Subgroups — C₆₇×#61711 #30740962

Order 17152.

1762 conjugacy classes of subgroups.

The subgroup lattice has 822 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
2	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3349	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3348	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3317	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3315	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3091	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	#559×C₆₇	—	2	2	no	—
17	#556×C₆₇	C₂²	1	2	yes	—
18	#555×C₆₇	C₂²	1	2	yes	—
19	#553×C₆₇	—	2	2	no	—
20	#552×C₆₇	—	2	2	no	—
21	#552×C₆₇	—	2	2	no	—
22	#552×C₆₇	C₂²	1	4	yes	—
23	#552×C₆₇	C₂²	1	4	yes	—
24	#550×C₆₇	C₂²	1	2	yes	—
25	#547×C₆₇	C₂²	1	2	yes	—
26	#538×C₆₇	—	2	1	no	—
27	#538×C₆₇	—	2	1	no	—
28	#535×C₆₇	—	2	1	no	—
29	#533×C₆₇	C₂²	1	1	yes	characteristic
30	#532×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#126×C₆₇	—	2	1	no	—
32	C₂×#125×C₆₇	—	2	1	no	—
33	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
34	#525×C₆₇	C₂²	1	2	yes	—
35	#525×C₆₇	C₂²	1	2	yes	—
36	C₂×#123×C₆₇	—	2	1	no	—
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	#520×C₆₇	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	—	2	1	no	—
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	#501×C₆₇	C₂²	1	2	yes	complemented
46	#501×C₆₇	C₂²	1	2	yes	complemented
47	#491×C₆₇	C₂²	1	2	yes	complemented
48	#490×C₆₇	C₂²	1	2	yes	complemented
49	#485×C₆₇	C₂²	1	4	yes	complemented
50	#485×C₆₇	C₂²	1	4	yes	complemented
51	#485×C₆₇	C₂²	1	4	yes	complemented
52	#484×C₆₇	C₂²	1	2	yes	—
53	#484×C₆₇	C₂²	1	4	yes	complemented
54	#483×C₆₇	C₂²	1	2	yes	—
55	#483×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	4	yes	complemented
57	#481×C₆₇	C₂²	1	2	yes	—
58	#481×C₆₇	C₂²	1	4	yes	complemented
59	#480×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	4	yes	complemented
62	#478×C₆₇	C₂²	1	4	yes	complemented
63	#477×C₆₇	C₂²	1	2	yes	complemented
64	#475×C₆₇	C₂²	1	2	yes	complemented
65	#470×C₆₇	C₂²	1	4	yes	complemented
66	#468×C₆₇	C₂²	1	4	yes	complemented
67	#467×C₆₇	C₂²	1	4	yes	complemented
68	#465×C₆₇	C₂²	1	4	yes	complemented
69	#462×C₆₇	C₂²	1	2	yes	complemented
70	#460×C₆₇	C₂²	1	2	yes	complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#452×C₆₇	C₂²	1	4	yes	complemented
73	#451×C₆₇	C₂²	1	2	yes	—
74	#448×C₆₇	C₂²	1	2	yes	—
75	#441×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	#435×C₆₇	C₂²	1	4	yes	—
78	#435×C₆₇	C₂²	1	4	yes	—
79	#432×C₆₇	C₂²	1	1	yes	characteristic
80	#432×C₆₇	C₂²	1	1	yes	characteristic
81	#428×C₆₇	C₂²	1	4	yes	complemented
82	#427×C₆₇	C₂²	1	4	yes	complemented
83	#417×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	—
87	C₂×#41×C₆₇	—	2	1	no	—
88	C₂×#41×C₆₇	C₂³	1	2	yes	—
89	C₂×#41×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	—	2	1	no	—
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
97	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
98	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
99	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
102	#127×C₆₇	—	2	2	no	—
103	#127×C₆₇	C₂³	1	1	yes	characteristic
104	#126×C₆₇	—	2	4	no	—
105	#126×C₆₇	—	2	4	no	—
106	#126×C₆₇	—	2	2	no	—
107	#126×C₆₇	—	2	2	no	—
108	#125×C₆₇	—	2	4	no	—
109	#125×C₆₇	—	2	4	no	—
