	complemented
790	#417	C₂²×C₆₇	1	2	yes	complemented
791	#416	C₂²×C₆₇	1	2	yes	complemented
792	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
793	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
794	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
795	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
796	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
797	C₂×#41	—	2	1	no	—
798	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
800	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₂²×D₄	—	2	1	no	—
802	C₂²×D₄	—	2	1	no	—
803	C₂²×D₄	—	2	1	no	—
804	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
805	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
806	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
807	C₂³×C₄	—	2	1	no	—
808	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
809	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
810	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
811	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
812	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
813	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
814	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
815	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
816	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
817	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
818	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
819	#127	—	2	1	no	—
820	#127	C₂³×C₆₇	1	1	yes	characteristic
821	#126	—	2	1	no	—
822	#126	—	2	1	no	—
823	#126	—	2	2	no	—
824	#126	—	2	2	no	—
825	#126	—	2	2	no	—
826	#126	—	2	2	no	—
827	#126	—	2	1	no	—
828	#125	—	2	2	no	—
829	#125	—	2	2	no	—
830	#125	—	2	2	no	—
831	#125	—	2	2	no	—
832	#125	—	2	1	no	—
833	#125	—	2	1	no	—
834	#125	—	2	1	no	—
835	#125	C₂³×C₆₇	1	2	yes	—
836	#125	C₂³×C₆₇	1	2	yes	—
837	#125	C₂³×C₆₇	1	1	yes	characteristic
838	#124	—	2	1	no	—
839	#124	—	2	1	no	—
840	#124	—	2	1	no	—
841	#124	C₂³×C₆₇	1	1	yes	characteristic
842	#123	—	2	2	no	—
843	#123	—	2	2	no	—
844	#123	—	2	2	no	—
845	#123	—	2	2	no	—
846	#123	—	2	1	no	—
847	#123	—	2	1	no	—
848	#123	—	2	1	no	—
849	#123	—	2	1	no	—
850	#123	—	2	1	no	—
851	#123	—	2	1	no	—
852	#123	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	—	2	1	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	1	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
860	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
861	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
862	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
863	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
865	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
866	#121	—	2	1	no	—
867	#121	—	2	1	no	—
868	#121	—	2	1	no	—
869	#121	—	2	1	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	1	no	—
875	#121	—	2	1	no	—
876	#121	—	2	1	no	—
877	#121	—	2	1	no	—
878	#121	—	2	1	no	—
879	#121	C₂³×C₆₇	1	1	yes	characteristic
880	#121	C₂³×C₆₇	1	1	yes	characteristic
881	#121	C₂³×C₆₇	1	1	yes	characteristic
882	#121	C₂³×C₆₇	1	1	yes	characteristic
883	#121	C₂³×C₆₇	1	1	yes	characteristic
884	#121	C₂³×C₆₇	1	1	yes	characteristic
885	#121	C₂³×C₆₇	1	1	yes	characteristic
886	#121	C₂³×C₆₇	1	1	yes	characteristic
887	#121	C₂³×C₆₇	1	1	yes	characteristic
888	#120	—	2	1	no	—
889	#120	—	2	1	no	—
890	#120	—	2	1	no	—
891	#120	—	2	1	no	—
892	#120	—	2	1	no	—
