Subgroups — C₆₇×#61581 #30740832

Order 17152.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3323	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3322	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3273	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3192	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3105	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3003	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
21	#553×C₆₇	—	2	2	no	—
22	#553×C₆₇	C₂²	1	2	yes	complemented
23	#552×C₆₇	C₂²	1	2	yes	complemented
24	#551×C₆₇	—	2	2	no	—
25	#548×C₆₇	C₂²	1	2	yes	complemented
26	#546×C₆₇	—	2	2	no	—
27	#546×C₆₇	—	2	2	no	—
28	#546×C₆₇	C₂²	1	4	yes	—
29	#546×C₆₇	C₂²	1	4	yes	complemented
30	#546×C₆₇	C₂²	1	2	yes	complemented
31	#539×C₆₇	—	2	1	no	—
32	#538×C₆₇	—	2	1	no	—
33	#534×C₆₇	—	2	1	no	—
34	#529×C₆₇	C₂²	1	2	yes	complemented
35	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#525×C₆₇	C₂²	1	2	yes	—
37	C₂×#123×C₆₇	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#121×C₆₇	—	2	1	no	—
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#120×C₆₇	—	2	1	no	—
44	#518×C₆₇	—	2	1	no	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
48	#495×C₆₇	C₂²	1	4	yes	complemented
49	#488×C₆₇	C₂²	1	4	yes	complemented
50	#485×C₆₇	C₂²	1	4	yes	complemented
51	#484×C₆₇	C₂²	1	2	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	complemented
53	#481×C₆₇	C₂²	1	2	yes	complemented
54	#480×C₆₇	C₂²	1	2	yes	complemented
55	#478×C₆₇	C₂²	1	4	yes	complemented
56	#470×C₆₇	C₂²	1	4	yes	complemented
57	#469×C₆₇	C₂²	1	4	yes	complemented
58	#468×C₆₇	C₂²	1	4	yes	complemented
59	#468×C₆₇	C₂²	1	4	yes	complemented
60	#464×C₆₇	C₂²	1	4	yes	complemented
61	#463×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#452×C₆₇	C₂²	1	4	yes	complemented
64	#452×C₆₇	C₂²	1	4	yes	complemented
65	#451×C₆₇	C₂²	1	2	yes	complemented
66	#450×C₆₇	C₂²	1	4	yes	complemented
67	#450×C₆₇	C₂²	1	2	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#448×C₆₇	C₂²	1	2	yes	complemented
71	#448×C₆₇	C₂²	1	2	yes	complemented
72	#447×C₆₇	C₂²	1	2	yes	—
73	#447×C₆₇	C₂²	1	2	yes	—
74	#447×C₆₇	C₂²	1	4	yes	complemented
75	#447×C₆₇	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
77	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
78	#436×C₆₇	C₂²	1	4	yes	complemented
79	#436×C₆₇	C₂²	1	4	yes	complemented
80	#431×C₆₇	C₂²	1	2	yes	complemented
81	#418×C₆₇	C₂²	1	4	yes	complemented
82	#417×C₆₇	C₂²	1	2	yes	complemented
83	#417×C₆₇	C₂²	1	2	yes	complemented
84	#407×C₆₇	C₂²	1	2	yes	complemented
85	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂⁵×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	—	2	1	no	—
90	C₂×#41×C₆₇	—	4	4	no	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂×#41×C₆₇	C₂³	1	2	yes	—
94	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
96	C₂²×D₄×C₆₇	—	2	1	no	—
97	C₂²×D₄×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	1	no	—
99	C₂²×D₄×C₆₇	—	2	1	no	—
100	C₂²×D₄×C₆₇	—	2	2	no	—
101	C₂²×D₄×C₆₇	—	4	4	no	—
102	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	—	2	1	no	—
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
111	#137×C₆₇	—	4	4	no	—
112	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
113	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
114	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	complemented
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
118	C₂×D₈×C₆₇	C₂³	1	4	yes	—
119	C₂×D₈×C₆₇	C₂³	1	4	yes	—
