Subgroups — C₆₇×#61185 #30740436

Order 17152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3329	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3321	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#448×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#419×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	#555×C₆₇	C₂²	1	2	yes	—
32	#553×C₆₇	C₂²	1	2	yes	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#551×C₆₇	—	2	2	no	—
35	D₄×Q₈×C₆₇	—	2	1	no	—
36	D₄×Q₈×C₆₇	—	2	1	no	—
37	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
38	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
39	#548×C₆₇	—	2	1	no	—
40	#548×C₆₇	—	2	1	no	—
41	#548×C₆₇	C₂²	1	2	yes	complemented
42	#548×C₆₇	C₂²	1	2	yes	complemented
43	#547×C₆₇	C₂²	1	2	yes	—
44	#546×C₆₇	—	2	2	no	—
45	#544×C₆₇	C₂²	1	1	yes	characteristic
46	#542×C₆₇	—	2	1	no	—
47	#540×C₆₇	—	2	1	no	—
48	#536×C₆₇	—	2	2	no	—
49	#536×C₆₇	C₂²	1	1	yes	characteristic
50	#536×C₆₇	C₂²	1	1	yes	characteristic
51	#535×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#525×C₆₇	—	2	2	no	—
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	#525×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#519×C₆₇	C₂²	1	1	yes	characteristic
60	#518×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
62	#491×C₆₇	C₂²	1	2	yes	complemented
63	#489×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#483×C₆₇	C₂²	1	2	yes	complemented
74	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#479×C₆₇	C₂²	1	2	yes	complemented
79	#479×C₆₇	C₂²	1	2	yes	complemented
80	#477×C₆₇	C₂²	1	2	yes	complemented
81	#475×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	—
83	#468×C₆₇	C₂²	1	2	yes	—
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#466×C₆₇	C₂²	1	2	yes	—
87	#465×C₆₇	C₂²	1	2	yes	—
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#463×C₆₇	C₂²	1	2	yes	complemented
91	#463×C₆₇	C₂²	1	2	yes	complemented
92	#461×C₆₇	C₂²	1	2	yes	complemented
93	#461×C₆₇	C₂²	1	2	yes	complemented
94	#449×C₆₇	C₂²	1	2	yes	complemented
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#448×C₆₇	C₂²	1	2	yes	—
97	#448×C₆₇	C₂²	1	2	yes	—
98	#448×C₆₇	C₂²	1	2	yes	—
99	#448×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	complemented
101	#448×C₆₇	C₂²	1	2	yes	complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
110	#428×C₆₇	C₂²	1	1	yes	characteristic
111	#427×C₆₇	C₂²	1	1	yes	characteristic
112	#427×C₆₇	C₂²	1	1	yes	characteristic
113	#424×C₆₇	C₂²	1	1	yes	characteristic
114	#419×C₆₇	C₂²	1	1	yes	characteristic
115	#419×C₆₇	C₂²	1	1	yes	characteristic
116	#419×C₆₇	C₂²	1	1	yes	characteristic
117	#419×C₆₇	C₂²	1	1	yes	characteristic
118	#419×C₆₇	C₂²	1	2	yes	complemented
119	#419×C₆₇	C₂²	1	2	yes	complemented
120	#419×C₆₇	C₂²	1	2	yes	complemented
121	#418×C₆₇	C₂²	1	1	yes	characteristic
122	#417×C₆₇	C₂²	1	1	yes	characteristic
123	#417×C₆₇	C₂²	1	2	yes	complemented
124	#416×C₆₇	C₂²	1	1	yes	characteristic
125	#416×C₆₇	C₂²	1	1	yes	characteristic
126	#416×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
130	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
134	#405×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	2	no	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	—	2	1	no	—
144	C₂²×Q₈×C₆₇	—	2	1	no	—
145	C₂²×Q₈×C₆₇	—	2	1	no	—
146	C₂²×Q₈×C₆₇	—	2	1	no	—
147	C₂²×Q₈×C₆₇	—	2	4	no	—
148	C₂²×Q₈×C₆₇	—	4	2	no	—
149	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₆₇	—	2	1	no	—
155	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₆₇	—	2	1	no	—
157	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
158	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
159	C₂×SD₁₆×C₆₇	—	2	4	no	—