110	#125×C₆₇	—	2	1	no	—
111	#125×C₆₇	—	2	1	no	—
112	#125×C₆₇	—	2	1	no	—
113	#125×C₆₇	C₂³	1	2	yes	—
114	#125×C₆₇	C₂³	1	2	yes	—
115	#124×C₆₇	—	2	2	no	—
116	#124×C₆₇	—	2	2	no	—
117	#124×C₆₇	—	2	2	no	—
118	#124×C₆₇	—	2	1	no	—
119	#123×C₆₇	—	2	4	no	—
120	#123×C₆₇	—	2	4	no	—
121	#123×C₆₇	—	2	2	no	—
122	#123×C₆₇	—	2	2	no	—
123	#123×C₆₇	—	2	2	no	—
124	#123×C₆₇	—	2	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	2	no	—
126	C₂²⋊Q₈×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	—	2	1	no	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
130	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
131	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
133	#121×C₆₇	—	2	2	no	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	1	no	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	C₂³	1	2	yes	—
139	#121×C₆₇	C₂³	1	2	yes	—
140	#121×C₆₇	C₂³	1	2	yes	—
141	#120×C₆₇	—	2	2	no	—
142	#120×C₆₇	—	2	2	no	—
143	C₄×Q₈×C₆₇	—	2	2	no	—
144	C₄×Q₈×C₆₇	—	2	1	no	—
145	C₄×Q₈×C₆₇	—	2	1	no	—
146	C₄×Q₈×C₆₇	—	2	1	no	—
147	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
150	C₄×D₄×C₆₇	—	2	2	no	—
151	C₄×D₄×C₆₇	—	2	2	no	—
152	C₄×D₄×C₆₇	—	2	2	no	—
153	C₄×D₄×C₆₇	—	2	2	no	—
154	C₄×D₄×C₆₇	—	2	2	no	—
155	C₄×D₄×C₆₇	—	2	1	no	—
156	C₄×D₄×C₆₇	D₄	1	2	yes	—
157	C₄×D₄×C₆₇	D₄	1	2	yes	—
158	C₄×D₄×C₆₇	C₂³	1	2	yes	—
159	C₄×D₄×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	C₂³	1	2	yes	—
161	#117×C₆₇	—	2	2	no	—
162	#117×C₆₇	—	2	1	no	—
163	#117×C₆₇	—	2	2	no	—
164	#117×C₆₇	—	2	4	no	—
165	#117×C₆₇	—	2	4	no	—
166	#117×C₆₇	C₂³	1	4	yes	—
167	#117×C₆₇	C₂³	1	2	yes	—
168	#117×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
177	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
182	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	—	2	1	no	—
188	C₂×C₄²×C₆₇	—	2	1	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	#107×C₆₇	C₂³	1	4	yes	—
191	#107×C₆₇	C₂³	1	4	yes	—
192	#107×C₆₇	C₂³	1	4	yes	—
193	#106×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	4	yes	—
195	#106×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	4	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	4	yes	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#102×C₆₇	C₂³	1	4	yes	—
204	#102×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
210	#97×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	2	yes	—
212	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
214	#41×C₆₇	—	4	4	no	—
215	#41×C₆₇	—	4	4	no	—
216	#41×C₆₇	—	4	4	no	—
217	C₂×Q₈×C₆₇	—	2	1	no	—
218	C₂×Q₈×C₆₇	—	2	1	no	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	—	4	2	no	—
221	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×D₄×C₆₇	—	2	2	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₇	—	2	1	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	1	no	—
237	C₂²×C₄×C₆₇	—	2	1	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	2	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	4	no	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	Q₁₆×C₆₇	—	4	4	no	—
255	SD₁₆×C₆₇	—	4	4	no	—
256	M₁₆×C₆₇	—	4	4	no	—
257	C₂×C₈×C₆₇	—	4	4	no	—
258	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
259	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	4	no	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	2	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	1	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	—	2	2	no	—
