Subgroups — C₆₇×#61187 #30740438

Order 17152.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1252 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×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3319	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3303	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3297	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×#3081	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×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×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, complemented
28	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#555×C₆₇	C₂²	1	2	yes	complemented
32	#553×C₆₇	C₂²	1	2	yes	complemented
33	#553×C₆₇	C₂²	1	2	yes	complemented
34	#551×C₆₇	—	2	2	no	—
35	#547×C₆₇	—	2	1	no	—
36	#547×C₆₇	—	2	1	no	—
37	#547×C₆₇	C₂²	1	2	yes	complemented
38	#547×C₆₇	C₂²	1	2	yes	complemented
39	#547×C₆₇	C₂²	1	2	yes	complemented
40	#546×C₆₇	—	2	1	no	—
41	#546×C₆₇	—	2	1	no	—
42	#546×C₆₇	—	2	2	no	—
43	#546×C₆₇	C₂²	1	2	yes	complemented
44	#546×C₆₇	C₂²	1	2	yes	complemented
45	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#542×C₆₇	—	2	1	no	—
47	#540×C₆₇	—	2	1	no	—
48	#536×C₆₇	C₂²	1	1	yes	characteristic
49	#536×C₆₇	C₂²	1	1	yes	characteristic
50	#535×C₆₇	C₂²	1	1	yes	characteristic
51	#534×C₆₇	—	2	2	no	—
52	#532×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#525×C₆₇	C₂²	1	1	yes	characteristic
55	#525×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#123×C₆₇	—	2	2	no	—
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#518×C₆₇	C₂²	1	1	yes	characteristic
60	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#483×C₆₇	C₂²	1	2	yes	complemented
73	#483×C₆₇	C₂²	1	1	yes	characteristic, 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	#478×C₆₇	C₂²	1	2	yes	complemented
79	#478×C₆₇	C₂²	1	2	yes	complemented
80	#476×C₆₇	C₂²	1	2	yes	complemented
81	#474×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#468×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#466×C₆₇	C₂²	1	2	yes	complemented
87	#465×C₆₇	C₂²	1	2	yes	complemented
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	#449×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#449×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	complemented
101	#447×C₆₇	C₂²	1	2	yes	complemented
102	#442×C₆₇	C₂²	1	2	yes	complemented
103	#442×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
105	C₄×D₈×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, complemented
111	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#418×C₆₇	C₂²	1	1	yes	characteristic
117	#418×C₆₇	C₂²	1	1	yes	characteristic
118	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#418×C₆₇	C₂²	1	2	yes	complemented
120	#417×C₆₇	C₂²	1	1	yes	characteristic
121	#417×C₆₇	C₂²	1	2	yes	complemented
122	#417×C₆₇	C₂²	1	2	yes	complemented
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	#416×C₆₇	C₂²	1	2	yes	complemented
128	#416×C₆₇	C₂²	1	2	yes	complemented
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₆₇	—	2	4	no	—
136	H(5,𝔽₂)×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	—	2	2	no	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	4	no	—
142	C₂×#41×C₆₇	—	4	2	no	—
143	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	2	yes	—
146	C₂×#41×C₆₇	C₂³	1	2	yes	—
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	—	2	1	no	—
150	C₂²×D₄×C₆₇	—	2	1	no	—
151	C₂²×D₄×C₆₇	—	2	2	no	—
152	C₂²×D₄×C₆₇	—	2	1	no	—
153	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
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	—	4	2	no	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×D₈×C₆₇	—	2	4	no	—
164	C₂×D₈×C₆₇	C₂³	1	2	yes	—
165	C₂×D₈×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	C₂³	1	2	yes	—
180	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	#127×C₆₇	—	2	1	no	—
182	#126×C₆₇	—	2	2	no	—
183	#126×C₆₇	—	2	2	no	—
184	#125×C₆₇	—	2	1	no	—
185	#125×C₆₇	C₂³	1	2	yes	—