160	C₂×SD₁₆×C₆₇	—	4	2	no	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×D₈×C₆₇	C₂³	1	2	yes	—
167	#131×C₆₇	—	4	2	no	—
168	C₂×M₁₆×C₆₇	—	4	2	no	—
169	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
176	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
177	C₄⋊Q₈×C₆₇	—	2	1	no	—
178	C₄⋊Q₈×C₆₇	—	2	1	no	—
179	C₄⋊Q₈×C₆₇	—	2	2	no	—
180	C₄⋊Q₈×C₆₇	—	2	2	no	—
181	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
183	#127×C₆₇	—	2	1	no	—
184	#126×C₆₇	—	2	2	no	—
185	#126×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	C₂³	1	2	yes	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	—	2	2	no	—
192	#124×C₆₇	—	2	2	no	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	C₂³	1	2	yes	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	1	no	—
206	C₂²⋊Q₈×C₆₇	—	2	1	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	—	2	2	no	—
212	C₂²⋊Q₈×C₆₇	—	2	2	no	—
213	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	D₄	1	1	yes	characteristic
227	#121×C₆₇	D₄	1	1	yes	characteristic
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	2	yes	—
231	#121×C₆₇	C₂³	1	2	yes	—
232	#121×C₆₇	C₂³	1	1	yes	characteristic
233	#121×C₆₇	C₂³	1	1	yes	characteristic
234	#120×C₆₇	—	2	1	no	—
235	#120×C₆₇	—	2	2	no	—
236	#120×C₆₇	D₄	1	2	yes	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×Q₈×C₆₇	—	2	1	no	—
239	C₄×Q₈×C₆₇	—	2	1	no	—
240	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
241	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	2	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	2	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	2	no	—
253	C₄×D₄×C₆₇	—	2	2	no	—
254	C₄×D₄×C₆₇	C₂³	1	2	yes	—
255	C₄×D₄×C₆₇	C₂³	1	2	yes	—
256	C₄×D₄×C₆₇	C₂³	1	2	yes	—
257	C₄×D₄×C₆₇	C₂³	1	2	yes	—
258	#117×C₆₇	—	2	1	no	—
259	#117×C₆₇	—	2	1	no	—
260	#117×C₆₇	—	2	2	no	—
261	#117×C₆₇	—	2	2	no	—
262	#117×C₆₇	C₂³	1	1	yes	characteristic
263	#117×C₆₇	C₂³	1	1	yes	characteristic
264	#117×C₆₇	C₂³	1	2	yes	—
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	#117×C₆₇	C₂³	1	1	yes	characteristic
267	#117×C₆₇	C₂³	1	1	yes	characteristic
268	#117×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	1	yes	characteristic
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	1	yes	characteristic
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#103×C₆₇	C₂³	1	2	yes	—
303	#103×C₆₇	C₂³	1	2	yes	—
304	#103×C₆₇	C₂³	1	2	yes	—
305	#103×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	1	yes	characteristic
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	2	yes	—
312	#102×C₆₇	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
319	#97×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₂⁴×C₆₇	—	2	1	no	—
322	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	4	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	4	2	no	—
329	#41×C₆₇	—	4	8	no	—
330	#41×C₆₇	—	4	4	no	—
331	#41×C₆₇	—	8	4	no	—
332	C₂×Q₈×C₆₇	—	2	1	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	1	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	—	2	2	no	—
339	C₂×Q₈×C₆₇	—	2	4	no	—
340	C₂×Q₈×C₆₇	—	2	4	no	—
341	C₂×Q₈×C₆₇	—	2	4	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	—	2	2	no	—
344	C₂×Q₈×C₆₇	—	4	4	no	—
345	C₂×Q₈×C₆₇	—	4	2	no	—
346	C₂×Q₈×C₆₇	—	4	2	no	—
347	C₂×Q₈×C₆₇	—	4	2	no	—
348	C₂×Q₈×C₆₇	—	4	4	no	—
349	C₂×Q₈×C₆₇	—	4	4	no	—
350	C₂×Q₈×C₆₇	—	4	4	no	—
351	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
352	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
353	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
354	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	1	no	—