295	C₂²⋊C₄×C₆₇	—	2	2	no	—
296	C₂²⋊C₄×C₆₇	—	2	2	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
300	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
301	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	2	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	—	2	2	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	—	2	2	no	—
309	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	—	2	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	4	1	no	—
317	C₂³×C₆₇	—	4	1	no	—
318	C₂³×C₆₇	—	4	1	no	—
319	C₂³×C₆₇	—	4	1	no	—
320	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
321	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₆₇	—	2	2	no	—
324	Q₈×C₆₇	—	2	2	no	—
325	Q₈×C₆₇	—	2	4	no	—
326	Q₈×C₆₇	—	4	2	no	—
327	Q₈×C₆₇	—	4	2	no	—
328	Q₈×C₆₇	—	8	1	no	—
329	D₄×C₆₇	—	2	4	no	—
330	D₄×C₆₇	—	4	2	no	—
331	D₄×C₆₇	—	4	2	no	—
332	D₄×C₆₇	—	4	2	no	—
333	D₄×C₆₇	—	4	4	no	—
334	D₄×C₆₇	—	8	1	no	—
335	D₄×C₆₇	—	8	2	no	—
336	D₄×C₆₇	—	8	2	no	—
337	D₄×C₆₇	—	8	2	no	—
338	D₄×C₆₇	—	8	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	4	no	—
341	C₂×C₄×C₆₇	—	2	4	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	4	2	no	—
351	C₂×C₄×C₆₇	—	4	2	no	—
352	C₂×C₄×C₆₇	—	4	1	no	—
353	C₂×C₄×C₆₇	—	4	1	no	—
354	C₂×C₄×C₆₇	—	4	1	no	—
355	C₂×C₄×C₆₇	—	4	4	no	—
356	C₂×C₄×C₆₇	—	4	2	no	—
357	C₂×C₄×C₆₇	—	4	8	no	—
358	C₂×C₄×C₆₇	—	4	2	no	—
359	C₂×C₄×C₆₇	—	4	2	no	—
360	C₂×C₄×C₆₇	—	4	2	no	—
361	C₂×C₄×C₆₇	—	8	2	no	—
362	C₂×C₄×C₆₇	—	8	2	no	—
363	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
371	C₈×C₆₇	—	2	4	no	—
372	C₈×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	2	1	no	—
374	C₂²×C₆₇	—	2	1	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	2	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	4	4	no	—
382	C₂²×C₆₇	—	4	2	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	8	2	no	—
386	C₂²×C₆₇	#575	1	2	yes	—
387	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₆₇	—	2	1	no	—
389	C₄×C₆₇	—	2	1	no	—
390	C₄×C₆₇	—	2	1	no	—
391	C₄×C₆₇	—	2	2	no	—
392	C₄×C₆₇	—	2	2	no	—
393	C₄×C₆₇	—	2	1	no	—
394	C₄×C₆₇	—	2	1	no	—
395	C₄×C₆₇	—	4	2	no	—
396	C₄×C₆₇	—	4	2	no	—
397	C₄×C₆₇	—	4	2	no	—
398	C₄×C₆₇	—	4	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	—	4	2	no	—
402	C₄×C₆₇	#585	1	2	yes	—
403	#61711	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₆₇	—	2	2	no	—
405	C₂×C₆₇	—	4	2	no	—
406	C₂×C₆₇	—	4	2	no	—
407	C₂×C₆₇	—	8	2	no	—
408	C₂×C₆₇	#3485	1	1	yes	characteristic
409	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
410	C₂×C₆₇	#3586	1	1	yes	characteristic
411	#3506	C₂×C₆₇	1	1	yes	characteristic
412	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#3349	C₂×C₆₇	1	4	yes	complemented
414	#3348	C₂×C₆₇	1	4	yes	complemented
415	#3317	C₂×C₆₇	1	4	yes	complemented
416	#3315	C₂×C₆₇	1	4	yes	complemented
417	#3236	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#3234	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#3196	C₂×C₆₇	1	2	yes	complemented
420	#3190	C₂×C₆₇	1	2	yes	complemented
421	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
423	#3092	C₂×C₆₇	1	2	yes	complemented
424	#3091	C₂×C₆₇	1	2	yes	complemented