120	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
122	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
123	#126×C₆₇	—	2	2	no	—
124	#126×C₆₇	—	2	2	no	—
125	#126×C₆₇	—	2	2	no	—
126	#125×C₆₇	—	2	2	no	—
127	#125×C₆₇	C₂³	1	2	yes	complemented
128	#124×C₆₇	—	2	2	no	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	C₂³	1	4	yes	—
131	#124×C₆₇	C₂³	1	2	yes	complemented
132	#123×C₆₇	—	2	2	no	—
133	#123×C₆₇	—	2	2	no	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	4	no	—
136	#123×C₆₇	—	2	4	no	—
137	#123×C₆₇	—	2	2	no	—
138	#123×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	—	2	1	no	—
150	#121×C₆₇	—	2	1	no	—
151	#121×C₆₇	—	2	1	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	4	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	—	2	2	no	—
156	#121×C₆₇	C₂³	1	2	yes	—
157	#121×C₆₇	C₂³	1	2	yes	—
158	#121×C₆₇	C₂³	1	2	yes	—
159	#121×C₆₇	C₂³	1	2	yes	—
160	#121×C₆₇	C₂³	1	2	yes	complemented
161	#120×C₆₇	—	2	2	no	—
162	#120×C₆₇	—	2	4	no	—
163	#120×C₆₇	—	2	4	no	—
164	#120×C₆₇	—	2	2	no	—
165	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	D₄	1	2	yes	—
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	C₂³	1	4	yes	—
175	C₄×D₄×C₆₇	C₂³	1	2	yes	—
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
178	#117×C₆₇	—	2	2	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
187	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	#107×C₆₇	C₂³	1	4	yes	complemented
201	#106×C₆₇	C₂³	1	4	yes	complemented
202	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
203	#103×C₆₇	C₂³	1	4	yes	complemented
204	#103×C₆₇	C₂³	1	4	yes	complemented
205	#103×C₆₇	C₂³	1	4	yes	complemented
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	4	yes	complemented
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
216	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	—	2	4	no	—
220	C₂⁴×C₆₇	—	2	1	no	—
221	C₂⁴×C₆₇	—	4	4	no	—
222	C₂⁴×C₆₇	—	4	4	no	—
223	C₂⁴×C₆₇	—	8	2	no	—
224	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
226	#41×C₆₇	—	2	4	no	—
227	#41×C₆₇	—	2	4	no	—
228	#41×C₆₇	—	4	2	no	—
229	#41×C₆₇	—	4	2	no	—
230	#41×C₆₇	—	4	4	no	—
231	#41×C₆₇	—	4	4	no	—
232	#41×C₆₇	—	4	4	no	—
233	C₂×Q₈×C₆₇	—	2	1	no	—
234	C₂×Q₈×C₆₇	—	2	1	no	—
235	C₂×Q₈×C₆₇	—	4	2	no	—
236	C₂×Q₈×C₆₇	—	4	2	no	—
237	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	8	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	1	no	—
252	C₂×D₄×C₆₇	—	2	1	no	—
253	C₂×D₄×C₆₇	—	4	4	no	—
254	C₂×D₄×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	—	4	8	no	—
258	C₂×D₄×C₆₇	—	4	4	no	—
259	C₂×D₄×C₆₇	—	4	4	no	—
260	C₂×D₄×C₆₇	—	4	4	no	—
261	C₂×D₄×C₆₇	—	8	2	no	—
262	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	1	no	—
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	1	no	—
271	C₂²×C₄×C₆₇	—	2	1	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	4	no	—
280	C₂²×C₄×C₆₇	—	8	2	no	—
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	Q₁₆×C₆₇	—	4	4	no	—
293	SD₁₆×C₆₇	—	2	8	no	—
294	SD₁₆×C₆₇	—	4	4	no	—
295	SD₁₆×C₆₇	—	4	4	no	—
296	D₈×C₆₇	—	2	8	no	—
297	D₈×C₆₇	—	4	4	no	—
298	M₁₆×C₆₇	—	4	4	no	—
299	M₁₆×C₆₇	—	4	2	no	—
300	M₁₆×C₆₇	—	4	2	no	—
301	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
302	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	1	no	—
307	C₄⋊C₄×C₆₇	—	2	1	no	—
308	C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	2	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	—	2	2	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	—	2	4	no	—