186	#124×C₆₇	—	2	1	no	—
187	#124×C₆₇	—	2	1	no	—
188	#124×C₆₇	—	2	2	no	—
189	#124×C₆₇	—	2	2	no	—
190	#124×C₆₇	C₂³	1	2	yes	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	1	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×C₆₇	—	2	2	no	—
195	#123×C₆₇	—	2	2	no	—
196	#123×C₆₇	—	2	2	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	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	D₄	1	1	yes	characteristic
225	#121×C₆₇	D₄	1	1	yes	characteristic
226	#121×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	1	yes	characteristic
231	#121×C₆₇	C₂³	1	1	yes	characteristic
232	#120×C₆₇	—	2	1	no	—
233	#120×C₆₇	—	2	2	no	—
234	#120×C₆₇	—	2	2	no	—
235	#120×C₆₇	—	2	2	no	—
236	#120×C₆₇	D₄	1	2	yes	—
237	C₄×Q₈×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
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	2	no	—
247	C₄×D₄×C₆₇	—	2	2	no	—
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	2	yes	—
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	C₄×D₄×C₆₇	C₂³	1	2	yes	—
252	C₄×D₄×C₆₇	C₂³	1	2	yes	—
253	C₄×D₄×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	2	no	—
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	1	yes	characteristic
259	#117×C₆₇	C₂³	1	2	yes	—
260	#117×C₆₇	C₂³	1	1	yes	characteristic
261	#117×C₆₇	C₂³	1	1	yes	characteristic
262	#117×C₆₇	C₂³	1	1	yes	characteristic
263	#117×C₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₆₇	—	2	2	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	1	yes	characteristic
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	#106×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
323	C₂⁴×C₆₇	—	2	2	no	—
324	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	4	no	—
328	#41×C₆₇	—	2	4	no	—
329	#41×C₆₇	—	2	4	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	2	no	—
335	#41×C₆₇	—	4	4	no	—
336	#41×C₆₇	—	4	4	no	—
337	#41×C₆₇	—	4	4	no	—
338	#41×C₆₇	—	8	4	no	—
339	C₂×Q₈×C₆₇	—	2	1	no	—
340	C₂×Q₈×C₆₇	—	2	2	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
344	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
345	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₇	—	2	4	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	—	2	2	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	1	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	1	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	1	no	—
358	C₂×D₄×C₆₇	—	2	1	no	—
359	C₂×D₄×C₆₇	—	2	2	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	—	4	2	no	—
364	C₂×D₄×C₆₇	—	4	4	no	—
365	C₂×D₄×C₆₇	—	4	8	no	—
366	C₂×D₄×C₆₇	—	4	4	no	—
367	C₂×D₄×C₆₇	—	8	2	no	—
368	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₇	#41	1	4	yes	complemented
373	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
375	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₆₇	—	2	2	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	1	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	1	no	—
381	C₂²×C₄×C₆₇	—	2	1	no	—
382	C₂²×C₄×C₆₇	—	2	2	no	—
383	C₂²×C₄×C₆₇	—	2	2	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	—	2	2	no	—
390	C₂²×C₄×C₆₇	—	2	2	no	—
391	C₂²×C₄×C₆₇	—	4	4	no	—
392	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	SD₁₆×C₆₇	—	4	2	no	—
402	D₈×C₆₇	—	2	4	no	—
403	D₈×C₆₇	—	2	4	no	—
404	D₈×C₆₇	—	4	2	no	—
405	M₁₆×C₆₇	—	2	2	no	—
406	M₁₆×C₆₇	—	2	2	no	—
407	M₁₆×C₆₇	—	4	2	no	—
408	M₁₆×C₆₇	—	4	2	no	—
409	C₂×C₈×C₆₇	—	2	2	no	—
410	C₂×C₈×C₆₇	—	2	2	no	—
411	C₂×C₈×C₆₇	—	4	2	no	—
412	C₂×C₈×C₆₇	—	4	2	no	—
413	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
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	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	—	2	1	no	—
420	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	1	no	—
453	C₂²⋊C₄×C₆₇	—	2	1	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
462	C₂²⋊C₄×C₆₇	—	2	2	no	—
463	C₂²⋊C₄×C₆₇	—	2	2	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
470	C₄²×C₆₇	—	2	1	no	—
471	C₄²×C₆₇	—	2	1	no	—
472	C₄²×C₆₇	—	2	1	no	—
