Subgroups — C₆₇×#61576 #30740827

Order 17152.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3311	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3003	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2973	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
18	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
19	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
20	#559×C₆₇	—	2	2	no	—
21	#556×C₆₇	C₂²	1	2	yes	complemented
22	#555×C₆₇	C₂²	1	2	yes	complemented
23	#553×C₆₇	—	2	2	no	—
24	#550×C₆₇	C₂²	1	2	yes	complemented
25	#547×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	—
30	#538×C₆₇	—	2	1	no	—
31	#538×C₆₇	—	2	1	no	—
32	#535×C₆₇	—	2	1	no	—
33	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
36	#525×C₆₇	C₂²	1	2	yes	—
37	#525×C₆₇	C₂²	1	2	yes	complemented
38	C₂×#123×C₆₇	—	2	1	no	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₆₇	—	2	1	no	—
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#120×C₆₇	—	2	1	no	—
43	#520×C₆₇	—	2	1	no	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
47	#497×C₆₇	C₂²	1	2	yes	complemented
48	#496×C₆₇	C₂²	1	2	yes	complemented
49	#489×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#485×C₆₇	C₂²	1	4	yes	complemented
52	#484×C₆₇	C₂²	1	2	yes	complemented
53	#482×C₆₇	C₂²	1	4	yes	complemented
54	#481×C₆₇	C₂²	1	2	yes	complemented
55	#476×C₆₇	C₂²	1	2	yes	complemented
56	#474×C₆₇	C₂²	1	2	yes	complemented
57	#470×C₆₇	C₂²	1	4	yes	complemented
58	#468×C₆₇	C₂²	1	4	yes	complemented
59	#466×C₆₇	C₂²	1	4	yes	complemented
60	#465×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#461×C₆₇	C₂²	1	2	yes	complemented
64	#459×C₆₇	C₂²	1	2	yes	complemented
65	#452×C₆₇	C₂²	1	4	yes	complemented
66	#452×C₆₇	C₂²	1	4	yes	complemented
67	#451×C₆₇	C₂²	1	2	yes	complemented
68	#450×C₆₇	C₂²	1	2	yes	—
69	#450×C₆₇	C₂²	1	2	yes	—
70	#450×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#449×C₆₇	C₂²	1	4	yes	complemented
73	#448×C₆₇	C₂²	1	2	yes	complemented
74	#447×C₆₇	C₂²	1	2	yes	—
75	#447×C₆₇	C₂²	1	2	yes	—
76	#447×C₆₇	C₂²	1	4	yes	complemented
77	#442×C₆₇	C₂²	1	4	yes	complemented
78	#440×C₆₇	C₂²	1	4	yes	complemented
79	#435×C₆₇	C₂²	1	4	yes	complemented
80	#435×C₆₇	C₂²	1	4	yes	complemented
81	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#418×C₆₇	C₂²	1	4	yes	complemented
84	#416×C₆₇	C₂²	1	4	yes	complemented
85	#407×C₆₇	C₂²	1	2	yes	—
86	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
87	C₂⁵×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	—	2	2	no	—
90	C₂×#41×C₆₇	—	4	4	no	—
91	C₂×#41×C₆₇	C₂³	1	4	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
94	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₆₇	—	2	1	no	—
96	C₂²×D₄×C₆₇	—	2	1	no	—
97	C₂²×D₄×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	4	4	no	—
100	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
103	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	—	2	1	no	—
105	C₂³×C₄×C₆₇	—	2	1	no	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
109	#135×C₆₇	—	4	8	no	—
110	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	complemented
111	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
114	C₂×D₈×C₆₇	C₂³	1	4	yes	—
115	C₂×D₈×C₆₇	C₂³	1	4	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
118	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
119	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