331	C₂²⋊C₄×C₆₇	—	2	2	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	—	2	2	no	—
334	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₄²×C₆₇	—	2	2	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	C₂×D₄	1	2	yes	—
341	C₄²×C₆₇	C₂⁴	1	2	yes	—
342	C₂³×C₆₇	—	2	4	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	4	1	no	—
349	C₂³×C₆₇	—	4	1	no	—
350	C₂³×C₆₇	—	4	1	no	—
351	C₂³×C₆₇	—	4	1	no	—
352	C₂³×C₆₇	—	4	8	no	—
353	C₂³×C₆₇	—	4	2	no	—
354	C₂³×C₆₇	—	4	2	no	—
355	C₂³×C₆₇	—	4	2	no	—
356	C₂³×C₆₇	—	4	8	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	4	2	no	—
359	C₂³×C₆₇	—	4	2	no	—
360	C₂³×C₆₇	—	8	4	no	—
361	C₂³×C₆₇	—	8	1	no	—
362	C₂³×C₆₇	—	8	1	no	—
363	C₂³×C₆₇	—	8	16	no	—
364	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
365	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₆₇	—	2	4	no	—
369	Q₈×C₆₇	—	2	2	no	—
370	Q₈×C₆₇	—	2	2	no	—
371	Q₈×C₆₇	—	4	2	no	—
372	Q₈×C₆₇	—	8	1	no	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	2	4	no	—
376	D₄×C₆₇	—	2	4	no	—
377	D₄×C₆₇	—	4	2	no	—
378	D₄×C₆₇	—	4	2	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	2	no	—
381	D₄×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	4	4	no	—
383	D₄×C₆₇	—	4	4	no	—
384	D₄×C₆₇	—	4	4	no	—
385	D₄×C₆₇	—	8	1	no	—
386	D₄×C₆₇	—	8	2	no	—
387	D₄×C₆₇	—	8	2	no	—
388	D₄×C₆₇	—	8	2	no	—
389	D₄×C₆₇	—	8	2	no	—
390	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	4	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	4	1	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	4	1	no	—
404	C₂×C₄×C₆₇	—	4	1	no	—
405	C₂×C₄×C₆₇	—	4	1	no	—
406	C₂×C₄×C₆₇	—	4	1	no	—
407	C₂×C₄×C₆₇	—	4	4	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	2	no	—
410	C₂×C₄×C₆₇	—	4	2	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	—	8	2	no	—
413	C₂×C₄×C₆₇	—	8	4	no	—
414	C₂×C₄×C₆₇	—	8	2	no	—
415	C₂×C₄×C₆₇	—	8	1	no	—
416	C₂×C₄×C₆₇	—	8	1	no	—
417	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
424	C₈×C₆₇	—	2	4	no	—
425	C₈×C₆₇	—	2	4	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	1	no	—
428	C₂²×C₆₇	—	2	1	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	2	2	no	—
431	C₂²×C₆₇	—	2	1	no	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	4	no	—
435	C₂²×C₆₇	—	2	1	no	—
436	C₂²×C₆₇	—	2	1	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	4	8	no	—
439	C₂²×C₆₇	—	4	4	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	2	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	8	2	no	—
449	C₂²×C₆₇	—	8	4	no	—
450	C₂²×C₆₇	—	8	16	no	—
451	C₂²×C₆₇	—	16	2	no	—
452	C₂²×C₆₇	#575	1	2	yes	—
453	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	1	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	4	2	no	—
461	C₄×C₆₇	—	4	2	no	—
462	C₄×C₆₇	—	4	2	no	—
463	C₄×C₆₇	—	4	2	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
466	#61581	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂×C₆₇	—	2	2	no	—
468	C₂×C₆₇	—	4	2	no	—
469	C₂×C₆₇	—	4	1	no	—
470	C₂×C₆₇	—	4	1	no	—
471	C₂×C₆₇	—	4	4	no	—
472	C₂×C₆₇	—	8	2	no	—
473	C₂×C₆₇	—	8	2	no	—
474	C₂×C₆₇	#3484	1	1	yes	characteristic
475	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
476	C₂×C₆₇	#3585	1	1	yes	characteristic
477	#3505	C₂×C₆₇	1	1	yes	characteristic, complemented
478	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#3323	C₂×C₆₇	1	4	yes	complemented
480	#3322	C₂×C₆₇	1	4	yes	complemented
481	#3275	C₂×C₆₇	1	4	yes	complemented
482	#3273	C₂×C₆₇	1	4	yes	complemented
483	#3211	C₂×C₆₇	1	2	yes	complemented