893	#120	—	2	1	no	—
894	C₄×Q₈	—	2	1	no	—
895	C₄×Q₈	—	2	1	no	—
896	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
897	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
898	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	—	2	1	no	—
903	C₄×D₄	—	2	1	no	—
904	C₄×D₄	—	2	1	no	—
905	C₄×D₄	—	2	1	no	—
906	C₄×D₄	—	2	1	no	—
907	C₄×D₄	—	2	1	no	—
908	C₄×D₄	—	2	1	no	—
909	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
910	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
911	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
912	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
913	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
919	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	—	2	1	no	—
923	#117	—	2	2	no	—
924	#117	—	2	2	no	—
925	#117	—	2	2	no	—
926	#117	—	2	2	no	—
927	#117	—	2	1	no	—
928	#117	C₂³×C₆₇	1	2	yes	—
929	#117	C₂³×C₆₇	1	2	yes	—
930	#117	C₂³×C₆₇	1	1	yes	characteristic
931	#117	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×C₄⋊C₄	—	2	1	no	—
933	C₂×C₄⋊C₄	—	2	1	no	—
934	C₂×C₄⋊C₄	—	2	1	no	—
935	C₂×C₄⋊C₄	—	2	1	no	—
936	C₂×C₄⋊C₄	—	2	1	no	—
937	C₂×C₄⋊C₄	—	2	1	no	—
938	C₂×C₄⋊C₄	—	2	1	no	—
939	C₂×C₄⋊C₄	—	2	1	no	—
940	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
944	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
945	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
948	C₂×C₂²⋊C₄	—	2	1	no	—
949	C₂×C₂²⋊C₄	—	2	1	no	—
950	C₂×C₂²⋊C₄	—	2	1	no	—
951	C₂×C₂²⋊C₄	—	2	1	no	—
952	C₂×C₂²⋊C₄	—	2	1	no	—
953	C₂×C₂²⋊C₄	—	2	1	no	—
954	C₂×C₂²⋊C₄	—	2	1	no	—
955	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
957	C₂×C₄²	—	2	1	no	—
958	C₂×C₄²	—	2	1	no	—
959	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
960	#107	C₂³×C₆₇	1	2	yes	—
961	#107	C₂³×C₆₇	1	2	yes	—
962	#107	C₂³×C₆₇	1	2	yes	—
963	#107	C₂³×C₆₇	1	2	yes	—
964	#107	C₂³×C₆₇	1	2	yes	—
965	#106	C₂³×C₆₇	1	2	yes	—
966	#106	C₂³×C₆₇	1	2	yes	—
967	#106	C₂³×C₆₇	1	2	yes	—
968	#106	C₂³×C₆₇	1	2	yes	—
969	#106	C₂³×C₆₇	1	2	yes	—
970	#106	C₂³×C₆₇	1	2	yes	—
971	#106	C₂³×C₆₇	1	2	yes	—
972	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
973	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
974	#103	C₂³×C₆₇	1	2	yes	—
975	#103	C₂³×C₆₇	1	2	yes	—
976	#103	C₂³×C₆₇	1	2	yes	—
977	#103	C₂³×C₆₇	1	2	yes	—
978	#103	C₂³×C₆₇	1	2	yes	—
979	#103	C₂³×C₆₇	1	2	yes	—
980	#103	C₂³×C₆₇	1	2	yes	—
981	#102	C₂³×C₆₇	1	2	yes	—
982	#102	C₂³×C₆₇	1	2	yes	—
983	#102	C₂³×C₆₇	1	2	yes	—
984	#102	C₂³×C₆₇	1	2	yes	—
985	#102	C₂³×C₆₇	1	2	yes	—
986	#102	C₂³×C₆₇	1	2	yes	—
987	#102	C₂³×C₆₇	1	2	yes	—
988	#102	C₂³×C₆₇	1	2	yes	—
989	#102	C₂³×C₆₇	1	2	yes	—
990	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
991	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
992	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
993	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
994	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
995	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
996	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
997	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
998	#97	C₂³×C₆₇	1	2	yes	—
999	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1000	C₂⁴	—	2	1	no	—
1001	C₂⁴	—	2	1	no	—
1002	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1003	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1004	#41	—	4	2	no	—