120	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
121	#127×C₆₇	—	2	2	no	—
122	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
123	#126×C₆₇	—	2	2	no	—
124	#126×C₆₇	—	2	2	no	—
125	#125×C₆₇	—	2	1	no	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	—	2	2	no	—
128	#124×C₆₇	—	2	2	no	—
129	#124×C₆₇	—	2	1	no	—
130	#124×C₆₇	—	2	1	no	—
131	#124×C₆₇	—	2	1	no	—
132	#124×C₆₇	C₂³	1	2	yes	—
133	#124×C₆₇	C₂³	1	2	yes	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	2	no	—
136	#123×C₆₇	—	2	4	no	—
137	#123×C₆₇	—	2	4	no	—
138	#123×C₆₇	—	2	2	no	—
139	#123×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
143	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	—	2	1	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	4	no	—
152	#121×C₆₇	—	2	2	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	C₂³	1	2	yes	—
155	#121×C₆₇	C₂³	1	4	yes	—
156	#121×C₆₇	C₂³	1	2	yes	—
157	#121×C₆₇	C₂³	1	2	yes	complemented
158	#120×C₆₇	—	2	2	no	—
159	#120×C₆₇	—	2	2	no	—
160	#120×C₆₇	—	2	4	no	—
161	#120×C₆₇	—	2	4	no	—
162	C₄×Q₈×C₆₇	—	2	2	no	—
163	C₄×Q₈×C₆₇	—	2	1	no	—
164	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
165	C₄×D₄×C₆₇	—	2	2	no	—
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	1	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	D₄	1	2	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	—
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
180	#117×C₆₇	—	2	1	no	—
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	C₂³	1	2	yes	—
183	#117×C₆₇	C₂³	1	2	yes	complemented
184	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	4	no	—
194	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	#107×C₆₇	C₂³	1	4	yes	complemented
199	#106×C₆₇	C₂³	1	4	yes	complemented
200	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
201	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
202	#103×C₆₇	C₂³	1	4	yes	complemented
203	#103×C₆₇	C₂³	1	4	yes	complemented
204	#103×C₆₇	C₂³	1	4	yes	complemented
205	#102×C₆₇	C₂³	1	4	yes	—
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	complemented
210	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
214	#97×C₆₇	C₂³	1	2	yes	complemented
215	#97×C₆₇	C₂³	1	2	yes	complemented
216	C₂⁴×C₆₇	—	2	1	no	—
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	4	no	—
219	C₂⁴×C₆₇	—	4	4	no	—
220	C₂⁴×C₆₇	—	4	4	no	—
221	C₂⁴×C₆₇	—	8	2	no	—
222	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
224	#41×C₆₇	—	2	8	no	—
225	#41×C₆₇	—	4	4	no	—
226	#41×C₆₇	—	4	4	no	—
227	#41×C₆₇	—	4	4	no	—
228	#41×C₆₇	—	4	4	no	—
229	#41×C₆₇	—	4	8	no	—
230	C₂×Q₈×C₆₇	—	2	1	no	—
231	C₂×Q₈×C₆₇	—	2	1	no	—
232	C₂×Q₈×C₆₇	—	2	1	no	—
233	C₂×Q₈×C₆₇	—	4	2	no	—
234	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	2	8	no	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	2	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	1	no	—
246	C₂×D₄×C₆₇	—	2	1	no	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	1	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	4	4	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂×D₄×C₆₇	—	4	2	no	—
253	C₂×D₄×C₆₇	—	4	8	no	—
254	C₂×D₄×C₆₇	—	4	4	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	—	8	2	no	—
257	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	1	no	—
264	C₂²×C₄×C₆₇	—	2	4	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	—	4	2	no	—