484	#3196	C₂×C₆₇	1	2	yes	complemented
485	#3193	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#3192	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3105	C₂×C₆₇	1	2	yes	complemented
488	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#3003	C₂×C₆₇	1	2	yes	complemented
491	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
492	C₆₇	#61581	1	1	yes	characteristic, direct product factor, Sylow
493	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
494	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
495	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
496	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
497	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
498	#553	—	2	2	no	—
499	#553	C₂²×C₆₇	1	2	yes	complemented
500	#552	C₂²×C₆₇	1	2	yes	complemented
501	#551	—	2	2	no	—
502	#548	C₂²×C₆₇	1	2	yes	complemented
503	#546	—	2	2	no	—
504	#546	—	2	2	no	—
505	#546	C₂²×C₆₇	1	4	yes	—
506	#546	C₂²×C₆₇	1	4	yes	complemented
507	#546	C₂²×C₆₇	1	2	yes	complemented
508	#539	—	2	1	no	—
509	#538	—	2	1	no	—
510	#534	—	2	1	no	—
511	#529	C₂²×C₆₇	1	2	yes	complemented
512	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
513	#525	C₂²×C₆₇	1	2	yes	—
514	C₂×#123	—	2	1	no	—
515	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
516	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
517	C₂×#121	—	2	1	no	—
518	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	C₂×#120	—	2	1	no	—
521	#518	—	2	1	no	—
522	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	C₂²×C₂²⋊C₄	—	2	1	no	—
525	#495	C₂²×C₆₇	1	4	yes	complemented
526	#488	C₂²×C₆₇	1	4	yes	complemented
527	#485	C₂²×C₆₇	1	4	yes	complemented
528	#484	C₂²×C₆₇	1	2	yes	complemented
529	#481	C₂²×C₆₇	1	2	yes	complemented
530	#481	C₂²×C₆₇	1	2	yes	complemented
531	#480	C₂²×C₆₇	1	2	yes	complemented
532	#478	C₂²×C₆₇	1	4	yes	complemented
533	#470	C₂²×C₆₇	1	4	yes	complemented
534	#469	C₂²×C₆₇	1	4	yes	complemented
535	#468	C₂²×C₆₇	1	4	yes	complemented
536	#468	C₂²×C₆₇	1	4	yes	complemented
537	#464	C₂²×C₆₇	1	4	yes	complemented
538	#463	C₂²×C₆₇	1	4	yes	complemented
539	#463	C₂²×C₆₇	1	4	yes	complemented
540	#452	C₂²×C₆₇	1	4	yes	complemented
541	#452	C₂²×C₆₇	1	4	yes	complemented
542	#451	C₂²×C₆₇	1	2	yes	complemented
543	#450	C₂²×C₆₇	1	2	yes	complemented
544	#450	C₂²×C₆₇	1	2	yes	complemented
545	#450	C₂²×C₆₇	1	4	yes	complemented
546	#449	C₂²×C₆₇	1	4	yes	complemented
547	#448	C₂²×C₆₇	1	2	yes	complemented
548	#448	C₂²×C₆₇	1	2	yes	complemented
549	#447	C₂²×C₆₇	1	2	yes	—
550	#447	C₂²×C₆₇	1	2	yes	—
551	#447	C₂²×C₆₇	1	4	yes	complemented
552	#447	C₂²×C₆₇	1	2	yes	complemented
553	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
554	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
555	#436	C₂²×C₆₇	1	4	yes	complemented
556	#436	C₂²×C₆₇	1	4	yes	complemented
557	#431	C₂²×C₆₇	1	2	yes	complemented
558	#418	C₂²×C₆₇	1	4	yes	complemented
559	#417	C₂²×C₆₇	1	2	yes	complemented
560	#417	C₂²×C₆₇	1	2	yes	complemented
561	#407	C₂²×C₆₇	1	2	yes	complemented
562	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	C₂⁵	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	4	4	no	—
568	C₂×#41	C₂³×C₆₇	1	2	yes	—
569	C₂×#41	C₂³×C₆₇	1	2	yes	—
570	C₂×#41	C₂³×C₆₇	1	2	yes	—
571	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	4	4	no	—
579	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
582	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
584	C₂³×C₄	—	2	1	no	—
585	C₂³×C₄	—	2	1	no	—