1005	#41	—	4	2	no	—
1006	#41	—	8	2	no	—
1007	C₂×Q₈	—	2	1	no	—
1008	C₂×Q₈	—	2	1	no	—
1009	C₂×Q₈	—	4	2	no	—
1010	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1012	C₂×D₄	—	2	1	no	—
1013	C₂×D₄	—	2	1	no	—
1014	C₂×D₄	—	2	1	no	—
1015	C₂×D₄	—	2	1	no	—
1016	C₂×D₄	—	2	1	no	—
1017	C₂×D₄	—	2	1	no	—
1018	C₂×D₄	—	2	1	no	—
1019	C₂×D₄	—	2	1	no	—
1020	C₂×D₄	—	2	1	no	—
1021	C₂×D₄	—	2	1	no	—
1022	C₂×D₄	—	2	1	no	—
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	1	no	—
1026	C₂×D₄	—	2	1	no	—
1027	C₂×D₄	—	4	2	no	—
1028	C₂×D₄	—	4	2	no	—
1029	C₂×D₄	—	4	2	no	—
1030	C₂×D₄	—	4	4	no	—
1031	C₂×D₄	—	8	2	no	—
1032	C₂×D₄	—	8	2	no	—
1033	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1034	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1035	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1037	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	1	no	—
1042	C₂²×C₄	—	2	1	no	—
1043	C₂²×C₄	—	2	1	no	—
1044	C₂²×C₄	—	2	2	no	—
1045	C₂²×C₄	—	2	2	no	—
1046	C₂²×C₄	—	2	1	no	—
1047	C₂²×C₄	—	2	1	no	—
1048	C₂²×C₄	—	2	1	no	—
1049	C₂²×C₄	—	2	1	no	—
1050	C₂²×C₄	—	2	1	no	—
1051	C₂²×C₄	—	2	1	no	—
1052	C₂²×C₄	—	2	1	no	—
1053	C₂²×C₄	—	4	2	no	—
1054	C₂²×C₄	—	4	2	no	—
1055	C₂²×C₄	—	4	4	no	—
1056	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1057	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1058	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1060	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1063	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1068	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1069	Q₁₆	—	4	2	no	—
1070	SD₁₆	—	4	2	no	—
1071	SD₁₆	—	4	2	no	—
1072	SD₁₆	—	4	2	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	C₂×C₈	—	4	2	no	—
1076	C₂×C₈	—	4	2	no	—
1077	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1078	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1079	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1080	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	—	2	2	no	—
1091	C₄⋊C₄	—	2	2	no	—
1092	C₄⋊C₄	—	2	2	no	—
1093	C₄⋊C₄	—	2	2	no	—
1094	C₄⋊C₄	—	2	2	no	—
1095	C₄⋊C₄	—	2	1	no	—
1096	C₄⋊C₄	—	2	1	no	—
1097	C₄⋊C₄	—	2	1	no	—
1098	C₄⋊C₄	—	2	1	no	—
1099	C₄⋊C₄	—	2	1	no	—
1100	C₄⋊C₄	—	2	1	no	—
1101	C₄⋊C₄	—	2	1	no	—
1102	C₄⋊C₄	—	2	1	no	—
1103	C₄⋊C₄	—	2	1	no	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1106	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1107	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1108	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1109	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1110	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1111	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1112	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1113	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1114	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1115	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1116	C₂²⋊C₄	—	2	2	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	1	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	1	no	—
1125	C₂²⋊C₄	—	2	1	no	—
1126	C₂²⋊C₄	—	2	1	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	1	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	1	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1142	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1143	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1147	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1148	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1149	C₄²	—	2	2	no	—