425	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
426	C₆₇	#61711	1	1	yes	characteristic, direct product factor, Sylow
427	#559	—	2	2	no	—
428	#556	C₂²×C₆₇	1	2	yes	—
429	#555	C₂²×C₆₇	1	2	yes	—
430	#553	—	2	2	no	—
431	#552	—	2	2	no	—
432	#552	—	2	2	no	—
433	#552	C₂²×C₆₇	1	4	yes	—
434	#552	C₂²×C₆₇	1	4	yes	—
435	#550	C₂²×C₆₇	1	2	yes	—
436	#547	C₂²×C₆₇	1	2	yes	—
437	#538	—	2	1	no	—
438	#538	—	2	1	no	—
439	#535	—	2	1	no	—
440	#533	C₂²×C₆₇	1	1	yes	characteristic
441	#532	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#126	—	2	1	no	—
443	C₂×#125	—	2	1	no	—
444	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
445	#525	C₂²×C₆₇	1	2	yes	—
446	#525	C₂²×C₆₇	1	2	yes	—
447	C₂×#123	—	2	1	no	—
448	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
450	#520	—	2	1	no	—
451	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
453	C₂×#117	—	2	1	no	—
454	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
455	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
456	#501	C₂²×C₆₇	1	2	yes	complemented
457	#501	C₂²×C₆₇	1	2	yes	complemented
458	#491	C₂²×C₆₇	1	2	yes	complemented
459	#490	C₂²×C₆₇	1	2	yes	complemented
460	#485	C₂²×C₆₇	1	4	yes	complemented
461	#485	C₂²×C₆₇	1	4	yes	complemented
462	#485	C₂²×C₆₇	1	4	yes	complemented
463	#484	C₂²×C₆₇	1	2	yes	—
464	#484	C₂²×C₆₇	1	4	yes	complemented
465	#483	C₂²×C₆₇	1	2	yes	—
466	#483	C₂²×C₆₇	1	2	yes	—
467	#482	C₂²×C₆₇	1	4	yes	complemented
468	#481	C₂²×C₆₇	1	2	yes	—
469	#481	C₂²×C₆₇	1	4	yes	complemented
470	#480	C₂²×C₆₇	1	2	yes	—
471	#480	C₂²×C₆₇	1	2	yes	—
472	#479	C₂²×C₆₇	1	4	yes	complemented
473	#478	C₂²×C₆₇	1	4	yes	complemented
474	#477	C₂²×C₆₇	1	2	yes	complemented
475	#475	C₂²×C₆₇	1	2	yes	complemented
476	#470	C₂²×C₆₇	1	4	yes	complemented
477	#468	C₂²×C₆₇	1	4	yes	complemented
478	#467	C₂²×C₆₇	1	4	yes	complemented
479	#465	C₂²×C₆₇	1	4	yes	complemented
480	#462	C₂²×C₆₇	1	2	yes	complemented
481	#460	C₂²×C₆₇	1	2	yes	complemented
482	#452	C₂²×C₆₇	1	4	yes	complemented
483	#452	C₂²×C₆₇	1	4	yes	complemented
484	#451	C₂²×C₆₇	1	2	yes	—
485	#448	C₂²×C₆₇	1	2	yes	—
486	#441	C₂²×C₆₇	1	4	yes	complemented
487	#440	C₂²×C₆₇	1	4	yes	complemented
488	#435	C₂²×C₆₇	1	4	yes	—
489	#435	C₂²×C₆₇	1	4	yes	—
490	#432	C₂²×C₆₇	1	1	yes	characteristic
491	#432	C₂²×C₆₇	1	1	yes	characteristic
492	#428	C₂²×C₆₇	1	4	yes	complemented
493	#427	C₂²×C₆₇	1	4	yes	complemented
494	#417	C₂²×C₆₇	1	4	yes	complemented
495	#416	C₂²×C₆₇	1	4	yes	complemented
496	#407	C₂²×C₆₇	1	2	yes	—
497	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
498	C₂×#41	—	2	1	no	—
499	C₂×#41	C₂³×C₆₇	1	2	yes	—
500	C₂×#41	C₂³×C₆₇	1	2	yes	—
501	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
506	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
508	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
509	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
510	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
513	#127	—	2	2	no	—
514	#127	C₂³×C₆₇	1	1	yes	characteristic
515	#126	—	2	4	no	—
516	#126	—	2	4	no	—
517	#126	—	2	2	no	—
518	#126	—	2	2	no	—
519	#125	—	2	4	no	—
520	#125	—	2	4	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	—	2	1	no	—
524	#125	C₂³×C₆₇	1	2	yes	—
525	#125	C₂³×C₆₇	1	2	yes	—
526	#124	—	2	2	no	—
527	#124	—	2	2	no	—
528	#124	—	2	2	no	—