586	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
588	#137	—	4	4	no	—
589	AGL(1,ℤ/8)	—	4	4	no	—
590	AGL(1,ℤ/8)	—	4	8	no	—
591	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	complemented
592	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
595	C₂×D₈	C₂³×C₆₇	1	4	yes	—
596	C₂×D₈	C₂³×C₆₇	1	4	yes	—
597	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
598	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
599	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	C₂³×C₆₇	1	2	yes	complemented
605	#124	—	2	2	no	—
606	#124	—	2	2	no	—
607	#124	C₂³×C₆₇	1	4	yes	—
608	#124	C₂³×C₆₇	1	2	yes	complemented
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	C₂²⋊Q₈	—	2	1	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
621	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
622	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	1	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	2	no	—
633	#121	C₂³×C₆₇	1	2	yes	—
634	#121	C₂³×C₆₇	1	2	yes	—
635	#121	C₂³×C₆₇	1	2	yes	—
636	#121	C₂³×C₆₇	1	2	yes	—
637	#121	C₂³×C₆₇	1	2	yes	complemented
638	#120	—	2	2	no	—
639	#120	—	2	4	no	—
640	#120	—	2	4	no	—
641	#120	—	2	2	no	—
642	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	D₄×C₆₇	1	2	yes	—
650	C₄×D₄	D₄×C₆₇	1	2	yes	—
651	C₄×D₄	C₂³×C₆₇	1	4	yes	—
652	C₄×D₄	C₂³×C₆₇	1	2	yes	—
653	C₄×D₄	C₂³×C₆₇	1	2	yes	—
654	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	4	no	—
672	C₂×C₂²⋊C₄	—	2	4	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	#107	C₂³×C₆₇	1	4	yes	complemented
678	#106	C₂³×C₆₇	1	4	yes	complemented
679	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
680	#103	C₂³×C₆₇	1	4	yes	complemented
681	#103	C₂³×C₆₇	1	4	yes	complemented
682	#103	C₂³×C₆₇	1	4	yes	complemented
683	#102	C₂³×C₆₇	1	4	yes	—
684	#102	C₂³×C₆₇	1	4	yes	—
685	#102	C₂³×C₆₇	1	4	yes	—
686	#102	C₂³×C₆₇	1	4	yes	—
687	#102	C₂³×C₆₇	1	4	yes	complemented
688	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
691	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
692	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
693	C₄×C₈	C₂³×C₆₇	1	4	yes	complemented
694	C₂⁴	—	2	1	no	—
695	C₂⁴	—	2	1	no	—
696	C₂⁴	—	2	4	no	—
697	C₂⁴	—	2	1	no	—
698	C₂⁴	—	4	4	no	—
699	C₂⁴	—	4	4	no	—
700	C₂⁴	—	8	2	no	—
701	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
702	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
703	#41	—	2	4	no	—
704	#41	—	2	4	no	—
705	#41	—	4	2	no	—
706	#41	—	4	2	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	8	2	no	—
739	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
740	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	8	2	no	—
758	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	Q₁₆	—	4	4	no	—
770	SD₁₆	—	2	8	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	2	8	no	—
774	D₈	—	4	4	no	—
775	M₁₆	—	4	4	no	—
776	M₁₆	—	4	2	no	—
777	M₁₆	—	4	2	no	—
778	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
779	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
812	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	C₂×D₄×C₆₇	1	2	yes	—
818	C₄²	C₂⁴×C₆₇	1	2	yes	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	8	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	8	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	8	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	1	no	—
840	C₂³	—	8	16	no	—
841	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
842	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