272	C₂²×C₄×C₆₇	—	4	4	no	—
273	C₂²×C₄×C₆₇	—	8	2	no	—
274	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
283	Q₁₆×C₆₇	—	4	4	no	—
284	SD₁₆×C₆₇	—	2	8	no	—
285	SD₁₆×C₆₇	—	4	4	no	—
286	SD₁₆×C₆₇	—	4	4	no	—
287	D₈×C₆₇	—	2	8	no	—
288	D₈×C₆₇	—	4	4	no	—
289	M₁₆×C₆₇	—	4	4	no	—
290	C₂×C₈×C₆₇	—	4	4	no	—
291	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
292	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	4	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	1	no	—
301	C₄⋊C₄×C₆₇	—	2	1	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂³×C₆₇	—	2	4	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	4	1	no	—
343	C₂³×C₆₇	—	4	1	no	—
344	C₂³×C₆₇	—	4	1	no	—
345	C₂³×C₆₇	—	4	1	no	—
346	C₂³×C₆₇	—	4	8	no	—
347	C₂³×C₆₇	—	4	2	no	—
348	C₂³×C₆₇	—	4	2	no	—
349	C₂³×C₆₇	—	4	2	no	—
350	C₂³×C₆₇	—	4	8	no	—
351	C₂³×C₆₇	—	4	2	no	—
352	C₂³×C₆₇	—	4	2	no	—
353	C₂³×C₆₇	—	8	4	no	—
354	C₂³×C₆₇	—	8	16	no	—
355	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
356	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
357	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₆₇	—	2	4	no	—
359	Q₈×C₆₇	—	2	4	no	—
360	Q₈×C₆₇	—	4	2	no	—
361	Q₈×C₆₇	—	4	2	no	—
362	Q₈×C₆₇	—	8	1	no	—
363	D₄×C₆₇	—	2	4	no	—
364	D₄×C₆₇	—	2	2	no	—
365	D₄×C₆₇	—	2	4	no	—
366	D₄×C₆₇	—	2	4	no	—
367	D₄×C₆₇	—	4	2	no	—
368	D₄×C₆₇	—	4	2	no	—
369	D₄×C₆₇	—	4	8	no	—
370	D₄×C₆₇	—	4	2	no	—
371	D₄×C₆₇	—	4	2	no	—
372	D₄×C₆₇	—	4	8	no	—
373	D₄×C₆₇	—	4	4	no	—
374	D₄×C₆₇	—	8	1	no	—
375	D₄×C₆₇	—	8	2	no	—
376	D₄×C₆₇	—	8	2	no	—
377	D₄×C₆₇	—	8	4	no	—
378	D₄×C₆₇	—	8	2	no	—
379	D₄×C₆₇	—	8	2	no	—
380	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	2	4	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	4	1	no	—
391	C₂×C₄×C₆₇	—	4	2	no	—
392	C₂×C₄×C₆₇	—	4	1	no	—
393	C₂×C₄×C₆₇	—	4	2	no	—
394	C₂×C₄×C₆₇	—	4	1	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	—	4	4	no	—
397	C₂×C₄×C₆₇	—	4	2	no	—
398	C₂×C₄×C₆₇	—	4	2	no	—
399	C₂×C₄×C₆₇	—	8	2	no	—
400	C₂×C₄×C₆₇	—	8	2	no	—
401	C₂×C₄×C₆₇	—	8	2	no	—
402	C₂×C₄×C₆₇	—	8	2	no	—
403	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
411	C₈×C₆₇	—	2	4	no	—
412	C₈×C₆₇	—	2	4	no	—
413	C₂²×C₆₇	—	2	1	no	—
414	C₂²×C₆₇	—	2	1	no	—
415	C₂²×C₆₇	—	2	2	no	—
416	C₂²×C₆₇	—	2	2	no	—
417	C₂²×C₆₇	—	2	2	no	—
418	C₂²×C₆₇	—	2	2	no	—
419	C₂²×C₆₇	—	2	4	no	—
420	C₂²×C₆₇	—	2	2	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	4	8	no	—
423	C₂²×C₆₇	—	4	4	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	2	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	8	2	no	—
433	C₂²×C₆₇	—	8	4	no	—
434	C₂²×C₆₇	—	8	16	no	—
435	C₂²×C₆₇	#575	1	2	yes	—
436	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₆₇	—	2	1	no	—
438	C₄×C₆₇	—	2	1	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	1	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
450	#61576	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂×C₆₇	—	2	2	no	—
452	C₂×C₆₇	—	4	2	no	—
453	C₂×C₆₇	—	4	2	no	—
454	C₂×C₆₇	—	4	4	no	—
455	C₂×C₆₇	—	8	2	no	—
456	C₂×C₆₇	—	8	2	no	—
457	C₂×C₆₇	#3484	1	1	yes	characteristic
458	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
459	C₂×C₆₇	#3585	1	1	yes	characteristic
460	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
461	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
462	#3319	C₂×C₆₇	1	4	yes	complemented
463	#3311	C₂×C₆₇	1	4	yes	complemented