360	C₂×D₄×C₆₇	—	2	2	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	2	2	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	1	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	—	2	2	no	—
367	C₂×D₄×C₆₇	—	8	2	no	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₆₇	—	2	1	no	—
375	C₂²×C₄×C₆₇	—	2	2	no	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	1	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	1	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	2	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	2	no	—
388	C₂²×C₄×C₆₇	—	2	2	no	—
389	C₂²×C₄×C₆₇	—	4	4	no	—
390	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	SD₁₆×C₆₇	—	2	4	no	—
398	SD₁₆×C₆₇	—	2	4	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	D₈×C₆₇	—	4	2	no	—
403	M₁₆×C₆₇	—	2	2	no	—
404	M₁₆×C₆₇	—	2	2	no	—
405	M₁₆×C₆₇	—	4	2	no	—
406	M₁₆×C₆₇	—	4	2	no	—
407	C₂×C₈×C₆₇	—	2	2	no	—
408	C₂×C₈×C₆₇	—	2	2	no	—
409	C₂×C₈×C₆₇	—	4	2	no	—
410	C₂×C₈×C₆₇	—	4	2	no	—
411	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
412	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	—	2	1	no	—
418	C₄⋊C₄×C₆₇	—	2	1	no	—
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	2	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	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	1	no	—
446	C₂²⋊C₄×C₆₇	—	2	1	no	—
447	C₂²⋊C₄×C₆₇	—	2	1	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	1	no	—
450	C₂²⋊C₄×C₆₇	—	2	1	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	2	no	—
456	C₂²⋊C₄×C₆₇	—	2	2	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
468	C₄²×C₆₇	—	2	1	no	—
469	C₄²×C₆₇	—	2	1	no	—
470	C₄²×C₆₇	—	2	1	no	—
471	C₄²×C₆₇	—	2	1	no	—
472	C₄²×C₆₇	—	2	2	no	—
473	C₄²×C₆₇	—	2	2	no	—
474	C₄²×C₆₇	—	2	2	no	—
475	C₄²×C₆₇	—	2	1	no	—
476	C₄²×C₆₇	C₂⁴	1	2	yes	—
477	C₂³×C₆₇	—	2	2	no	—
478	C₂³×C₆₇	—	2	2	no	—
479	C₂³×C₆₇	—	2	1	no	—
480	C₂³×C₆₇	—	2	2	no	—
481	C₂³×C₆₇	—	4	1	no	—
482	C₂³×C₆₇	—	4	2	no	—
483	C₂³×C₆₇	—	8	1	no	—
484	C₂³×C₆₇	—	8	1	no	—
485	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
489	Q₈×C₆₇	—	2	4	no	—
490	Q₈×C₆₇	—	2	2	no	—
491	Q₈×C₆₇	—	2	2	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	2	1	no	—
494	Q₈×C₆₇	—	2	2	no	—
495	Q₈×C₆₇	—	2	1	no	—
496	Q₈×C₆₇	—	4	4	no	—
497	Q₈×C₆₇	—	4	4	no	—
498	Q₈×C₆₇	—	4	4	no	—
499	Q₈×C₆₇	—	4	2	no	—
500	Q₈×C₆₇	—	8	2	no	—
501	Q₈×C₆₇	C₂×#41	1	4	yes	—
502	D₄×C₆₇	—	2	4	no	—
503	D₄×C₆₇	—	2	4	no	—
504	D₄×C₆₇	—	2	2	no	—
505	D₄×C₆₇	—	2	2	no	—
506	D₄×C₆₇	—	2	1	no	—
507	D₄×C₆₇	—	2	1	no	—
508	D₄×C₆₇	—	2	2	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	4	no	—
511	D₄×C₆₇	—	4	2	no	—
512	D₄×C₆₇	—	4	2	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	4	4	no	—
515	D₄×C₆₇	—	4	2	no	—
516	D₄×C₆₇	—	8	2	no	—
517	D₄×C₆₇	—	8	2	no	—
518	D₄×C₆₇	—	8	2	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	4	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	2	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	4	no	—
541	C₂×C₄×C₆₇	—	4	4	no	—
542	C₂×C₄×C₆₇	—	4	4	no	—
543	C₂×C₄×C₆₇	—	4	2	no	—
544	C₂×C₄×C₆₇	—	4	2	no	—
545	C₂×C₄×C₆₇	—	4	2	no	—
546	C₂×C₄×C₆₇	—	8	2	no	—
547	C₂×C₄×C₆₇	—	8	2	no	—
548	C₂×C₄×C₆₇	—	8	1	no	—
549	C₂×C₄×C₆₇	—	8	1	no	—
550	C₂×C₄×C₆₇	—	8	2	no	—
551	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
558	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
559	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
560	C₈×C₆₇	—	2	1	no	—
561	C₈×C₆₇	—	2	1	no	—
562	C₈×C₆₇	—	2	1	no	—
563	C₈×C₆₇	—	2	1	no	—
564	C₈×C₆₇	—	2	2	no	—
565	C₈×C₆₇	—	2	2	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	1	no	—
568	C₂²×C₆₇	—	2	1	no	—
569	C₂²×C₆₇	—	2	1	no	—
570	C₂²×C₆₇	—	2	1	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	1	no	—
573	C₂²×C₆₇	—	2	2	no	—
574	C₂²×C₆₇	—	2	2	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	4	4	no	—