529	#124	—	2	1	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
541	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
542	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	1	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	C₂³×C₆₇	1	2	yes	—
550	#121	C₂³×C₆₇	1	2	yes	—
551	#121	C₂³×C₆₇	1	2	yes	—
552	#120	—	2	2	no	—
553	#120	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
559	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	D₄×C₆₇	1	2	yes	—
568	C₄×D₄	D₄×C₆₇	1	2	yes	—
569	C₄×D₄	C₂³×C₆₇	1	2	yes	—
570	C₄×D₄	C₂³×C₆₇	1	2	yes	—
571	C₄×D₄	C₂³×C₆₇	1	2	yes	—
572	#117	—	2	2	no	—
573	#117	—	2	1	no	—
574	#117	—	2	2	no	—
575	#117	—	2	4	no	—
576	#117	—	2	4	no	—
577	#117	C₂³×C₆₇	1	4	yes	—
578	#117	C₂³×C₆₇	1	2	yes	—
579	#117	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	2	no	—
588	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	—	2	1	no	—
600	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
601	#107	C₂³×C₆₇	1	4	yes	—
602	#107	C₂³×C₆₇	1	4	yes	—
603	#107	C₂³×C₆₇	1	4	yes	—
604	#106	C₂³×C₆₇	1	4	yes	—
605	#106	C₂³×C₆₇	1	4	yes	—
606	#106	C₂³×C₆₇	1	4	yes	—
607	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
608	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
609	#103	C₂³×C₆₇	1	4	yes	—
610	#103	C₂³×C₆₇	1	4	yes	—
611	#103	C₂³×C₆₇	1	4	yes	—
612	#103	C₂³×C₆₇	1	4	yes	—
613	#103	C₂³×C₆₇	1	4	yes	—
614	#102	C₂³×C₆₇	1	4	yes	—
615	#102	C₂³×C₆₇	1	4	yes	—
616	#102	C₂³×C₆₇	1	4	yes	—
617	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
618	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
619	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
620	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
621	#97	C₂³×C₆₇	1	2	yes	—
622	#97	C₂³×C₆₇	1	2	yes	—
623	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
624	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
625	#41	—	4	4	no	—
626	#41	—	4	4	no	—
627	#41	—	4	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
633	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
643	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	4	no	—
656	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
661	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
665	Q₁₆	—	4	4	no	—
666	SD₁₆	—	4	4	no	—
667	M₁₆	—	4	4	no	—
668	C₂×C₈	—	4	4	no	—
669	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
670	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
692	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
711	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
712	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
713	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
721	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
722	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
732	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
733	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
734	Q₈	—	2	2	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	4	no	—
737	Q₈	—	4	2	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	8	1	no	—
740	D₄	—	2	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	4	no	—
745	D₄	—	8	1	no	—
746	D₄	—	8	2	no	—
747	D₄	—	8	2	no	—
748	D₄	—	8	2	no	—
749	D₄	—	8	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	8	2	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