464	#3268	C₂×C₆₇	1	4	yes	complemented
465	#3267	C₂×C₆₇	1	4	yes	complemented
466	#3215	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3213	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3196	C₂×C₆₇	1	2	yes	complemented
469	#3188	C₂×C₆₇	1	2	yes	complemented
470	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
471	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3003	C₂×C₆₇	1	2	yes	complemented
473	#3002	C₂×C₆₇	1	2	yes	complemented
474	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
475	C₆₇	#61576	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
477	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
479	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
480	#559	—	2	2	no	—
481	#556	C₂²×C₆₇	1	2	yes	complemented
482	#555	C₂²×C₆₇	1	2	yes	complemented
483	#553	—	2	2	no	—
484	#550	C₂²×C₆₇	1	2	yes	complemented
485	#547	C₂²×C₆₇	1	2	yes	complemented
486	#546	—	2	2	no	—
487	#546	—	2	2	no	—
488	#546	C₂²×C₆₇	1	4	yes	—
489	#546	C₂²×C₆₇	1	4	yes	—
490	#538	—	2	1	no	—
491	#538	—	2	1	no	—
492	#535	—	2	1	no	—
493	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
494	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
495	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
496	#525	C₂²×C₆₇	1	2	yes	—
497	#525	C₂²×C₆₇	1	2	yes	complemented
498	C₂×#123	—	2	1	no	—
499	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#121	—	2	1	no	—
501	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#120	—	2	1	no	—
503	#520	—	2	1	no	—
504	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
506	C₂²×C₂²⋊C₄	—	2	1	no	—
507	#497	C₂²×C₆₇	1	2	yes	complemented
508	#496	C₂²×C₆₇	1	2	yes	complemented
509	#489	C₂²×C₆₇	1	2	yes	complemented
510	#489	C₂²×C₆₇	1	2	yes	complemented
511	#485	C₂²×C₆₇	1	4	yes	complemented
512	#484	C₂²×C₆₇	1	2	yes	complemented
513	#482	C₂²×C₆₇	1	4	yes	complemented
514	#481	C₂²×C₆₇	1	2	yes	complemented
515	#476	C₂²×C₆₇	1	2	yes	complemented
516	#474	C₂²×C₆₇	1	2	yes	complemented
517	#470	C₂²×C₆₇	1	4	yes	complemented
518	#468	C₂²×C₆₇	1	4	yes	complemented
519	#466	C₂²×C₆₇	1	4	yes	complemented
520	#465	C₂²×C₆₇	1	4	yes	complemented
521	#464	C₂²×C₆₇	1	4	yes	complemented
522	#463	C₂²×C₆₇	1	4	yes	complemented
523	#461	C₂²×C₆₇	1	2	yes	complemented
524	#459	C₂²×C₆₇	1	2	yes	complemented
525	#452	C₂²×C₆₇	1	4	yes	complemented
526	#452	C₂²×C₆₇	1	4	yes	complemented
527	#451	C₂²×C₆₇	1	2	yes	complemented
528	#450	C₂²×C₆₇	1	2	yes	—
529	#450	C₂²×C₆₇	1	2	yes	—
530	#450	C₂²×C₆₇	1	4	yes	complemented
531	#449	C₂²×C₆₇	1	4	yes	complemented
532	#449	C₂²×C₆₇	1	4	yes	complemented
533	#448	C₂²×C₆₇	1	2	yes	complemented
534	#447	C₂²×C₆₇	1	2	yes	—
535	#447	C₂²×C₆₇	1	2	yes	—
536	#447	C₂²×C₆₇	1	4	yes	complemented
537	#442	C₂²×C₆₇	1	4	yes	complemented
538	#440	C₂²×C₆₇	1	4	yes	complemented
539	#435	C₂²×C₆₇	1	4	yes	complemented
540	#435	C₂²×C₆₇	1	4	yes	complemented
541	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	#418	C₂²×C₆₇	1	4	yes	complemented
544	#416	C₂²×C₆₇	1	4	yes	complemented
545	#407	C₂²×C₆₇	1	2	yes	—
546	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
547	C₂⁵	—	2	1	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	4	4	no	—
551	C₂×#41	C₂³×C₆₇	1	4	yes	—
552	C₂×#41	C₂³×C₆₇	1	2	yes	—
553	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
554	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	4	4	no	—