473	C₄²×C₆₇	—	2	1	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	4	no	—
480	C₂³×C₆₇	—	2	2	no	—
481	C₂³×C₆₇	—	2	1	no	—
482	C₂³×C₆₇	—	4	1	no	—
483	C₂³×C₆₇	—	4	1	no	—
484	C₂³×C₆₇	—	4	4	no	—
485	C₂³×C₆₇	—	4	2	no	—
486	C₂³×C₆₇	—	8	1	no	—
487	C₂³×C₆₇	—	8	1	no	—
488	C₂³×C₆₇	—	8	1	no	—
489	C₂³×C₆₇	—	8	1	no	—
490	C₂³×C₆₇	—	8	2	no	—
491	C₂³×C₆₇	—	8	2	no	—
492	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
493	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
494	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
496	Q₈×C₆₇	—	2	2	no	—
497	Q₈×C₆₇	—	2	2	no	—
498	Q₈×C₆₇	—	2	1	no	—
499	Q₈×C₆₇	—	2	2	no	—
500	Q₈×C₆₇	—	2	1	no	—
501	Q₈×C₆₇	—	4	2	no	—
502	Q₈×C₆₇	—	8	2	no	—
503	D₄×C₆₇	—	2	4	no	—
504	D₄×C₆₇	—	2	4	no	—
505	D₄×C₆₇	—	2	2	no	—
506	D₄×C₆₇	—	2	2	no	—
507	D₄×C₆₇	—	2	1	no	—
508	D₄×C₆₇	—	2	2	no	—
509	D₄×C₆₇	—	2	1	no	—
510	D₄×C₆₇	—	2	2	no	—
511	D₄×C₆₇	—	4	2	no	—
512	D₄×C₆₇	—	4	2	no	—
513	D₄×C₆₇	—	4	4	no	—
514	D₄×C₆₇	—	4	4	no	—
515	D₄×C₆₇	—	4	4	no	—
516	D₄×C₆₇	—	4	4	no	—
517	D₄×C₆₇	—	4	4	no	—
518	D₄×C₆₇	—	4	2	no	—
519	D₄×C₆₇	—	4	2	no	—
520	D₄×C₆₇	—	8	1	no	—
521	D₄×C₆₇	—	8	2	no	—
522	D₄×C₆₇	—	8	1	no	—
523	D₄×C₆₇	—	8	2	no	—
524	D₄×C₆₇	—	8	2	no	—
525	D₄×C₆₇	C₂×#41	1	4	yes	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	2	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	2	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	4	4	no	—
545	C₂×C₄×C₆₇	—	4	4	no	—
546	C₂×C₄×C₆₇	—	4	4	no	—
547	C₂×C₄×C₆₇	—	4	2	no	—
548	C₂×C₄×C₆₇	—	4	2	no	—
549	C₂×C₄×C₆₇	—	4	2	no	—
550	C₂×C₄×C₆₇	—	8	2	no	—
551	C₂×C₄×C₆₇	—	8	2	no	—
552	C₂×C₄×C₆₇	—	8	2	no	—
553	C₂×C₄×C₆₇	—	8	2	no	—
554	C₂×C₄×C₆₇	—	8	1	no	—
555	C₂×C₄×C₆₇	—	8	1	no	—
556	C₂×C₄×C₆₇	—	8	2	no	—
557	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
564	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
566	C₈×C₆₇	—	2	1	no	—
567	C₈×C₆₇	—	2	1	no	—
568	C₈×C₆₇	—	2	1	no	—
569	C₈×C₆₇	—	2	1	no	—
570	C₈×C₆₇	—	2	2	no	—
571	C₈×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	1	no	—
573	C₂²×C₆₇	—	2	1	no	—
574	C₂²×C₆₇	—	2	1	no	—
575	C₂²×C₆₇	—	2	1	no	—
576	C₂²×C₆₇	—	2	2	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	2	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	2	no	—
583	C₂²×C₆₇	—	2	4	no	—
584	C₂²×C₆₇	—	4	2	no	—
585	C₂²×C₆₇	—	4	2	no	—
586	C₂²×C₆₇	—	4	2	no	—
587	C₂²×C₆₇	—	4	1	no	—
588	C₂²×C₆₇	—	4	2	no	—
589	C₂²×C₆₇	—	4	1	no	—
590	C₂²×C₆₇	—	4	1	no	—
591	C₂²×C₆₇	—	4	2	no	—
592	C₂²×C₆₇	—	8	2	no	—
593	C₂²×C₆₇	—	8	4	no	—
594	C₂²×C₆₇	—	16	2	no	—
595	C₂²×C₆₇	—	16	4	no	—
596	C₂²×C₆₇	#546	1	2	yes	—
597	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₆₇	—	2	2	no	—
599	C₄×C₆₇	—	2	2	no	—
600	C₄×C₆₇	—	2	1	no	—
601	C₄×C₆₇	—	2	1	no	—
602	C₄×C₆₇	—	2	2	no	—
603	C₄×C₆₇	—	4	1	no	—
604	C₄×C₆₇	—	4	1	no	—
605	C₄×C₆₇	—	4	1	no	—
606	C₄×C₆₇	—	4	1	no	—
607	C₄×C₆₇	—	4	1	no	—
608	C₄×C₆₇	—	4	2	no	—
609	C₄×C₆₇	—	4	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	2	no	—
612	C₄×C₆₇	#546	1	2	yes	—
613	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
614	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	#61187	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
616	C₂×C₆₇	—	2	2	no	—
617	C₂×C₆₇	—	4	1	no	—
618	C₂×C₆₇	—	4	1	no	—
619	C₂×C₆₇	—	4	2	no	—
620	C₂×C₆₇	—	4	4	no	—
621	C₂×C₆₇	—	8	2	no	—
622	C₂×C₆₇	—	8	1	no	—
623	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
624	C₂×C₆₇	#3584	1	1	yes	characteristic
625	C₂×C₆₇	#3585	1	1	yes	characteristic
626	#3494	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3330	C₂×C₆₇	1	2	yes	complemented
629	#3322	C₂×C₆₇	1	2	yes	complemented
630	#3319	C₂×C₆₇	1	2	yes	complemented
631	#3307	C₂×C₆₇	1	2	yes	complemented
632	#3307	C₂×C₆₇	1	2	yes	complemented
633	#3306	C₂×C₆₇	1	2	yes	complemented
634	#3303	C₂×C₆₇	1	2	yes	complemented
635	#3297	C₂×C₆₇	1	2	yes	complemented
636	#3137	C₂×C₆₇	1	1	yes	characteristic, complemented
637	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
638	#3091	C₂×C₆₇	1	1	yes	characteristic, complemented