577	C₂²×C₆₇	—	4	2	no	—
578	C₂²×C₆₇	—	4	1	no	—
579	C₂²×C₆₇	—	4	1	no	—
580	C₂²×C₆₇	—	4	2	no	—
581	C₂²×C₆₇	—	4	2	no	—
582	C₂²×C₆₇	—	4	1	no	—
583	C₂²×C₆₇	—	16	2	no	—
584	C₂²×C₆₇	#546	1	2	yes	—
585	C₂²×C₆₇	#577	1	2	yes	—
586	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
587	C₄×C₆₇	—	2	2	no	—
588	C₄×C₆₇	—	2	1	no	—
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	2	4	no	—
591	C₄×C₆₇	—	2	2	no	—
592	C₄×C₆₇	—	2	2	no	—
593	C₄×C₆₇	—	4	1	no	—
594	C₄×C₆₇	—	4	1	no	—
595	C₄×C₆₇	—	4	1	no	—
596	C₄×C₆₇	—	4	1	no	—
597	C₄×C₆₇	—	4	2	no	—
598	C₄×C₆₇	—	4	1	no	—
599	C₄×C₆₇	—	4	1	no	—
600	C₄×C₆₇	—	4	2	no	—
601	C₄×C₆₇	—	4	1	no	—
602	C₄×C₆₇	#546	1	2	yes	—
603	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
604	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
605	#61185	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
606	C₂×C₆₇	—	2	2	no	—
607	C₂×C₆₇	—	2	2	no	—
608	C₂×C₆₇	—	4	2	no	—
609	C₂×C₆₇	—	4	1	no	—
610	C₂×C₆₇	—	8	1	no	—
611	C₂×C₆₇	—	8	2	no	—
612	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
613	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
614	C₂×C₆₇	#3586	1	1	yes	characteristic
615	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3329	C₂×C₆₇	1	2	yes	complemented
618	#3326	C₂×C₆₇	1	2	yes	complemented
619	#3321	C₂×C₆₇	1	2	yes	complemented
620	#3320	C₂×C₆₇	1	2	yes	complemented
621	#3320	C₂×C₆₇	1	2	yes	complemented
622	#3308	C₂×C₆₇	1	2	yes	complemented
623	#3301	C₂×C₆₇	1	2	yes	complemented
624	#3298	C₂×C₆₇	1	2	yes	complemented
625	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
633	C₂×#448	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
637	C₂×#419	C₂×C₆₇	1	1	yes	characteristic, complemented
638	C₆₇	#61185	1	1	yes	characteristic, direct product factor, Sylow
639	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
640	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
642	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
643	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
645	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
646	#555	C₂²×C₆₇	1	2	yes	—
647	#553	C₂²×C₆₇	1	2	yes	—
648	#553	C₂²×C₆₇	1	2	yes	—
649	#551	—	2	2	no	—
650	D₄×Q₈	—	2	1	no	—
651	D₄×Q₈	—	2	1	no	—
652	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
653	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
654	#548	—	2	1	no	—
655	#548	—	2	1	no	—
656	#548	C₂²×C₆₇	1	2	yes	complemented
657	#548	C₂²×C₆₇	1	2	yes	complemented
658	#547	C₂²×C₆₇	1	2	yes	—
659	#546	—	2	2	no	—
660	#544	C₂²×C₆₇	1	1	yes	characteristic
661	#542	—	2	1	no	—
662	#540	—	2	1	no	—
663	#536	—	2	2	no	—
664	#536	C₂²×C₆₇	1	1	yes	characteristic
665	#536	C₂²×C₆₇	1	1	yes	characteristic
666	#535	C₂²×C₆₇	1	1	yes	characteristic
667	#532	—	2	1	no	—
668	#529	—	2	1	no	—
669	#525	—	2	2	no	—
670	#525	C₂²×C₆₇	1	1	yes	characteristic
671	#525	C₂²×C₆₇	1	1	yes	characteristic
672	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
673	#520	C₂²×C₆₇	1	1	yes	characteristic
674	#519	C₂²×C₆₇	1	1	yes	characteristic
675	#518	C₂²×C₆₇	1	1	yes	characteristic
676	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
677	#491	C₂²×C₆₇	1	2	yes	complemented
678	#489	C₂²×C₆₇	1	2	yes	complemented
679	#488	C₂²×C₆₇	1	2	yes	complemented
680	#487	C₂²×C₆₇	1	2	yes	complemented
681	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#485	C₂²×C₆₇	1	2	yes	complemented
683	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#485	C₂²×C₆₇	1	2	yes	complemented
685	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#484	C₂²×C₆₇	1	2	yes	complemented
687	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#483	C₂²×C₆₇	1	2	yes	complemented