1150	C₄²	—	2	2	no	—
1151	C₄²	—	2	2	no	—
1152	C₄²	—	2	2	no	—
1153	C₄²	—	2	1	no	—
1154	C₄²	—	2	1	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1157	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1158	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1159	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	2	no	—
1162	C₂³	—	2	2	no	—
1163	C₂³	—	2	1	no	—
1164	C₂³	—	2	1	no	—
1165	C₂³	—	2	1	no	—
1166	C₂³	—	4	1	no	—
1167	C₂³	—	4	1	no	—
1168	C₂³	—	4	1	no	—
1169	C₂³	—	4	2	no	—
1170	C₂³	—	4	2	no	—
1171	C₂³	—	8	1	no	—
1172	C₂³	—	8	1	no	—
1173	C₂³	—	8	1	no	—
1174	C₂³	—	8	1	no	—
1175	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1176	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1177	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1178	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1179	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1180	Q₈	—	2	2	no	—
1181	Q₈	—	2	2	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	4	2	no	—
1184	Q₈	—	8	1	no	—
1185	D₄	—	2	2	no	—
1186	D₄	—	2	2	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	2	no	—
1189	D₄	—	2	2	no	—
1190	D₄	—	4	1	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	2	no	—
1198	D₄	—	8	1	no	—
1199	D₄	—	8	1	no	—
1200	D₄	—	8	1	no	—
1201	D₄	—	8	1	no	—
1202	D₄	—	8	1	no	—
1203	D₄	—	8	1	no	—
1204	D₄	—	8	1	no	—
1205	D₄	—	8	1	no	—
1206	D₄	—	8	1	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	2	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	1	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	1	no	—
1226	C₂×C₄	—	4	1	no	—
1227	C₂×C₄	—	4	1	no	—
1228	C₂×C₄	—	4	1	no	—
1229	C₂×C₄	—	4	2	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	4	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	4	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	8	1	no	—
1237	C₂×C₄	—	8	1	no	—
1238	C₂×C₄	—	8	1	no	—
1239	C₂×C₄	—	8	1	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	1	no	—
1242	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1243	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1244	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1245	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1246	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1247	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1248	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1249	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1250	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1251	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1252	C₈	—	2	2	no	—
1253	C₈	—	2	2	no	—
1254	C₈	—	2	2	no	—
1255	C₈	—	2	2	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	4	4	no	—
1270	C₂²	—	4	1	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	1	no	—
1277	C₂²	—	4	1	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	16	2	no	—
1281	C₂²	—	16	2	no	—
1282	C₂²	#575×C₆₇	1	2	yes	—
1283	C₂²	#577×C₆₇	1	2	yes	—
1284	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	4	2	no	—
1295	C₄	—	4	2	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	2	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	2	no	—
1302	C₄	—	4	1	no	—
1303	C₄	#585×C₆₇	1	2	yes	—
1304	C₂	—	2	2	no	—