843	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	1	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	1	no	—
893	C₂×C₄	—	8	1	no	—
894	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
900	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
901	C₈	—	2	4	no	—
902	C₈	—	2	4	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	4	no	—
916	C₂²	—	4	8	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	2	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	16	2	no	—
929	C₂²	#575×C₆₇	1	2	yes	—
930	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
943	C₂	—	2	2	no	—
944	C₂	—	4	2	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	4	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₆₇×#3484	1	1	yes	characteristic
951	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
952	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3505	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3323	C₂	semidirect
4. C₆₇×#3322	C₂	semidirect
5. C₆₇×#3275	C₂	semidirect
6. C₆₇×#3273	C₂	semidirect
7. C₆₇×#3211	C₂	semidirect
8. C₆₇×#3196	C₂	semidirect
9. C₆₇×#3193	C₂	semidirect
10. C₆₇×#3192	C₂	semidirect
11. C₆₇×#3105	C₂	semidirect
12. C₆₇×#3007	C₂	semidirect
13. C₆₇×#3006	C₂	semidirect
14. C₆₇×#3003	C₂	semidirect
15. C₆₇×#2975	C₂	semidirect
17. C₂³×D₄×C₆₇	C₂²	semidirect
18. C₂×#137×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
22. #553×C₆₇	C₂²	semidirect
23. #552×C₆₇	C₂²	semidirect
25. #548×C₆₇	C₂²	semidirect
29. #546×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
34. #529×C₆₇	C₂²	semidirect
35. C₂×#124×C₆₇	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
39. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
42. C₂×#121×C₆₇	C₂²	semidirect
46. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. #495×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #484×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
53. #481×C₆₇	C₂²	semidirect
54. #480×C₆₇	C₂²	semidirect
55. #478×C₆₇	C₂²	semidirect
56. #470×C₆₇	C₂²	semidirect
57. #469×C₆₇	C₂²	semidirect
58. #468×C₆₇	C₂²	semidirect
59. #468×C₆₇	C₂²	semidirect
60. #464×C₆₇	C₂²	semidirect
61. #463×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #452×C₆₇	C₂²	semidirect
64. #452×C₆₇	C₂²	semidirect
65. #451×C₆₇	C₂²	semidirect
66. #450×C₆₇	C₂²	semidirect
67. #450×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #448×C₆₇	C₂²	semidirect
71. #448×C₆₇	C₂²	semidirect
74. #447×C₆₇	C₂²	semidirect
75. #447×C₆₇	C₂²	semidirect
76. C₄×SD₁₆×C₆₇	C₂²	semidirect
77. C₄×D₈×C₆₇	C₂²	semidirect
78. #436×C₆₇	C₂²	semidirect
79. #436×C₆₇	C₂²	semidirect
80. #431×C₆₇	C₂²	semidirect
81. #418×C₆₇	C₂²	semidirect
82. #417×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
84. #407×C₆₇	C₂²	semidirect
85. #407×C₆₇	C₂²	semidirect
86. #407×C₆₇	C₂²	semidirect
95. C₂²×Q₈×C₆₇	C₂³	semidirect
106. C₂²×D₄×C₆₇	C₂³	semidirect
114. C₂×Q₁₆×C₆₇	C₂³	semidirect
117. C₂×SD₁₆×C₆₇	C₂³	semidirect
121. C₂×M₁₆×C₆₇	C₂³	semidirect
122. C₂×M₁₆×C₆₇	C₂³	semidirect
127. #125×C₆₇	C₂³	semidirect
131. #124×C₆₇	C₂³	semidirect
146. C₂²⋊Q₈×C₆₇	C₂³	semidirect
160. #121×C₆₇	C₂³	semidirect
165. C₄×Q₈×C₆₇	C₂³	semidirect
177. C₄×D₄×C₆₇	C₂³	semidirect
185. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
186. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
200. #107×C₆₇	C₂³	semidirect
201. #106×C₆₇	C₂³	semidirect
202. C₄⋊C₈×C₆₇	C₂³	semidirect
203. #103×C₆₇	C₂³	semidirect
204. #103×C₆₇	C₂³	semidirect
205. #103×C₆₇	C₂³	semidirect
