Subgroups — C₆₇×#61672 #30740923

Order 17152.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3321	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3204	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3011	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	—
22	C₂×#137×C₆₇	C₂²	1	2	yes	—
23	C₂×#135×C₆₇	C₂²	1	2	yes	—
24	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	—
25	#562×C₆₇	—	2	2	no	—
26	#555×C₆₇	—	2	1	no	—
27	#555×C₆₇	C₂²	1	1	yes	characteristic
28	#554×C₆₇	C₂²	1	1	yes	characteristic
29	#553×C₆₇	—	2	1	no	—
30	#552×C₆₇	C₂²	1	2	yes	—
31	#550×C₆₇	—	2	1	no	—
32	#550×C₆₇	C₂²	1	2	yes	—
33	D₄×Q₈×C₆₇	—	2	1	no	—
34	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
36	#548×C₆₇	—	2	2	no	—
37	#548×C₆₇	C₂²	1	2	yes	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#548×C₆₇	C₂²	1	2	yes	—
40	#547×C₆₇	C₂²	1	1	yes	characteristic
41	#544×C₆₇	—	2	1	no	—
42	#542×C₆₇	—	2	2	no	—
43	#540×C₆₇	—	2	1	no	—
44	#537×C₆₇	—	2	1	no	—
45	#537×C₆₇	—	2	1	no	—
46	#537×C₆₇	C₂²	1	2	yes	—
47	#537×C₆₇	C₂²	1	2	yes	—
48	#536×C₆₇	C₂²	1	2	yes	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	—	2	2	no	—
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#529×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
55	#497×C₆₇	C₂²	1	2	yes	—
56	#497×C₆₇	C₂²	1	1	yes	characteristic
57	#496×C₆₇	C₂²	1	1	yes	characteristic
58	#491×C₆₇	C₂²	1	1	yes	characteristic
59	#490×C₆₇	C₂²	1	1	yes	characteristic
60	#489×C₆₇	C₂²	1	2	yes	—
61	#485×C₆₇	C₂²	1	2	yes	—
62	#484×C₆₇	C₂²	1	1	yes	characteristic
63	#483×C₆₇	C₂²	1	2	yes	—
64	#483×C₆₇	C₂²	1	2	yes	—
65	#482×C₆₇	C₂²	1	2	yes	—
66	#481×C₆₇	C₂²	1	2	yes	—
67	#481×C₆₇	C₂²	1	1	yes	characteristic
68	#479×C₆₇	C₂²	1	2	yes	—
69	#475×C₆₇	C₂²	1	2	yes	—
70	#470×C₆₇	C₂²	1	2	yes	—
71	#470×C₆₇	C₂²	1	2	yes	—
72	#469×C₆₇	C₂²	1	2	yes	—
73	#468×C₆₇	C₂²	1	2	yes	—
74	#467×C₆₇	C₂²	1	2	yes	—
75	#465×C₆₇	C₂²	1	2	yes	—
76	#465×C₆₇	C₂²	1	2	yes	—
77	#465×C₆₇	C₂²	1	2	yes	—
78	#464×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	—
80	#463×C₆₇	C₂²	1	2	yes	—
81	#462×C₆₇	C₂²	1	2	yes	—
82	#462×C₆₇	C₂²	1	2	yes	—
83	#460×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	—
90	#452×C₆₇	C₂²	1	2	yes	—
91	#451×C₆₇	C₂²	1	1	yes	characteristic
92	#451×C₆₇	C₂²	1	2	yes	—
93	#451×C₆₇	C₂²	1	2	yes	—
94	#451×C₆₇	C₂²	1	2	yes	—
95	#451×C₆₇	C₂²	1	2	yes	—
96	#451×C₆₇	C₂²	1	2	yes	—
97	#449×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	1	yes	characteristic
101	#448×C₆₇	C₂²	1	2	yes	—
102	#448×C₆₇	C₂²	1	2	yes	—
103	#441×C₆₇	C₂²	1	2	yes	—
104	#441×C₆₇	C₂²	1	2	yes	—
105	#441×C₆₇	C₂²	1	2	yes	—