1305	C₂	—	2	2	no	—
1306	C₂	—	4	1	no	—
1307	C₂	—	4	1	no	—
1308	C₂	—	4	1	no	—
1309	C₂	—	8	1	no	—
1310	C₂	—	8	1	no	—
1311	C₂	—	8	1	no	—
1312	C₂	C₆₇×#3485	1	1	yes	characteristic
1313	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1314	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#3351	C₂	semidirect
4. C₆₇×#3348	C₂	semidirect
5. C₆₇×#3344	C₂	semidirect
6. C₆₇×#3337	C₂	semidirect
7. C₆₇×#3323	C₂	semidirect
8. C₆₇×#3317	C₂	semidirect
9. C₆₇×#3310	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₆₇×#3234	C₂	semidirect
12. C₆₇×#3232	C₂	semidirect
13. C₆₇×#3196	C₂	semidirect
14. C₆₇×#3193	C₂	semidirect
15. C₆₇×#3190	C₂	semidirect
16. C₆₇×#3187	C₂	semidirect
17. C₆₇×#3117	C₂	semidirect
18. C₆₇×#3103	C₂	semidirect
19. C₆₇×#3094	C₂	semidirect
20. C₆₇×#3092	C₂	semidirect
21. C₆₇×#3091	C₂	semidirect
22. C₂×#481×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
36. #552×C₆₇	C₂²	semidirect
51. C₂×#125×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
60. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
63. C₂×#117×C₆₇	C₂²	semidirect
64. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
67. #490×C₆₇	C₂²	semidirect
68. #488×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #485×C₆₇	C₂²	semidirect
71. #485×C₆₇	C₂²	semidirect
72. #484×C₆₇	C₂²	semidirect
73. #484×C₆₇	C₂²	semidirect
74. #484×C₆₇	C₂²	semidirect
75. #483×C₆₇	C₂²	semidirect
76. #483×C₆₇	C₂²	semidirect
77. #483×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #482×C₆₇	C₂²	semidirect
80. #482×C₆₇	C₂²	semidirect
83. #481×C₆₇	C₂²	semidirect
84. #481×C₆₇	C₂²	semidirect
85. #481×C₆₇	C₂²	semidirect
86. #481×C₆₇	C₂²	semidirect
87. #481×C₆₇	C₂²	semidirect
88. #481×C₆₇	C₂²	semidirect
90. #480×C₆₇	C₂²	semidirect
91. #480×C₆₇	C₂²	semidirect
92. #480×C₆₇	C₂²	semidirect
93. #479×C₆₇	C₂²	semidirect
94. #479×C₆₇	C₂²	semidirect
95. #478×C₆₇	C₂²	semidirect
96. #478×C₆₇	C₂²	semidirect
97. #478×C₆₇	C₂²	semidirect
98. #475×C₆₇	C₂²	semidirect
99. #470×C₆₇	C₂²	semidirect
100. #468×C₆₇	C₂²	semidirect
101. #468×C₆₇	C₂²	semidirect
102. #468×C₆₇	C₂²	semidirect
103. #467×C₆₇	C₂²	semidirect
104. #465×C₆₇	C₂²	semidirect
105. #465×C₆₇	C₂²	semidirect
106. #465×C₆₇	C₂²	semidirect
107. #464×C₆₇	C₂²	semidirect
108. #460×C₆₇	C₂²	semidirect
109. #452×C₆₇	C₂²	semidirect
110. #452×C₆₇	C₂²	semidirect
111. #451×C₆₇	C₂²	semidirect
112. #450×C₆₇	C₂²	semidirect
113. #450×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
116. #448×C₆₇	C₂²	semidirect
117. #441×C₆₇	C₂²	semidirect
118. #440×C₆₇	C₂²	semidirect
119. C₄×SD₁₆×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #432×C₆₇	C₂²	semidirect
126. #431×C₆₇	C₂²	semidirect
127. #428×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
129. #427×C₆₇	C₂²	semidirect
130. C₂×#106×C₆₇	C₂²	semidirect
131. #418×C₆₇	C₂²	semidirect
132. #417×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×#102×C₆₇	C₂²	semidirect
135. #407×C₆₇	C₂²	semidirect
136. #407×C₆₇	C₂²	semidirect
137. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
138. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
646. #61729	C₆₇	direct (N × H)
659. C₂×#552	C₂×C₆₇	semidirect
660. #3351	C₂×C₆₇	semidirect
661. #3348	C₂×C₆₇	semidirect
662. #3344	C₂×C₆₇	semidirect
663. #3337	C₂×C₆₇	semidirect
664. #3323	C₂×C₆₇	semidirect
665. #3317	C₂×C₆₇	semidirect
666. #3310	C₂×C₆₇	semidirect