639	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
640	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
641	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
642	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
643	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
644	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
645	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
646	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
647	#2897	C₂×C₆₇	1	1	yes	characteristic, complemented
648	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
649	C₆₇	#61187	1	1	yes	characteristic, direct product factor, Sylow
650	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
651	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
652	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
653	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
655	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
656	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#555	C₂²×C₆₇	1	2	yes	complemented
658	#553	C₂²×C₆₇	1	2	yes	complemented
659	#553	C₂²×C₆₇	1	2	yes	complemented
660	#551	—	2	2	no	—
661	#547	—	2	1	no	—
662	#547	—	2	1	no	—
663	#547	C₂²×C₆₇	1	2	yes	complemented
664	#547	C₂²×C₆₇	1	2	yes	complemented
665	#547	C₂²×C₆₇	1	2	yes	complemented
666	#546	—	2	1	no	—
667	#546	—	2	1	no	—
668	#546	—	2	2	no	—
669	#546	C₂²×C₆₇	1	2	yes	complemented
670	#546	C₂²×C₆₇	1	2	yes	complemented
671	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#542	—	2	1	no	—
673	#540	—	2	1	no	—
674	#536	C₂²×C₆₇	1	1	yes	characteristic
675	#536	C₂²×C₆₇	1	1	yes	characteristic
676	#535	C₂²×C₆₇	1	1	yes	characteristic
677	#534	—	2	2	no	—
678	#532	—	2	1	no	—
679	#529	—	2	1	no	—
680	#525	C₂²×C₆₇	1	1	yes	characteristic
681	#525	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×#123	—	2	2	no	—
683	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#520	C₂²×C₆₇	1	1	yes	characteristic
685	#518	C₂²×C₆₇	1	1	yes	characteristic
686	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#491	C₂²×C₆₇	1	2	yes	complemented
689	#489	C₂²×C₆₇	1	2	yes	complemented
690	#488	C₂²×C₆₇	1	2	yes	complemented
691	#487	C₂²×C₆₇	1	2	yes	complemented
692	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#485	C₂²×C₆₇	1	2	yes	complemented
695	#485	C₂²×C₆₇	1	2	yes	complemented
696	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#484	C₂²×C₆₇	1	2	yes	complemented
698	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#483	C₂²×C₆₇	1	2	yes	complemented
700	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#478	C₂²×C₆₇	1	2	yes	complemented
705	#478	C₂²×C₆₇	1	2	yes	complemented
706	#476	C₂²×C₆₇	1	2	yes	complemented
707	#474	C₂²×C₆₇	1	2	yes	complemented
708	#469	C₂²×C₆₇	1	2	yes	complemented
709	#468	C₂²×C₆₇	1	2	yes	complemented
710	#468	C₂²×C₆₇	1	2	yes	complemented
711	#468	C₂²×C₆₇	1	2	yes	complemented
712	#466	C₂²×C₆₇	1	2	yes	complemented
713	#465	C₂²×C₆₇	1	2	yes	complemented
714	#465	C₂²×C₆₇	1	2	yes	complemented
715	#465	C₂²×C₆₇	1	2	yes	complemented
716	#463	C₂²×C₆₇	1	2	yes	complemented
717	#463	C₂²×C₆₇	1	2	yes	complemented
718	#461	C₂²×C₆₇	1	2	yes	complemented
719	#461	C₂²×C₆₇	1	2	yes	complemented
720	#449	C₂²×C₆₇	1	2	yes	complemented
721	#449	C₂²×C₆₇	1	2	yes	complemented
722	#449	C₂²×C₆₇	1	2	yes	complemented
723	#449	C₂²×C₆₇	1	2	yes	complemented
724	#449	C₂²×C₆₇	1	2	yes	complemented
725	#449	C₂²×C₆₇	1	2	yes	complemented
726	#447	C₂²×C₆₇	1	2	yes	complemented
727	#447	C₂²×C₆₇	1	2	yes	complemented
728	#442	C₂²×C₆₇	1	2	yes	complemented
729	#442	C₂²×C₆₇	1	2	yes	complemented
730	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
731	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
732	#436	C₂²×C₆₇	1	2	yes	complemented
733	#435	C₂²×C₆₇	1	2	yes	complemented
734	#435	C₂²×C₆₇	1	2	yes	complemented
735	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
736	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