106	#440×C₆₇	C₂²	1	2	yes	—
107	#435×C₆₇	C₂²	1	2	yes	—
108	#435×C₆₇	C₂²	1	2	yes	—
109	#435×C₆₇	C₂²	1	2	yes	—
110	#435×C₆₇	C₂²	1	2	yes	—
111	#432×C₆₇	C₂²	1	1	yes	characteristic
112	#432×C₆₇	C₂²	1	1	yes	characteristic
113	#419×C₆₇	C₂²	1	2	yes	—
114	#417×C₆₇	C₂²	1	2	yes	—
115	#416×C₆₇	C₂²	1	2	yes	—
116	C₂×#103×C₆₇	C₂²	1	2	yes	—
117	#408×C₆₇	C₂²	1	2	yes	—
118	#408×C₆₇	C₂²	1	2	yes	—
119	2₋¹⁺⁴×C₆₇	—	4	4	no	—
120	2₋¹⁺⁴×C₆₇	—	4	4	no	—
121	C₂×#41×C₆₇	—	2	2	no	—
122	C₂×#41×C₆₇	—	2	2	no	—
123	C₂×#41×C₆₇	—	2	2	no	—
124	C₂×#41×C₆₇	C₂³	1	2	yes	—
125	C₂×#41×C₆₇	C₂³	1	2	yes	—
126	C₂×#41×C₆₇	C₂³	1	2	yes	—
127	C₂×#41×C₆₇	C₂³	1	2	yes	—
128	C₂×#41×C₆₇	C₂³	1	2	yes	—
129	C₂²×Q₈×C₆₇	—	2	2	no	—
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
132	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
133	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
134	#137×C₆₇	—	4	4	no	—
135	#137×C₆₇	—	4	4	no	—
136	#135×C₆₇	—	4	4	no	—
137	C₂×Q₁₆×C₆₇	—	4	4	no	—
138	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	—	2	2	no	—
155	C₄⋊Q₈×C₆₇	—	2	2	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	#127×C₆₇	—	2	2	no	—
162	#127×C₆₇	D₄	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	1	yes	characteristic
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	1	no	—
166	#125×C₆₇	—	2	2	no	—
167	#125×C₆₇	—	2	1	no	—
168	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	C₂³	1	1	yes	characteristic
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	D₄	1	2	yes	—
176	#124×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	C₂³	1	1	yes	characteristic
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	1	no	—
182	#123×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	—	2	2	no	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	D₄	1	2	yes	—
216	#121×C₆₇	D₄	1	1	yes	characteristic
217	#121×C₆₇	D₄	1	1	yes	characteristic
218	#121×C₆₇	C₂³	1	1	yes	characteristic
219	#121×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	C₂³	1	2	yes	—
221	#121×C₆₇	C₂³	1	2	yes	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	#117×C₆₇	—	2	1	no	—
244	#117×C₆₇	—	2	1	no	—
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	—	2	1	no	—
247	#117×C₆₇	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
250	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
252	C₂×C₄²×C₆₇	—	2	1	no	—
253	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
254	#107×C₆₇	C₂³	1	2	yes	—
255	#106×C₆₇	C₂³	1	2	yes	—
256	#106×C₆₇	C₂³	1	2	yes	—
257	#106×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#103×C₆₇	C₂³	1	2	yes	—