775	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
781	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
782	C₈	—	2	4	no	—
783	C₈	—	2	4	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	8	2	no	—
797	C₂²	#575×C₆₇	1	2	yes	—
798	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	#585×C₆₇	1	2	yes	—
814	C₂	—	2	2	no	—
815	C₂	—	4	2	no	—
816	C₂	—	4	2	no	—
817	C₂	—	8	2	no	—
818	C₂	C₆₇×#3485	1	1	yes	characteristic
819	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
820	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#552×C₆₇	C₂	semidirect
3. C₆₇×#3349	C₂	semidirect
4. C₆₇×#3348	C₂	semidirect
5. C₆₇×#3317	C₂	semidirect
6. C₆₇×#3315	C₂	semidirect
7. C₆₇×#3236	C₂	semidirect
8. C₆₇×#3234	C₂	semidirect
9. C₆₇×#3196	C₂	semidirect
10. C₆₇×#3190	C₂	semidirect
11. C₆₇×#3113	C₂	semidirect
12. C₆₇×#3112	C₂	semidirect
13. C₆₇×#3092	C₂	semidirect
14. C₆₇×#3091	C₂	semidirect
15. C₆₇×#2973	C₂	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #491×C₆₇	C₂²	semidirect
48. #490×C₆₇	C₂²	semidirect
49. #485×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
58. #481×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #477×C₆₇	C₂²	semidirect
64. #475×C₆₇	C₂²	semidirect
65. #470×C₆₇	C₂²	semidirect
66. #468×C₆₇	C₂²	semidirect
67. #467×C₆₇	C₂²	semidirect
68. #465×C₆₇	C₂²	semidirect
69. #462×C₆₇	C₂²	semidirect
70. #460×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #452×C₆₇	C₂²	semidirect
75. #441×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
81. #428×C₆₇	C₂²	semidirect
82. #427×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
84. #416×C₆₇	C₂²	semidirect
403. #61711	C₆₇	direct (N × H)
412. C₂×#552	C₂×C₆₇	semidirect
413. #3349	C₂×C₆₇	semidirect
414. #3348	C₂×C₆₇	semidirect
415. #3317	C₂×C₆₇	semidirect
416. #3315	C₂×C₆₇	semidirect
417. #3236	C₂×C₆₇	semidirect
418. #3234	C₂×C₆₇	semidirect
419. #3196	C₂×C₆₇	semidirect
420. #3190	C₂×C₆₇	semidirect
421. #3113	C₂×C₆₇	semidirect
422. #3112	C₂×C₆₇	semidirect
423. #3092	C₂×C₆₇	semidirect
424. #3091	C₂×C₆₇	semidirect
425. #2973	C₂×C₆₇	semidirect
426. C₆₇	#61711	direct (N × H)
456. #501	C₂²×C₆₇	semidirect
457. #501	C₂²×C₆₇	semidirect
458. #491	C₂²×C₆₇	semidirect
459. #490	C₂²×C₆₇	semidirect
460. #485	C₂²×C₆₇	semidirect
461. #485	C₂²×C₆₇	semidirect
462. #485	C₂²×C₆₇	semidirect
464. #484	C₂²×C₆₇	semidirect
467. #482	C₂²×C₆₇	semidirect
469. #481	C₂²×C₆₇	semidirect
472. #479	C₂²×C₆₇	semidirect
473. #478	C₂²×C₆₇	semidirect
474. #477	C₂²×C₆₇	semidirect
475. #475	C₂²×C₆₇	semidirect
476. #470	C₂²×C₆₇	semidirect
477. #468	C₂²×C₆₇	semidirect
478. #467	C₂²×C₆₇	semidirect
479. #465	C₂²×C₆₇	semidirect
480. #462	C₂²×C₆₇	semidirect
481. #460	C₂²×C₆₇	semidirect
482. #452	C₂²×C₆₇	semidirect
483. #452	C₂²×C₆₇	semidirect
486. #441	C₂²×C₆₇	semidirect
487. #440	C₂²×C₆₇	semidirect
492. #428	C₂²×C₆₇	semidirect
493. #427	C₂²×C₆₇	semidirect
494. #417	C₂²×C₆₇	semidirect
495. #416	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₂×#552×C₆₇	2
C₆₇×#3349	2
C₆₇×#3348	2
C₆₇×#3317	2
C₆₇×#3315	2
C₆₇×#3236	2
C₆₇×#3234	2
C₆₇×#3196	2
C₆₇×#3190	2
C₆₇×#3113	2
C₆₇×#3112	2
C₆₇×#3092	2
C₆₇×#3091	2
C₆₇×#2973	2
#61711	67

Subgroups — C67×#61711 #30740962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61711 #30740962