742	#418	C₂²×C₆₇	1	1	yes	characteristic
743	#418	C₂²×C₆₇	1	1	yes	characteristic
744	#418	C₂²×C₆₇	1	2	yes	complemented
745	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	#417	C₂²×C₆₇	1	1	yes	characteristic
747	#417	C₂²×C₆₇	1	2	yes	complemented
748	#417	C₂²×C₆₇	1	2	yes	complemented
749	#417	C₂²×C₆₇	1	2	yes	complemented
750	#416	C₂²×C₆₇	1	1	yes	characteristic
751	#416	C₂²×C₆₇	1	1	yes	characteristic
752	#416	C₂²×C₆₇	1	2	yes	complemented
753	#416	C₂²×C₆₇	1	2	yes	complemented
754	#416	C₂²×C₆₇	1	2	yes	complemented
755	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
757	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
758	#408	C₂²×C₆₇	1	1	yes	characteristic
759	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	H(5,𝔽₂)	—	2	4	no	—
762	H(5,𝔽₂)	—	4	2	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	2	2	no	—
765	C₂×#41	—	2	1	no	—
766	C₂×#41	—	2	1	no	—
767	C₂×#41	—	2	4	no	—
768	C₂×#41	—	4	2	no	—
769	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×#41	C₂³×C₆₇	1	2	yes	—
771	C₂×#41	C₂³×C₆₇	1	2	yes	—
772	C₂×#41	C₂³×C₆₇	1	2	yes	—
773	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	—	2	1	no	—
777	C₂²×D₄	—	2	2	no	—
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
780	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
781	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
782	C₂³×C₄	—	2	1	no	—
783	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
784	AGL(1,ℤ/8)	—	4	2	no	—
785	C₂×SD₁₆	—	4	2	no	—
786	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
789	C₂×D₈	—	2	4	no	—
790	C₂×D₈	C₂³×C₆₇	1	2	yes	—
791	C₂×D₈	C₂³×C₆₇	1	2	yes	—
792	C₂×D₈	C₂³×C₆₇	1	2	yes	—
793	#131	—	4	2	no	—
794	C₂×M₁₆	—	4	2	no	—
795	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
796	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
798	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
799	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
802	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
803	C₄⋊Q₈	—	2	1	no	—
804	C₄⋊Q₈	—	2	1	no	—
805	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
806	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
807	#127	—	2	1	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#125	—	2	1	no	—
811	#125	C₂³×C₆₇	1	2	yes	—
812	#124	—	2	1	no	—
813	#124	—	2	1	no	—
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	C₂³×C₆₇	1	2	yes	—
817	#123	—	2	2	no	—
818	#123	—	2	1	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	D₄×C₆₇	1	2	yes	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
836	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
838	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
839	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	D₄×C₆₇	1	1	yes	characteristic
851	#121	D₄×C₆₇	1	1	yes	characteristic
852	#121	C₂³×C₆₇	1	2	yes	—
853	#121	C₂³×C₆₇	1	2	yes	—
854	#121	C₂³×C₆₇	1	1	yes	characteristic
855	#121	C₂³×C₆₇	1	1	yes	characteristic
856	#121	C₂³×C₆₇	1	2	yes	—
857	#121	C₂³×C₆₇	1	2	yes	—
858	#120	—	2	1	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	#120	D₄×C₆₇	1	2	yes	—
863	C₄×Q₈	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	—	2	2	no	—
874	C₄×D₄	C₂³×C₆₇	1	2	yes	—
875	C₄×D₄	C₂³×C₆₇	1	2	yes	—
876	C₄×D₄	C₂³×C₆₇	1	2	yes	—
877	C₄×D₄	C₂³×C₆₇	1	2	yes	—
878	C₄×D₄	C₂³×C₆₇	1	2	yes	—
879	C₄×D₄	C₂³×C₆₇	1	2	yes	—
880	#117	—	2	1	no	—
881	#117	—	2	1	no	—
882	#117	—	2	2	no	—
883	#117	C₂³×C₆₇	1	1	yes	characteristic
884	#117	C₂³×C₆₇	1	1	yes	characteristic
885	#117	C₂³×C₆₇	1	1	yes	characteristic
886	#117	C₂³×C₆₇	1	1	yes	characteristic
887	#117	C₂³×C₆₇	1	1	yes	characteristic
888	#117	C₂³×C₆₇	1	2	yes	—
889	#117	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	—	2	2	no	—
891	C₂×C₄⋊C₄	—	2	2	no	—
892	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
896	C₂×C₂²⋊C₄	—	2	1	no	—
897	C₂×C₂²⋊C₄	—	2	1	no	—
898	C₂×C₂²⋊C₄	—	2	2	no	—
899	C₂×C₂²⋊C₄	—	2	2	no	—
900	C₂×C₂²⋊C₄	—	2	2	no	—
901	C₂×C₂²⋊C₄	—	2	2	no	—
902	C₂×C₄²	—	2	1	no	—