689	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#479	C₂²×C₆₇	1	2	yes	complemented
694	#479	C₂²×C₆₇	1	2	yes	complemented
695	#477	C₂²×C₆₇	1	2	yes	complemented
696	#475	C₂²×C₆₇	1	2	yes	complemented
697	#469	C₂²×C₆₇	1	2	yes	—
698	#468	C₂²×C₆₇	1	2	yes	—
699	#468	C₂²×C₆₇	1	2	yes	complemented
700	#468	C₂²×C₆₇	1	2	yes	complemented
701	#466	C₂²×C₆₇	1	2	yes	—
702	#465	C₂²×C₆₇	1	2	yes	—
703	#465	C₂²×C₆₇	1	2	yes	complemented
704	#465	C₂²×C₆₇	1	2	yes	complemented
705	#463	C₂²×C₆₇	1	2	yes	complemented
706	#463	C₂²×C₆₇	1	2	yes	complemented
707	#461	C₂²×C₆₇	1	2	yes	complemented
708	#461	C₂²×C₆₇	1	2	yes	complemented
709	#449	C₂²×C₆₇	1	2	yes	complemented
710	#449	C₂²×C₆₇	1	2	yes	complemented
711	#448	C₂²×C₆₇	1	2	yes	—
712	#448	C₂²×C₆₇	1	2	yes	—
713	#448	C₂²×C₆₇	1	2	yes	—
714	#448	C₂²×C₆₇	1	2	yes	—
715	#448	C₂²×C₆₇	1	2	yes	complemented
716	#448	C₂²×C₆₇	1	2	yes	complemented
717	#440	C₂²×C₆₇	1	2	yes	complemented
718	#440	C₂²×C₆₇	1	2	yes	complemented
719	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
720	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
721	#436	C₂²×C₆₇	1	2	yes	complemented
722	#435	C₂²×C₆₇	1	2	yes	complemented
723	#435	C₂²×C₆₇	1	2	yes	complemented
724	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
725	#428	C₂²×C₆₇	1	1	yes	characteristic
726	#427	C₂²×C₆₇	1	1	yes	characteristic
727	#427	C₂²×C₆₇	1	1	yes	characteristic
728	#424	C₂²×C₆₇	1	1	yes	characteristic
729	#419	C₂²×C₆₇	1	1	yes	characteristic
730	#419	C₂²×C₆₇	1	1	yes	characteristic
731	#419	C₂²×C₆₇	1	1	yes	characteristic
732	#419	C₂²×C₆₇	1	1	yes	characteristic
733	#419	C₂²×C₆₇	1	2	yes	complemented
734	#419	C₂²×C₆₇	1	2	yes	complemented
735	#419	C₂²×C₆₇	1	2	yes	complemented
736	#418	C₂²×C₆₇	1	1	yes	characteristic
737	#417	C₂²×C₆₇	1	1	yes	characteristic
738	#417	C₂²×C₆₇	1	2	yes	complemented
739	#416	C₂²×C₆₇	1	1	yes	characteristic
740	#416	C₂²×C₆₇	1	1	yes	characteristic
741	#416	C₂²×C₆₇	1	2	yes	complemented
742	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
743	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
745	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
746	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
747	#408	C₂²×C₆₇	1	1	yes	characteristic
748	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
749	#405	C₂²×C₆₇	1	1	yes	characteristic
750	2₋¹⁺⁴	—	2	4	no	—
751	2₋¹⁺⁴	—	4	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	2	no	—
755	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×#41	C₂³×C₆₇	1	2	yes	—
757	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
758	C₂²×Q₈	—	2	1	no	—
759	C₂²×Q₈	—	2	1	no	—
760	C₂²×Q₈	—	2	1	no	—
761	C₂²×Q₈	—	2	1	no	—
762	C₂²×Q₈	—	2	4	no	—
763	C₂²×Q₈	—	4	2	no	—
764	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
765	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
766	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
767	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
768	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
769	C₂²×D₄	—	2	1	no	—
770	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂³×C₄	—	2	1	no	—
772	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
773	AGL(1,ℤ/8)	—	4	2	no	—
774	C₂×SD₁₆	—	2	4	no	—
775	C₂×SD₁₆	—	4	2	no	—
776	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
781	C₂×D₈	C₂³×C₆₇	1	2	yes	—
782	#131	—	4	2	no	—
783	C₂×M₁₆	—	4	2	no	—
784	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
786	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
788	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
790	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
791	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	—	2	1	no	—