210. #102×C₆₇	C₂³	semidirect
214. C₂²⋊C₈×C₆₇	C₂³	semidirect
215. C₂²⋊C₈×C₆₇	C₂³	semidirect
216. C₄×C₈×C₆₇	C₂³	semidirect
466. #61581	C₆₇	direct (N × H)
477. #3505	C₂×C₆₇	semidirect
478. C₂×#546	C₂×C₆₇	semidirect
479. #3323	C₂×C₆₇	semidirect
480. #3322	C₂×C₆₇	semidirect
481. #3275	C₂×C₆₇	semidirect
482. #3273	C₂×C₆₇	semidirect
483. #3211	C₂×C₆₇	semidirect
484. #3196	C₂×C₆₇	semidirect
485. #3193	C₂×C₆₇	semidirect
486. #3192	C₂×C₆₇	semidirect
487. #3105	C₂×C₆₇	semidirect
488. #3007	C₂×C₆₇	semidirect
489. #3006	C₂×C₆₇	semidirect
490. #3003	C₂×C₆₇	semidirect
491. #2975	C₂×C₆₇	semidirect
492. C₆₇	#61581	direct (N × H)
494. C₂³×D₄	C₂²×C₆₇	semidirect
495. C₂×#137	C₂²×C₆₇	semidirect
496. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
497. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
499. #553	C₂²×C₆₇	semidirect
500. #552	C₂²×C₆₇	semidirect
502. #548	C₂²×C₆₇	semidirect
506. #546	C₂²×C₆₇	semidirect
507. #546	C₂²×C₆₇	semidirect
511. #529	C₂²×C₆₇	semidirect
512. C₂×#124	C₂²×C₆₇	semidirect
515. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
516. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
519. C₂×#121	C₂²×C₆₇	semidirect
523. C₂×C₄×D₄	C₂²×C₆₇	semidirect
525. #495	C₂²×C₆₇	semidirect
526. #488	C₂²×C₆₇	semidirect
527. #485	C₂²×C₆₇	semidirect
528. #484	C₂²×C₆₇	semidirect
529. #481	C₂²×C₆₇	semidirect
530. #481	C₂²×C₆₇	semidirect
531. #480	C₂²×C₆₇	semidirect
532. #478	C₂²×C₆₇	semidirect
533. #470	C₂²×C₆₇	semidirect
534. #469	C₂²×C₆₇	semidirect
535. #468	C₂²×C₆₇	semidirect
536. #468	C₂²×C₆₇	semidirect
537. #464	C₂²×C₆₇	semidirect
538. #463	C₂²×C₆₇	semidirect
539. #463	C₂²×C₆₇	semidirect
540. #452	C₂²×C₆₇	semidirect
541. #452	C₂²×C₆₇	semidirect
542. #451	C₂²×C₆₇	semidirect
543. #450	C₂²×C₆₇	semidirect
544. #450	C₂²×C₆₇	semidirect
545. #450	C₂²×C₆₇	semidirect
546. #449	C₂²×C₆₇	semidirect
547. #448	C₂²×C₆₇	semidirect
548. #448	C₂²×C₆₇	semidirect
551. #447	C₂²×C₆₇	semidirect
552. #447	C₂²×C₆₇	semidirect
553. C₄×SD₁₆	C₂²×C₆₇	semidirect
554. C₄×D₈	C₂²×C₆₇	semidirect
555. #436	C₂²×C₆₇	semidirect
556. #436	C₂²×C₆₇	semidirect
557. #431	C₂²×C₆₇	semidirect
558. #418	C₂²×C₆₇	semidirect
559. #417	C₂²×C₆₇	semidirect
560. #417	C₂²×C₆₇	semidirect
561. #407	C₂²×C₆₇	semidirect
562. #407	C₂²×C₆₇	semidirect
563. #407	C₂²×C₆₇	semidirect
572. C₂²×Q₈	C₂³×C₆₇	semidirect
583. C₂²×D₄	C₂³×C₆₇	semidirect
591. C₂×Q₁₆	C₂³×C₆₇	semidirect
594. C₂×SD₁₆	C₂³×C₆₇	semidirect
598. C₂×M₁₆	C₂³×C₆₇	semidirect
599. C₂×M₁₆	C₂³×C₆₇	semidirect
604. #125	C₂³×C₆₇	semidirect
608. #124	C₂³×C₆₇	semidirect
623. C₂²⋊Q₈	C₂³×C₆₇	semidirect
637. #121	C₂³×C₆₇	semidirect
642. C₄×Q₈	C₂³×C₆₇	semidirect
654. C₄×D₄	C₂³×C₆₇	semidirect
662. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
663. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
677. #107	C₂³×C₆₇	semidirect
678. #106	C₂³×C₆₇	semidirect
679. C₄⋊C₈	C₂³×C₆₇	semidirect
680. #103	C₂³×C₆₇	semidirect
681. #103	C₂³×C₆₇	semidirect
682. #103	C₂³×C₆₇	semidirect
687. #102	C₂³×C₆₇	semidirect
691. C₂²⋊C₈	C₂³×C₆₇	semidirect
692. C₂²⋊C₈	C₂³×C₆₇	semidirect
693. C₄×C₈	C₂³×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3505	2
C₂×#546×C₆₇	2
C₆₇×#3323	2
C₆₇×#3322	2
C₆₇×#3275	2
C₆₇×#3273	2
C₆₇×#3211	2
C₆₇×#3196	2
C₆₇×#3193	2
C₆₇×#3192	2
C₆₇×#3105	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#3003	2
C₆₇×#2975	2
#61581	67

Subgroups — C67×#61581 #30740832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61581 #30740832