903	#107	C₂³×C₆₇	1	1	yes	characteristic
904	#107	C₂³×C₆₇	1	1	yes	characteristic
905	#107	C₂³×C₆₇	1	1	yes	characteristic
906	#107	C₂³×C₆₇	1	1	yes	characteristic
907	#107	C₂³×C₆₇	1	2	yes	—
908	#106	C₂³×C₆₇	1	1	yes	characteristic
909	#106	C₂³×C₆₇	1	1	yes	characteristic
910	#106	C₂³×C₆₇	1	1	yes	characteristic
911	#106	C₂³×C₆₇	1	1	yes	characteristic
912	#106	C₂³×C₆₇	1	2	yes	—
913	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
914	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
915	#103	C₂³×C₆₇	1	2	yes	—
916	#103	C₂³×C₆₇	1	2	yes	—
917	#103	C₂³×C₆₇	1	1	yes	characteristic
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	#103	C₂³×C₆₇	1	2	yes	—
922	#103	C₂³×C₆₇	1	2	yes	—
923	#103	C₂³×C₆₇	1	2	yes	—
924	#103	C₂³×C₆₇	1	2	yes	—
925	#103	C₂³×C₆₇	1	2	yes	—
926	#102	C₂³×C₆₇	1	2	yes	—
927	#102	C₂³×C₆₇	1	2	yes	—
928	#102	C₂³×C₆₇	1	1	yes	characteristic
929	#102	C₂³×C₆₇	1	2	yes	—
930	#102	C₂³×C₆₇	1	2	yes	—
931	#102	C₂³×C₆₇	1	1	yes	characteristic
932	#102	C₂³×C₆₇	1	1	yes	characteristic
933	#102	C₂³×C₆₇	1	1	yes	characteristic
934	#102	C₂³×C₆₇	1	2	yes	—
935	#102	C₂³×C₆₇	1	2	yes	—
936	#102	C₂³×C₆₇	1	2	yes	—
937	#102	C₂³×C₆₇	1	2	yes	—
938	#102	C₂³×C₆₇	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
940	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
941	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
942	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
943	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
945	#97	C₂³×C₆₇	1	2	yes	—
946	C₄×C₈	C₂³×C₆₇	1	2	yes	—
947	C₂⁴	—	2	1	no	—
948	C₂⁴	—	2	1	no	—
949	C₂⁴	—	2	2	no	—
950	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
951	#41	—	2	2	no	—
952	#41	—	2	2	no	—
953	#41	—	2	4	no	—
954	#41	—	2	4	no	—
955	#41	—	2	4	no	—
956	#41	—	2	2	no	—
957	#41	—	2	2	no	—
958	#41	—	4	2	no	—
959	#41	—	4	2	no	—
960	#41	—	4	2	no	—
961	#41	—	4	4	no	—
962	#41	—	4	4	no	—
963	#41	—	4	4	no	—
964	#41	—	8	4	no	—
965	C₂×Q₈	—	2	1	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
971	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₂×D₄	—	2	4	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	4	no	—
991	C₂×D₄	—	4	8	no	—
992	C₂×D₄	—	4	4	no	—
993	C₂×D₄	—	8	2	no	—
994	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₂×D₄	#41×C₆₇	1	4	yes	complemented
999	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1001	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	2	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	4	4	no	—
1018	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1019	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1023	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1025	SD₁₆	—	4	2	no	—
1026	SD₁₆	—	4	2	no	—
1027	SD₁₆	—	4	2	no	—
1028	D₈	—	2	4	no	—
1029	D₈	—	2	4	no	—
1030	D₈	—	4	2	no	—
1031	M₁₆	—	2	2	no	—
1032	M₁₆	—	2	2	no	—
1033	M₁₆	—	4	2	no	—
1034	M₁₆	—	4	2	no	—
1035	C₂×C₈	—	2	2	no	—
1036	C₂×C₈	—	2	2	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1041	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1044	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1059	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1060	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1063	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1093	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1094	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1095	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1096	C₄²	—	2	1	no	—
1097	C₄²	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	2	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	C₂⁴×C₆₇	1	2	yes	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	4	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	—	4	4	no	—
1111	C₂³	—	4	2	no	—
1112	C₂³	—	8	1	no	—
1113	C₂³	—	8	1	no	—
1114	C₂³	—	8	1	no	—
1115	C₂³	—	8	1	no	—
1116	C₂³	—	8	2	no	—
1117	C₂³	—	8	2	no	—