261	#103×C₆₇	C₂³	1	2	yes	—
262	#103×C₆₇	C₂³	1	2	yes	—
263	#103×C₆₇	C₂³	1	2	yes	—
264	#103×C₆₇	C₂³	1	2	yes	—
265	#103×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#102×C₆₇	C₂³	1	2	yes	—
272	#102×C₆₇	C₂³	1	2	yes	—
273	#102×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	#97×C₆₇	C₂³	1	2	yes	—
284	#97×C₆₇	C₂³	1	1	yes	characteristic
285	#97×C₆₇	C₂³	1	1	yes	characteristic
286	#41×C₆₇	—	2	4	no	—
287	#41×C₆₇	—	2	4	no	—
288	#41×C₆₇	—	4	2	no	—
289	#41×C₆₇	—	4	2	no	—
290	#41×C₆₇	—	4	2	no	—
291	#41×C₆₇	—	4	2	no	—
292	#41×C₆₇	—	4	2	no	—
293	#41×C₆₇	—	4	2	no	—
294	#41×C₆₇	—	4	8	no	—
295	#41×C₆₇	—	4	8	no	—
296	#41×C₆₇	—	4	2	no	—
297	#41×C₆₇	—	4	2	no	—
298	#41×C₆₇	—	4	8	no	—
299	C₂×Q₈×C₆₇	—	2	4	no	—
300	C₂×Q₈×C₆₇	—	2	1	no	—
301	C₂×Q₈×C₆₇	—	2	2	no	—
302	C₂×Q₈×C₆₇	—	2	2	no	—
303	C₂×Q₈×C₆₇	—	2	1	no	—
304	C₂×Q₈×C₆₇	—	2	2	no	—
305	C₂×Q₈×C₆₇	—	2	4	no	—
306	C₂×Q₈×C₆₇	—	2	4	no	—
307	C₂×Q₈×C₆₇	—	4	2	no	—
308	C₂×Q₈×C₆₇	—	4	2	no	—
309	C₂×Q₈×C₆₇	—	4	2	no	—
310	C₂×Q₈×C₆₇	—	4	2	no	—
311	C₂×Q₈×C₆₇	—	4	8	no	—
312	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
313	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
314	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
317	C₂×D₄×C₆₇	—	2	2	no	—
318	C₂×D₄×C₆₇	—	2	2	no	—
319	C₂×D₄×C₆₇	—	2	2	no	—
320	C₂×D₄×C₆₇	—	2	1	no	—
321	C₂×D₄×C₆₇	—	2	2	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	2	2	no	—
324	C₂×D₄×C₆₇	—	2	2	no	—
325	C₂×D₄×C₆₇	—	2	1	no	—
326	C₂×D₄×C₆₇	—	2	1	no	—
327	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
334	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	—	2	1	no	—
336	C₂²×C₄×C₆₇	—	2	2	no	—
337	C₂²×C₄×C₆₇	—	2	2	no	—
338	C₂²×C₄×C₆₇	—	2	1	no	—
339	C₂²×C₄×C₆₇	—	2	2	no	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	1	no	—
342	C₂²×C₄×C₆₇	—	2	2	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	2	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
351	Q₁₆×C₆₇	—	2	4	no	—
352	Q₁₆×C₆₇	—	2	4	no	—
353	Q₁₆×C₆₇	—	2	4	no	—
354	Q₁₆×C₆₇	—	4	2	no	—
355	Q₁₆×C₆₇	—	4	2	no	—
356	Q₁₆×C₆₇	—	4	2	no	—
357	SD₁₆×C₆₇	—	2	4	no	—
358	SD₁₆×C₆₇	—	4	2	no	—
359	SD₁₆×C₆₇	—	4	2	no	—
360	SD₁₆×C₆₇	—	4	2	no	—
361	SD₁₆×C₆₇	—	4	2	no	—
362	D₈×C₆₇	—	4	2	no	—
363	M₁₆×C₆₇	—	4	2	no	—
364	M₁₆×C₆₇	—	4	2	no	—
365	C₂×C₈×C₆₇	—	4	2	no	—
366	C₂×C₈×C₆₇	—	4	2	no	—
367	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
369	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
370	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₆₇	—	2	1	no	—
372	C₄⋊C₄×C₆₇	—	2	2	no	—
373	C₄⋊C₄×C₆₇	—	2	2	no	—
374	C₄⋊C₄×C₆₇	—	2	2	no	—