794	C₄⋊Q₈	—	2	2	no	—
795	C₄⋊Q₈	—	2	2	no	—
796	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
797	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
798	#127	—	2	1	no	—
799	#126	—	2	2	no	—
800	#126	—	2	2	no	—
801	#125	—	2	1	no	—
802	#125	C₂³×C₆₇	1	2	yes	—
803	#124	—	2	1	no	—
804	#124	—	2	1	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	2	no	—
809	#124	C₂³×C₆₇	1	2	yes	—
810	#123	—	2	2	no	—
811	#123	—	2	1	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	D₄×C₆₇	1	2	yes	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
829	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	D₄×C₆₇	1	1	yes	characteristic
842	#121	D₄×C₆₇	1	1	yes	characteristic
843	#121	C₂³×C₆₇	1	2	yes	—
844	#121	C₂³×C₆₇	1	2	yes	—
845	#121	C₂³×C₆₇	1	1	yes	characteristic
846	#121	C₂³×C₆₇	1	1	yes	characteristic
847	#121	C₂³×C₆₇	1	2	yes	—
848	#121	C₂³×C₆₇	1	2	yes	—
849	#120	—	2	1	no	—
850	#120	—	2	2	no	—
851	#120	D₄×C₆₇	1	2	yes	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	—	2	1	no	—
855	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
856	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	C₂³×C₆₇	1	2	yes	—
870	C₄×D₄	C₂³×C₆₇	1	2	yes	—
871	C₄×D₄	C₂³×C₆₇	1	2	yes	—
872	C₄×D₄	C₂³×C₆₇	1	2	yes	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	2	no	—
876	#117	—	2	2	no	—
877	#117	C₂³×C₆₇	1	1	yes	characteristic
878	#117	C₂³×C₆₇	1	1	yes	characteristic
879	#117	C₂³×C₆₇	1	1	yes	characteristic
880	#117	C₂³×C₆₇	1	1	yes	characteristic
881	#117	C₂³×C₆₇	1	1	yes	characteristic
882	#117	C₂³×C₆₇	1	2	yes	—
883	#117	C₂³×C₆₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
888	C₂×C₂²⋊C₄	—	2	1	no	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	—	2	2	no	—
891	C₂×C₄²	—	2	1	no	—
892	#107	C₂³×C₆₇	1	1	yes	characteristic
893	#107	C₂³×C₆₇	1	1	yes	characteristic
894	#107	C₂³×C₆₇	1	1	yes	characteristic
895	#107	C₂³×C₆₇	1	1	yes	characteristic
896	#107	C₂³×C₆₇	1	2	yes	—
897	#106	C₂³×C₆₇	1	1	yes	characteristic
898	#106	C₂³×C₆₇	1	1	yes	characteristic
899	#106	C₂³×C₆₇	1	1	yes	characteristic
900	#106	C₂³×C₆₇	1	1	yes	characteristic
901	#106	C₂³×C₆₇	1	2	yes	—
902	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
903	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
904	#103	C₂³×C₆₇	1	2	yes	—
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	1	yes	characteristic
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	2	yes	—
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	2	yes	—
913	#103	C₂³×C₆₇	1	2	yes	—
914	#103	C₂³×C₆₇	1	2	yes	—
915	#103	C₂³×C₆₇	1	2	yes	—
916	#103	C₂³×C₆₇	1	2	yes	—
917	#103	C₂³×C₆₇	1	2	yes	—
918	#103	C₂³×C₆₇	1	1	yes	characteristic
919	#103	C₂³×C₆₇	1	1	yes	characteristic
920	#103	C₂³×C₆₇	1	1	yes	characteristic
921	#102	C₂³×C₆₇	1	1	yes	characteristic
922	#102	C₂³×C₆₇	1	1	yes	characteristic
923	#102	C₂³×C₆₇	1	1	yes	characteristic
924	#102	C₂³×C₆₇	1	1	yes	characteristic
925	#102	C₂³×C₆₇	1	2	yes	—
926	#102	C₂³×C₆₇	1	2	yes	—
927	#102	C₂³×C₆₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
931	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
932	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
934	#97	C₂³×C₆₇	1	2	yes	—
935	C₄×C₈	C₂³×C₆₇	1	2	yes	—
936	C₂⁴	—	2	1	no	—
937	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	4	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	4	2	no	—
944	#41	—	4	8	no	—
945	#41	—	4	4	no	—
946	#41	—	8	4	no	—
947	C₂×Q₈	—	2	1	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	4	no	—
956	C₂×Q₈	—	2	4	no	—
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	—	2	2	no	—
959	C₂×Q₈	—	4	4	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	—	4	2	no	—
963	C₂×Q₈	—	4	4	no	—