560	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
563	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₂³×C₄	—	2	1	no	—
565	C₂³×C₄	—	2	1	no	—
566	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
568	AGL(1,ℤ/8)	—	4	8	no	—
569	#135	—	4	8	no	—
570	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	complemented
571	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
573	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
574	C₂×D₈	C₂³×C₆₇	1	4	yes	—
575	C₂×D₈	C₂³×C₆₇	1	4	yes	—
576	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
577	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
578	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
579	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
580	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
581	#127	—	2	2	no	—
582	#127	C₂³×C₆₇	1	1	yes	characteristic, complemented
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#125	—	2	1	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	1	no	—
590	#124	—	2	1	no	—
591	#124	—	2	1	no	—
592	#124	C₂³×C₆₇	1	2	yes	—
593	#124	C₂³×C₆₇	1	2	yes	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	4	no	—
597	#123	—	2	4	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
603	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	4	no	—
611	#121	—	2	4	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	C₂³×C₆₇	1	4	yes	—
615	#121	C₂³×C₆₇	1	2	yes	—
616	#121	C₂³×C₆₇	1	2	yes	—
617	#121	C₂³×C₆₇	1	2	yes	complemented
618	#120	—	2	2	no	—
619	#120	—	2	2	no	—
620	#120	—	2	4	no	—
621	#120	—	2	4	no	—
622	C₄×Q₈	—	2	2	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	D₄×C₆₇	1	2	yes	—
634	C₄×D₄	D₄×C₆₇	1	2	yes	—
635	C₄×D₄	C₂³×C₆₇	1	2	yes	—
636	C₄×D₄	C₂³×C₆₇	1	2	yes	—
637	C₄×D₄	C₂³×C₆₇	1	2	yes	—
638	C₄×D₄	C₂³×C₆₇	1	2	yes	—
639	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	C₂³×C₆₇	1	2	yes	—
643	#117	C₂³×C₆₇	1	2	yes	complemented
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	4	no	—
654	C₂×C₂²⋊C₄	—	2	4	no	—
655	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
658	#107	C₂³×C₆₇	1	4	yes	complemented
659	#106	C₂³×C₆₇	1	4	yes	complemented
660	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
661	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
662	#103	C₂³×C₆₇	1	4	yes	complemented
663	#103	C₂³×C₆₇	1	4	yes	complemented
664	#103	C₂³×C₆₇	1	4	yes	complemented
665	#102	C₂³×C₆₇	1	4	yes	—
666	#102	C₂³×C₆₇	1	4	yes	—
667	#102	C₂³×C₆₇	1	4	yes	—
668	#102	C₂³×C₆₇	1	4	yes	—
669	#102	C₂³×C₆₇	1	4	yes	complemented
670	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
674	#97	C₂³×C₆₇	1	2	yes	complemented
675	#97	C₂³×C₆₇	1	2	yes	complemented
676	C₂⁴	—	2	1	no	—
677	C₂⁴	—	2	1	no	—
678	C₂⁴	—	2	4	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	4	4	no	—
681	C₂⁴	—	8	2	no	—
682	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
684	#41	—	2	8	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	8	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	8	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	8	2	no	—
717	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
719	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	—	8	2	no	—
734	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	4	4	no	—
746	SD₁₆	—	4	4	no	—
747	D₈	—	2	8	no	—
748	D₈	—	4	4	no	—
749	M₁₆	—	4	4	no	—