375	C₄⋊C₄×C₆₇	—	2	1	no	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	1	no	—
378	C₄⋊C₄×C₆₇	—	2	1	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	1	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
398	C₂²⋊C₄×C₆₇	—	2	2	no	—
399	C₂²⋊C₄×C₆₇	—	2	2	no	—
400	C₂²⋊C₄×C₆₇	—	2	2	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	—	2	2	no	—
403	C₂²⋊C₄×C₆₇	—	2	2	no	—
404	C₂²⋊C₄×C₆₇	—	2	2	no	—
405	C₂²⋊C₄×C₆₇	—	2	1	no	—
406	C₂²⋊C₄×C₆₇	—	2	1	no	—
407	C₂²⋊C₄×C₆₇	—	2	1	no	—
408	C₂²⋊C₄×C₆₇	—	2	2	no	—
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	1	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
419	C₄²×C₆₇	—	2	2	no	—
420	C₄²×C₆₇	—	2	2	no	—
421	C₄²×C₆₇	—	2	2	no	—
422	C₄²×C₆₇	—	2	2	no	—
423	C₄²×C₆₇	—	2	1	no	—
424	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
426	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂³×C₆₇	—	2	1	no	—
429	C₂³×C₆₇	—	2	2	no	—
430	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
431	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	Q₈×C₆₇	—	2	4	no	—
434	Q₈×C₆₇	—	2	2	no	—
435	Q₈×C₆₇	—	2	2	no	—
436	Q₈×C₆₇	—	2	2	no	—
437	Q₈×C₆₇	—	2	2	no	—
438	Q₈×C₆₇	—	2	2	no	—
439	Q₈×C₆₇	—	2	2	no	—
440	Q₈×C₆₇	—	4	2	no	—
441	Q₈×C₆₇	—	4	4	no	—
442	Q₈×C₆₇	—	4	4	no	—
443	Q₈×C₆₇	—	8	1	no	—
444	Q₈×C₆₇	—	8	2	no	—
445	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
446	D₄×C₆₇	—	2	2	no	—
447	D₄×C₆₇	—	2	2	no	—
448	D₄×C₆₇	—	2	2	no	—
449	D₄×C₆₇	—	4	1	no	—
450	D₄×C₆₇	—	4	1	no	—
451	D₄×C₆₇	—	4	2	no	—
452	D₄×C₆₇	—	4	2	no	—
453	D₄×C₆₇	—	4	2	no	—
454	D₄×C₆₇	—	4	2	no	—
455	D₄×C₆₇	—	4	4	no	—
456	D₄×C₆₇	—	4	4	no	—
457	D₄×C₆₇	—	4	2	no	—
458	D₄×C₆₇	—	4	4	no	—
459	D₄×C₆₇	—	8	1	no	—
460	D₄×C₆₇	—	8	1	no	—
461	D₄×C₆₇	—	8	2	no	—
462	D₄×C₆₇	—	8	2	no	—
463	D₄×C₆₇	—	8	2	no	—
464	D₄×C₆₇	—	8	2	no	—
465	C₂×C₄×C₆₇	—	2	4	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	4	1	no	—
480	C₂×C₄×C₆₇	—	4	1	no	—
481	C₂×C₄×C₆₇	—	4	4	no	—
482	C₂×C₄×C₆₇	—	4	4	no	—
483	C₂×C₄×C₆₇	—	4	4	no	—
484	C₂×C₄×C₆₇	—	4	4	no	—
485	C₂×C₄×C₆₇	—	4	2	no	—
486	C₂×C₄×C₆₇	—	4	4	no	—
487	C₂×C₄×C₆₇	—	8	2	no	—
488	C₂×C₄×C₆₇	—	8	2	no	—
489	C₂×C₄×C₆₇	—	8	1	no	—
490	C₂×C₄×C₆₇	—	8	2	no	—
491	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
499	C₈×C₆₇	—	2	2	no	—
500	C₈×C₆₇	—	2	2	no	—
501	C₈×C₆₇	—	2	2	no	—
502	C₈×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	2	1	no	—
504	C₂²×C₆₇	—	2	1	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	2	2	no	—
507	C₂²×C₆₇	—	2	2	no	—
508	C₂²×C₆₇	—	2	2	no	—
509	C₂²×C₆₇	—	2	1	no	—
510	C₂²×C₆₇	—	2	2	no	—
511	C₂²×C₆₇	—	2	2	no	—