964	C₂×Q₈	—	4	4	no	—
965	C₂×Q₈	—	4	4	no	—
966	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
967	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
968	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
969	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
984	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
987	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	4	4	no	—
1005	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1012	SD₁₆	—	2	4	no	—
1013	SD₁₆	—	2	4	no	—
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	D₈	—	4	2	no	—
1018	M₁₆	—	2	2	no	—
1019	M₁₆	—	2	2	no	—
1020	M₁₆	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	C₂×C₈	—	2	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1080	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	1	no	—
1091	C₄²	C₂⁴×C₆₇	1	2	yes	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	—	4	2	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	1	no	—
1100	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1101	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1102	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1103	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1104	Q₈	—	2	4	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	4	4	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	4	no	—
1114	Q₈	—	4	2	no	—
1115	Q₈	—	8	2	no	—
1116	Q₈	C₂×#41×C₆₇	1	4	yes	—
1117	D₄	—	2	4	no	—
1118	D₄	—	2	4	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	4	no	—
1157	C₂×C₄	—	4	4	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	4	2	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	8	1	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1170	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1171	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1172	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1173	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1174	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	1	no	—
1179	C₈	—	2	2	no	—
1180	C₈	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	4	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	16	2	no	—
1199	C₂²	#546×C₆₇	1	2	yes	—
1200	C₂²	#577×C₆₇	1	2	yes	—
1201	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1202	C₄	—	2	2	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	4	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	#546×C₆₇	1	2	yes	—
1218	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1219	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1220	C₂	—	2	2	no	—
1221	C₂	—	2	2	no	—
1222	C₂	—	4	1	no	—
1223	C₂	—	4	2	no	—
1224	C₂	—	8	2	no	—
1225	C₂	—	8	1	no	—
1226	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1227	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1228	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3494	C₂	semidirect
2. C₆₇×#3486	C₂	semidirect
3. C₆₇×#3329	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3321	C₂	semidirect
6. C₆₇×#3320	C₂	semidirect
7. C₆₇×#3320	C₂	semidirect
8. C₆₇×#3308	C₂	semidirect
9. C₆₇×#3301	C₂	semidirect
10. C₆₇×#3298	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3091	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3057	C₂	semidirect
16. C₆₇×#3055	C₂	semidirect
17. C₆₇×#3042	C₂	semidirect
18. C₆₇×#3010	C₂	semidirect
19. C₂×#448×C₆₇	C₂	semidirect
20. C₆₇×#2949	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₂×#419×C₆₇	C₂	semidirect
37. D₄×Q₈×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
41. #548×C₆₇	C₂²	semidirect
42. #548×C₆₇	C₂²	semidirect
62. #491×C₆₇	C₂²	semidirect
63. #489×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
71. #484×C₆₇	C₂²	semidirect