667. #3296	C₂×C₆₇	semidirect
668. #3234	C₂×C₆₇	semidirect
669. #3232	C₂×C₆₇	semidirect
670. #3196	C₂×C₆₇	semidirect
671. #3193	C₂×C₆₇	semidirect
672. #3190	C₂×C₆₇	semidirect
673. #3187	C₂×C₆₇	semidirect
674. #3117	C₂×C₆₇	semidirect
675. #3103	C₂×C₆₇	semidirect
676. #3094	C₂×C₆₇	semidirect
677. #3092	C₂×C₆₇	semidirect
678. #3091	C₂×C₆₇	semidirect
679. C₂×#481	C₂×C₆₇	semidirect
680. #2974	C₂×C₆₇	semidirect
681. C₆₇	#61729	direct (N × H)
692. #552	C₂²×C₆₇	semidirect
693. #552	C₂²×C₆₇	semidirect
694. #552	C₂²×C₆₇	semidirect
709. C₂×#125	C₂²×C₆₇	semidirect
713. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
714. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
718. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
721. C₂×#117	C₂²×C₆₇	semidirect
722. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
723. #501	C₂²×C₆₇	semidirect
724. #499	C₂²×C₆₇	semidirect
725. #490	C₂²×C₆₇	semidirect
726. #488	C₂²×C₆₇	semidirect
727. #485	C₂²×C₆₇	semidirect
728. #485	C₂²×C₆₇	semidirect
729. #485	C₂²×C₆₇	semidirect
730. #484	C₂²×C₆₇	semidirect
731. #484	C₂²×C₆₇	semidirect
732. #484	C₂²×C₆₇	semidirect
733. #483	C₂²×C₆₇	semidirect
734. #483	C₂²×C₆₇	semidirect
735. #483	C₂²×C₆₇	semidirect
736. #482	C₂²×C₆₇	semidirect
737. #482	C₂²×C₆₇	semidirect
738. #482	C₂²×C₆₇	semidirect
741. #481	C₂²×C₆₇	semidirect
742. #481	C₂²×C₆₇	semidirect
743. #481	C₂²×C₆₇	semidirect
744. #481	C₂²×C₆₇	semidirect
745. #481	C₂²×C₆₇	semidirect
746. #481	C₂²×C₆₇	semidirect
748. #480	C₂²×C₆₇	semidirect
749. #480	C₂²×C₆₇	semidirect
750. #480	C₂²×C₆₇	semidirect
751. #479	C₂²×C₆₇	semidirect
752. #479	C₂²×C₆₇	semidirect
753. #478	C₂²×C₆₇	semidirect
754. #478	C₂²×C₆₇	semidirect
755. #478	C₂²×C₆₇	semidirect
756. #475	C₂²×C₆₇	semidirect
757. #470	C₂²×C₆₇	semidirect
758. #468	C₂²×C₆₇	semidirect
759. #468	C₂²×C₆₇	semidirect
760. #468	C₂²×C₆₇	semidirect
761. #467	C₂²×C₆₇	semidirect
762. #465	C₂²×C₆₇	semidirect
763. #465	C₂²×C₆₇	semidirect
764. #465	C₂²×C₆₇	semidirect
765. #464	C₂²×C₆₇	semidirect
766. #460	C₂²×C₆₇	semidirect
767. #452	C₂²×C₆₇	semidirect
768. #452	C₂²×C₆₇	semidirect
769. #451	C₂²×C₆₇	semidirect
770. #450	C₂²×C₆₇	semidirect
771. #450	C₂²×C₆₇	semidirect
773. #448	C₂²×C₆₇	semidirect
774. #448	C₂²×C₆₇	semidirect
775. #441	C₂²×C₆₇	semidirect
776. #440	C₂²×C₆₇	semidirect
777. C₄×SD₁₆	C₂²×C₆₇	semidirect
778. C₄×SD₁₆	C₂²×C₆₇	semidirect
779. #436	C₂²×C₆₇	semidirect
781. #435	C₂²×C₆₇	semidirect
782. C₈×D₄	C₂²×C₆₇	semidirect
783. #432	C₂²×C₆₇	semidirect
784. #431	C₂²×C₆₇	semidirect
785. #428	C₂²×C₆₇	semidirect
786. #428	C₂²×C₆₇	semidirect
787. #427	C₂²×C₆₇	semidirect
788. C₂×#106	C₂²×C₆₇	semidirect
789. #418	C₂²×C₆₇	semidirect
790. #417	C₂²×C₆₇	semidirect
791. #416	C₂²×C₆₇	semidirect
792. C₂×#102	C₂²×C₆₇	semidirect
793. #407	C₂²×C₆₇	semidirect
794. #407	C₂²×C₆₇	semidirect
795. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
796. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3519	2
C₂×#552×C₆₇	2
C₆₇×#3351	2
C₆₇×#3348	2
C₆₇×#3344	2
C₆₇×#3337	2
C₆₇×#3323	2
C₆₇×#3317	2
C₆₇×#3310	2
C₆₇×#3296	2
C₆₇×#3234	2
C₆₇×#3232	2
C₆₇×#3196	2
C₆₇×#3193	2
C₆₇×#3190	2
C₆₇×#3187	2
C₆₇×#3117	2
C₆₇×#3103	2
C₆₇×#3094	2
C₆₇×#3092	2
C₆₇×#3091	2
C₂×#481×C₆₇	2
C₆₇×#2974	2
#61729	67

Subgroups — C67×#61729 #30740980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61729 #30740980