1118	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1119	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1120	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1122	Q₈	—	2	2	no	—
1123	Q₈	—	2	2	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	2	2	no	—
1126	Q₈	—	2	1	no	—
1127	Q₈	—	4	2	no	—
1128	Q₈	—	8	2	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	4	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	2	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	2	no	—
1145	D₄	—	4	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	2	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	1	no	—
1151	D₄	C₂×#41×C₆₇	1	4	yes	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	2	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	8	2	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	2	no	—
1179	C₂×C₄	—	8	2	no	—
1180	C₂×C₄	—	8	1	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1184	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1185	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1186	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1187	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1189	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1190	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1191	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1192	C₈	—	2	1	no	—
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	1	no	—
1196	C₈	—	2	2	no	—
1197	C₈	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	4	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	8	2	no	—
1219	C₂²	—	8	4	no	—
1220	C₂²	—	16	2	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	#546×C₆₇	1	2	yes	—
1223	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1224	C₄	—	2	2	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	2	no	—
1238	C₄	#546×C₆₇	1	2	yes	—
1239	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1240	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	4	4	no	—
1246	C₂	—	8	1	no	—
1247	C₂	—	8	2	no	—
1248	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1249	C₂	C₆₇×#3584	1	1	yes	characteristic
1250	C₂	C₆₇×#3585	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×#3485	C₂	semidirect
3. C₆₇×#3330	C₂	semidirect
4. C₆₇×#3322	C₂	semidirect
5. C₆₇×#3319	C₂	semidirect
6. C₆₇×#3307	C₂	semidirect
7. C₆₇×#3307	C₂	semidirect
8. C₆₇×#3306	C₂	semidirect
9. C₆₇×#3303	C₂	semidirect
10. C₆₇×#3297	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3091	C₂	semidirect
14. C₆₇×#3081	C₂	semidirect
15. C₆₇×#3057	C₂	semidirect
16. C₆₇×#3055	C₂	semidirect
17. C₆₇×#3042	C₂	semidirect
18. C₆₇×#3008	C₂	semidirect
19. C₂×#449×C₆₇	C₂	semidirect
20. C₆₇×#2948	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2897	C₂	semidirect
23. C₆₇×#2896	C₂	semidirect
27. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
31. #555×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
39. #547×C₆₇	C₂²	semidirect
43. #546×C₆₇	C₂²	semidirect
44. #546×C₆₇	C₂²	semidirect
45. #544×C₆₇	C₂²	semidirect
57. C₂×#121×C₆₇	C₂²	semidirect
60. #518×C₆₇	C₂²	semidirect
61. C₂×#117×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. #478×C₆₇	C₂²	semidirect
79. #478×C₆₇	C₂²	semidirect
80. #476×C₆₇	C₂²	semidirect
81. #474×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #468×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #466×C₆₇	C₂²	semidirect
87. #465×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
96. #449×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
99. #449×C₆₇	C₂²	semidirect
100. #447×C₆₇	C₂²	semidirect
101. #447×C₆₇	C₂²	semidirect
102. #442×C₆₇	C₂²	semidirect
103. #442×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
105. C₄×D₈×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. C₈×D₄×C₆₇	C₂²	semidirect
110. #428×C₆₇	C₂²	semidirect
111. #427×C₆₇	C₂²	semidirect
112. #427×C₆₇	C₂²	semidirect
113. #424×C₆₇	C₂²	semidirect
114. #419×C₆₇	C₂²	semidirect
115. #419×C₆₇	C₂²	semidirect
118. #418×C₆₇	C₂²	semidirect
119. #418×C₆₇	C₂²	semidirect