750	C₂×C₈	—	4	4	no	—
751	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
752	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
787	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
793	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
794	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₂³	—	2	4	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	8	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	16	no	—
815	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
816	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
817	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
818	Q₈	—	2	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	1	no	—
823	D₄	—	2	4	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	1	no	—
835	D₄	—	8	4	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
870	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
871	C₈	—	2	4	no	—
872	C₈	—	2	4	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	8	2	no	—
893	C₂²	—	8	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	#575×C₆₇	1	2	yes	—
896	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₆₇×#3484	1	1	yes	characteristic
917	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
918	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×#3506	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3319	C₂	semidirect
4. C₆₇×#3311	C₂	semidirect
5. C₆₇×#3268	C₂	semidirect
6. C₆₇×#3267	C₂	semidirect
7. C₆₇×#3215	C₂	semidirect
8. C₆₇×#3213	C₂	semidirect
9. C₆₇×#3196	C₂	semidirect
10. C₆₇×#3188	C₂	semidirect
11. C₆₇×#3110	C₂	semidirect
12. C₆₇×#3109	C₂	semidirect
13. C₆₇×#3003	C₂	semidirect
14. C₆₇×#3002	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
18. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
19. C₂×#135×C₆₇	C₂²	semidirect
21. #556×C₆₇	C₂²	semidirect
22. #555×C₆₇	C₂²	semidirect
24. #550×C₆₇	C₂²	semidirect
25. #547×C₆₇	C₂²	semidirect
33. #533×C₆₇	C₂²	semidirect
34. #532×C₆₇	C₂²	semidirect
37. #525×C₆₇	C₂²	semidirect
47. #497×C₆₇	C₂²	semidirect
48. #496×C₆₇	C₂²	semidirect
49. #489×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #485×C₆₇	C₂²	semidirect
52. #484×C₆₇	C₂²	semidirect
53. #482×C₆₇	C₂²	semidirect
54. #481×C₆₇	C₂²	semidirect
55. #476×C₆₇	C₂²	semidirect
56. #474×C₆₇	C₂²	semidirect
57. #470×C₆₇	C₂²	semidirect
58. #468×C₆₇	C₂²	semidirect
59. #466×C₆₇	C₂²	semidirect
60. #465×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #461×C₆₇	C₂²	semidirect
64. #459×C₆₇	C₂²	semidirect
65. #452×C₆₇	C₂²	semidirect
66. #452×C₆₇	C₂²	semidirect
67. #451×C₆₇	C₂²	semidirect
70. #450×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
72. #449×C₆₇	C₂²	semidirect
73. #448×C₆₇	C₂²	semidirect
76. #447×C₆₇	C₂²	semidirect
77. #442×C₆₇	C₂²	semidirect
78. #440×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #435×C₆₇	C₂²	semidirect
81. #432×C₆₇	C₂²	semidirect
82. #432×C₆₇	C₂²	semidirect
83. #418×C₆₇	C₂²	semidirect
84. #416×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
93. C₂×#41×C₆₇	C₂³	semidirect
110. C₂×Q₁₆×C₆₇	C₂³	semidirect
113. C₂×SD₁₆×C₆₇	C₂³	semidirect
117. C₂²×C₈×C₆₇	C₂³	semidirect
118. C₄⋊Q₈×C₆₇	C₂³	semidirect
119. C₄⋊Q₈×C₆₇	C₂³	semidirect
120. C₄⋊Q₈×C₆₇	C₂³	semidirect
122. #127×C₆₇	C₂³	semidirect
145. C₂²⋊Q₈×C₆₇	C₂³	semidirect
157. #121×C₆₇	C₂³	semidirect
164. C₄×Q₈×C₆₇	C₂³	semidirect