72. #483×C₆₇	C₂²	semidirect
73. #483×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #481×C₆₇	C₂²	semidirect
77. #480×C₆₇	C₂²	semidirect
78. #479×C₆₇	C₂²	semidirect
79. #479×C₆₇	C₂²	semidirect
80. #477×C₆₇	C₂²	semidirect
81. #475×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #463×C₆₇	C₂²	semidirect
91. #463×C₆₇	C₂²	semidirect
92. #461×C₆₇	C₂²	semidirect
93. #461×C₆₇	C₂²	semidirect
94. #449×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
101. #448×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
105. C₄×SD₁₆×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. C₈×D₄×C₆₇	C₂²	semidirect
118. #419×C₆₇	C₂²	semidirect
119. #419×C₆₇	C₂²	semidirect
120. #419×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
126. #416×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
130. C₂×#103×C₆₇	C₂²	semidirect
131. C₂×#103×C₆₇	C₂²	semidirect
352. C₂×Q₈×C₆₇	#41	semidirect
605. #61185	C₆₇	direct (N × H)
615. #3494	C₂×C₆₇	semidirect
616. #3486	C₂×C₆₇	semidirect
617. #3329	C₂×C₆₇	semidirect
618. #3326	C₂×C₆₇	semidirect
619. #3321	C₂×C₆₇	semidirect
620. #3320	C₂×C₆₇	semidirect
621. #3320	C₂×C₆₇	semidirect
622. #3308	C₂×C₆₇	semidirect
623. #3301	C₂×C₆₇	semidirect
624. #3298	C₂×C₆₇	semidirect
625. #3137	C₂×C₆₇	semidirect
626. #3097	C₂×C₆₇	semidirect
627. #3091	C₂×C₆₇	semidirect
628. #3082	C₂×C₆₇	semidirect
629. #3057	C₂×C₆₇	semidirect
630. #3055	C₂×C₆₇	semidirect
631. #3042	C₂×C₆₇	semidirect
632. #3010	C₂×C₆₇	semidirect
633. C₂×#448	C₂×C₆₇	semidirect
634. #2949	C₂×C₆₇	semidirect
635. #2933	C₂×C₆₇	semidirect
636. #2898	C₂×C₆₇	semidirect
637. C₂×#419	C₂×C₆₇	semidirect
638. C₆₇	#61185	direct (N × H)
652. D₄×Q₈	C₂²×C₆₇	semidirect
653. D₄×Q₈	C₂²×C₆₇	semidirect
656. #548	C₂²×C₆₇	semidirect
657. #548	C₂²×C₆₇	semidirect
677. #491	C₂²×C₆₇	semidirect
678. #489	C₂²×C₆₇	semidirect
679. #488	C₂²×C₆₇	semidirect
680. #487	C₂²×C₆₇	semidirect
681. #485	C₂²×C₆₇	semidirect
682. #485	C₂²×C₆₇	semidirect
683. #485	C₂²×C₆₇	semidirect
684. #485	C₂²×C₆₇	semidirect
685. #484	C₂²×C₆₇	semidirect
686. #484	C₂²×C₆₇	semidirect
687. #483	C₂²×C₆₇	semidirect
688. #483	C₂²×C₆₇	semidirect
689. #482	C₂²×C₆₇	semidirect
690. #482	C₂²×C₆₇	semidirect
691. #481	C₂²×C₆₇	semidirect
692. #480	C₂²×C₆₇	semidirect
693. #479	C₂²×C₆₇	semidirect
694. #479	C₂²×C₆₇	semidirect
695. #477	C₂²×C₆₇	semidirect
696. #475	C₂²×C₆₇	semidirect
699. #468	C₂²×C₆₇	semidirect
700. #468	C₂²×C₆₇	semidirect
703. #465	C₂²×C₆₇	semidirect
704. #465	C₂²×C₆₇	semidirect
705. #463	C₂²×C₆₇	semidirect
706. #463	C₂²×C₆₇	semidirect
707. #461	C₂²×C₆₇	semidirect
708. #461	C₂²×C₆₇	semidirect
709. #449	C₂²×C₆₇	semidirect
710. #449	C₂²×C₆₇	semidirect
715. #448	C₂²×C₆₇	semidirect
716. #448	C₂²×C₆₇	semidirect
717. #440	C₂²×C₆₇	semidirect
718. #440	C₂²×C₆₇	semidirect
719. C₄×SD₁₆	C₂²×C₆₇	semidirect
720. C₄×SD₁₆	C₂²×C₆₇	semidirect
721. #436	C₂²×C₆₇	semidirect
722. #435	C₂²×C₆₇	semidirect
723. #435	C₂²×C₆₇	semidirect
724. C₈×D₄	C₂²×C₆₇	semidirect
733. #419	C₂²×C₆₇	semidirect
734. #419	C₂²×C₆₇	semidirect
735. #419	C₂²×C₆₇	semidirect
738. #417	C₂²×C₆₇	semidirect
741. #416	C₂²×C₆₇	semidirect
744. C₂×#103	C₂²×C₆₇	semidirect
745. C₂×#103	C₂²×C₆₇	semidirect
746. C₂×#103	C₂²×C₆₇	semidirect
967. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3494	2
C₆₇×#3486	2
C₆₇×#3329	2
C₆₇×#3326	2
C₆₇×#3321	2
C₆₇×#3320	2
C₆₇×#3308	2
C₆₇×#3301	2
C₆₇×#3298	2
C₆₇×#3137	2
C₆₇×#3097	2
C₆₇×#3091	2
C₆₇×#3082	2
C₆₇×#3057	2
C₆₇×#3055	2
C₆₇×#3042	2
C₆₇×#3010	2
C₂×#448×C₆₇	2
C₆₇×#2949	2
C₆₇×#2933	2
C₆₇×#2898	2
C₂×#419×C₆₇	2
#61185	67

Subgroups — C67×#61185 #30740436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61185 #30740436