121. #417×C₆₇	C₂²	semidirect
122. #417×C₆₇	C₂²	semidirect
123. #417×C₆₇	C₂²	semidirect
126. #416×C₆₇	C₂²	semidirect
127. #416×C₆₇	C₂²	semidirect
128. #416×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
131. C₂×#102×C₆₇	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
134. #405×C₆₇	C₂²	semidirect
372. C₂×D₄×C₆₇	#41	semidirect
615. #61187	C₆₇	direct (N × H)
626. #3494	C₂×C₆₇	semidirect
627. #3485	C₂×C₆₇	semidirect
628. #3330	C₂×C₆₇	semidirect
629. #3322	C₂×C₆₇	semidirect
630. #3319	C₂×C₆₇	semidirect
631. #3307	C₂×C₆₇	semidirect
632. #3307	C₂×C₆₇	semidirect
633. #3306	C₂×C₆₇	semidirect
634. #3303	C₂×C₆₇	semidirect
635. #3297	C₂×C₆₇	semidirect
636. #3137	C₂×C₆₇	semidirect
637. #3097	C₂×C₆₇	semidirect
638. #3091	C₂×C₆₇	semidirect
639. #3081	C₂×C₆₇	semidirect
640. #3057	C₂×C₆₇	semidirect
641. #3055	C₂×C₆₇	semidirect
642. #3042	C₂×C₆₇	semidirect
643. #3008	C₂×C₆₇	semidirect
644. C₂×#449	C₂×C₆₇	semidirect
645. #2948	C₂×C₆₇	semidirect
646. #2933	C₂×C₆₇	semidirect
647. #2897	C₂×C₆₇	semidirect
648. #2896	C₂×C₆₇	semidirect
649. C₆₇	#61187	direct (N × H)
653. C₂²×SD₁₆	C₂²×C₆₇	semidirect
656. C₂²×M₁₆	C₂²×C₆₇	semidirect
657. #555	C₂²×C₆₇	semidirect
658. #553	C₂²×C₆₇	semidirect
659. #553	C₂²×C₆₇	semidirect
663. #547	C₂²×C₆₇	semidirect
664. #547	C₂²×C₆₇	semidirect
665. #547	C₂²×C₆₇	semidirect
669. #546	C₂²×C₆₇	semidirect
670. #546	C₂²×C₆₇	semidirect
671. #544	C₂²×C₆₇	semidirect
683. C₂×#121	C₂²×C₆₇	semidirect
686. #518	C₂²×C₆₇	semidirect
687. C₂×#117	C₂²×C₆₇	semidirect
688. #491	C₂²×C₆₇	semidirect
689. #489	C₂²×C₆₇	semidirect
690. #488	C₂²×C₆₇	semidirect
691. #487	C₂²×C₆₇	semidirect
692. #485	C₂²×C₆₇	semidirect
693. #485	C₂²×C₆₇	semidirect
694. #485	C₂²×C₆₇	semidirect
695. #485	C₂²×C₆₇	semidirect
696. #484	C₂²×C₆₇	semidirect
697. #484	C₂²×C₆₇	semidirect
698. #483	C₂²×C₆₇	semidirect
699. #483	C₂²×C₆₇	semidirect
700. #482	C₂²×C₆₇	semidirect
701. #482	C₂²×C₆₇	semidirect
702. #481	C₂²×C₆₇	semidirect
703. #480	C₂²×C₆₇	semidirect
704. #478	C₂²×C₆₇	semidirect
705. #478	C₂²×C₆₇	semidirect
706. #476	C₂²×C₆₇	semidirect
707. #474	C₂²×C₆₇	semidirect
708. #469	C₂²×C₆₇	semidirect
709. #468	C₂²×C₆₇	semidirect
710. #468	C₂²×C₆₇	semidirect
711. #468	C₂²×C₆₇	semidirect
712. #466	C₂²×C₆₇	semidirect
713. #465	C₂²×C₆₇	semidirect
714. #465	C₂²×C₆₇	semidirect
715. #465	C₂²×C₆₇	semidirect
716. #463	C₂²×C₆₇	semidirect
717. #463	C₂²×C₆₇	semidirect
718. #461	C₂²×C₆₇	semidirect
719. #461	C₂²×C₆₇	semidirect
720. #449	C₂²×C₆₇	semidirect
721. #449	C₂²×C₆₇	semidirect
722. #449	C₂²×C₆₇	semidirect
723. #449	C₂²×C₆₇	semidirect
724. #449	C₂²×C₆₇	semidirect
725. #449	C₂²×C₆₇	semidirect
726. #447	C₂²×C₆₇	semidirect
727. #447	C₂²×C₆₇	semidirect
728. #442	C₂²×C₆₇	semidirect
729. #442	C₂²×C₆₇	semidirect
730. C₄×D₈	C₂²×C₆₇	semidirect
731. C₄×D₈	C₂²×C₆₇	semidirect
732. #436	C₂²×C₆₇	semidirect
733. #435	C₂²×C₆₇	semidirect
734. #435	C₂²×C₆₇	semidirect
735. C₈×D₄	C₂²×C₆₇	semidirect
736. #428	C₂²×C₆₇	semidirect
737. #427	C₂²×C₆₇	semidirect
738. #427	C₂²×C₆₇	semidirect
739. #424	C₂²×C₆₇	semidirect
740. #419	C₂²×C₆₇	semidirect
741. #419	C₂²×C₆₇	semidirect
744. #418	C₂²×C₆₇	semidirect
745. #418	C₂²×C₆₇	semidirect
747. #417	C₂²×C₆₇	semidirect
748. #417	C₂²×C₆₇	semidirect
749. #417	C₂²×C₆₇	semidirect
752. #416	C₂²×C₆₇	semidirect
753. #416	C₂²×C₆₇	semidirect
754. #416	C₂²×C₆₇	semidirect
755. C₂×#103	C₂²×C₆₇	semidirect
757. C₂×#102	C₂²×C₆₇	semidirect
759. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
760. #405	C₂²×C₆₇	semidirect
998. C₂×D₄	#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×#3485	2
C₆₇×#3330	2
C₆₇×#3322	2
C₆₇×#3319	2
C₆₇×#3307	2
C₆₇×#3306	2
C₆₇×#3303	2
C₆₇×#3297	2
C₆₇×#3137	2
C₆₇×#3097	2
C₆₇×#3091	2
C₆₇×#3081	2
C₆₇×#3057	2
C₆₇×#3055	2
C₆₇×#3042	2
C₆₇×#3008	2
C₂×#449×C₆₇	2
C₆₇×#2948	2
C₆₇×#2933	2
C₆₇×#2897	2
C₆₇×#2896	2
#61187	67

Subgroups — C67×#61187 #30740438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61187 #30740438