179. C₄×D₄×C₆₇	C₂³	semidirect
183. #117×C₆₇	C₂³	semidirect
198. #107×C₆₇	C₂³	semidirect
199. #106×C₆₇	C₂³	semidirect
200. C₄⋊C₈×C₆₇	C₂³	semidirect
201. C₄⋊C₈×C₆₇	C₂³	semidirect
202. #103×C₆₇	C₂³	semidirect
203. #103×C₆₇	C₂³	semidirect
204. #103×C₆₇	C₂³	semidirect
209. #102×C₆₇	C₂³	semidirect
213. C₂²⋊C₈×C₆₇	C₂³	semidirect
214. #97×C₆₇	C₂³	semidirect
215. #97×C₆₇	C₂³	semidirect
450. #61576	C₆₇	direct (N × H)
460. #3506	C₂×C₆₇	semidirect
461. C₂×#546	C₂×C₆₇	semidirect
462. #3319	C₂×C₆₇	semidirect
463. #3311	C₂×C₆₇	semidirect
464. #3268	C₂×C₆₇	semidirect
465. #3267	C₂×C₆₇	semidirect
466. #3215	C₂×C₆₇	semidirect
467. #3213	C₂×C₆₇	semidirect
468. #3196	C₂×C₆₇	semidirect
469. #3188	C₂×C₆₇	semidirect
470. #3110	C₂×C₆₇	semidirect
471. #3109	C₂×C₆₇	semidirect
472. #3003	C₂×C₆₇	semidirect
473. #3002	C₂×C₆₇	semidirect
474. #2973	C₂×C₆₇	semidirect
475. C₆₇	#61576	direct (N × H)
478. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
479. C₂×#135	C₂²×C₆₇	semidirect
481. #556	C₂²×C₆₇	semidirect
482. #555	C₂²×C₆₇	semidirect
484. #550	C₂²×C₆₇	semidirect
485. #547	C₂²×C₆₇	semidirect
493. #533	C₂²×C₆₇	semidirect
494. #532	C₂²×C₆₇	semidirect
497. #525	C₂²×C₆₇	semidirect
507. #497	C₂²×C₆₇	semidirect
508. #496	C₂²×C₆₇	semidirect
509. #489	C₂²×C₆₇	semidirect
510. #489	C₂²×C₆₇	semidirect
511. #485	C₂²×C₆₇	semidirect
512. #484	C₂²×C₆₇	semidirect
513. #482	C₂²×C₆₇	semidirect
514. #481	C₂²×C₆₇	semidirect
515. #476	C₂²×C₆₇	semidirect
516. #474	C₂²×C₆₇	semidirect
517. #470	C₂²×C₆₇	semidirect
518. #468	C₂²×C₆₇	semidirect
519. #466	C₂²×C₆₇	semidirect
520. #465	C₂²×C₆₇	semidirect
521. #464	C₂²×C₆₇	semidirect
522. #463	C₂²×C₆₇	semidirect
523. #461	C₂²×C₆₇	semidirect
524. #459	C₂²×C₆₇	semidirect
525. #452	C₂²×C₆₇	semidirect
526. #452	C₂²×C₆₇	semidirect
527. #451	C₂²×C₆₇	semidirect
530. #450	C₂²×C₆₇	semidirect
531. #449	C₂²×C₆₇	semidirect
532. #449	C₂²×C₆₇	semidirect
533. #448	C₂²×C₆₇	semidirect
536. #447	C₂²×C₆₇	semidirect
537. #442	C₂²×C₆₇	semidirect
538. #440	C₂²×C₆₇	semidirect
539. #435	C₂²×C₆₇	semidirect
540. #435	C₂²×C₆₇	semidirect
541. #432	C₂²×C₆₇	semidirect
542. #432	C₂²×C₆₇	semidirect
543. #418	C₂²×C₆₇	semidirect
544. #416	C₂²×C₆₇	semidirect
546. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
553. C₂×#41	C₂³×C₆₇	semidirect
570. C₂×Q₁₆	C₂³×C₆₇	semidirect
573. C₂×SD₁₆	C₂³×C₆₇	semidirect
577. C₂²×C₈	C₂³×C₆₇	semidirect
578. C₄⋊Q₈	C₂³×C₆₇	semidirect
579. C₄⋊Q₈	C₂³×C₆₇	semidirect
580. C₄⋊Q₈	C₂³×C₆₇	semidirect
582. #127	C₂³×C₆₇	semidirect
605. C₂²⋊Q₈	C₂³×C₆₇	semidirect
617. #121	C₂³×C₆₇	semidirect
624. C₄×Q₈	C₂³×C₆₇	semidirect
639. C₄×D₄	C₂³×C₆₇	semidirect
643. #117	C₂³×C₆₇	semidirect
658. #107	C₂³×C₆₇	semidirect
659. #106	C₂³×C₆₇	semidirect
660. C₄⋊C₈	C₂³×C₆₇	semidirect
661. C₄⋊C₈	C₂³×C₆₇	semidirect
662. #103	C₂³×C₆₇	semidirect
663. #103	C₂³×C₆₇	semidirect
664. #103	C₂³×C₆₇	semidirect
669. #102	C₂³×C₆₇	semidirect
673. C₂²⋊C₈	C₂³×C₆₇	semidirect
674. #97	C₂³×C₆₇	semidirect
675. #97	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×#3506	2
C₂×#546×C₆₇	2
C₆₇×#3319	2
C₆₇×#3311	2
C₆₇×#3268	2
C₆₇×#3267	2
C₆₇×#3215	2
C₆₇×#3213	2
C₆₇×#3196	2
C₆₇×#3188	2
C₆₇×#3110	2
C₆₇×#3109	2
C₆₇×#3003	2
C₆₇×#3002	2
C₆₇×#2973	2
#61576	67

Subgroups — C67×#61576 #30740827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61576 #30740827