512	C₂²×C₆₇	—	4	1	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	1	no	—
518	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₆₇	—	2	1	no	—
520	C₄×C₆₇	—	2	1	no	—
521	C₄×C₆₇	—	2	1	no	—
522	C₄×C₆₇	—	2	1	no	—
523	C₄×C₆₇	—	2	4	no	—
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	2	2	no	—
526	C₄×C₆₇	—	2	2	no	—
527	C₄×C₆₇	—	4	1	no	—
528	C₄×C₆₇	—	4	1	no	—
529	C₄×C₆₇	—	4	2	no	—
530	C₄×C₆₇	—	4	2	no	—
531	C₄×C₆₇	—	4	2	no	—
532	C₄×C₆₇	—	4	2	no	—
533	C₄×C₆₇	—	4	1	no	—
534	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
535	#61672	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₂×C₆₇	—	4	1	no	—
537	C₂×C₆₇	—	4	2	no	—
538	C₂×C₆₇	—	4	2	no	—
539	C₂×C₆₇	—	8	1	no	—
540	C₂×C₆₇	—	8	2	no	—
541	C₂×C₆₇	#3484	1	1	yes	characteristic
542	C₂×C₆₇	#3586	1	1	yes	characteristic
543	C₂×C₆₇	#3586	1	1	yes	characteristic
544	#3547	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#3321	C₂×C₆₇	1	2	yes	complemented
547	#3317	C₂×C₆₇	1	2	yes	complemented
548	#3316	C₂×C₆₇	1	2	yes	complemented
549	#3312	C₂×C₆₇	1	2	yes	complemented
550	#3271	C₂×C₆₇	1	2	yes	complemented
551	#3270	C₂×C₆₇	1	2	yes	complemented
552	#3270	C₂×C₆₇	1	2	yes	complemented
553	#3269	C₂×C₆₇	1	2	yes	complemented
554	#3219	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#3204	C₂×C₆₇	1	2	yes	complemented
557	#3201	C₂×C₆₇	1	2	yes	complemented
558	#3117	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#3013	C₂×C₆₇	1	2	yes	complemented
561	#3011	C₂×C₆₇	1	2	yes	complemented
562	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
563	C₆₇	#61672	1	1	yes	characteristic, direct product factor, Sylow
564	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
565	C₂×#137	C₂²×C₆₇	1	2	yes	—
566	C₂×#137	C₂²×C₆₇	1	2	yes	—
567	C₂×#135	C₂²×C₆₇	1	2	yes	—
568	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	—
569	#562	—	2	2	no	—
570	#555	—	2	1	no	—
571	#555	C₂²×C₆₇	1	1	yes	characteristic
572	#554	C₂²×C₆₇	1	1	yes	characteristic
573	#553	—	2	1	no	—
574	#552	C₂²×C₆₇	1	2	yes	—
575	#550	—	2	1	no	—
576	#550	C₂²×C₆₇	1	2	yes	—
577	D₄×Q₈	—	2	1	no	—
578	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
579	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
580	#548	—	2	2	no	—
581	#548	C₂²×C₆₇	1	2	yes	—
582	#548	C₂²×C₆₇	1	2	yes	—
583	#548	C₂²×C₆₇	1	2	yes	—
584	#547	C₂²×C₆₇	1	1	yes	characteristic
585	#544	—	2	1	no	—
586	#542	—	2	2	no	—
587	#540	—	2	1	no	—
588	#537	—	2	1	no	—
589	#537	—	2	1	no	—
590	#537	C₂²×C₆₇	1	2	yes	—
591	#537	C₂²×C₆₇	1	2	yes	—
592	#536	C₂²×C₆₇	1	2	yes	—
593	#533	C₂²×C₆₇	1	1	yes	characteristic
594	#532	—	2	2	no	—
595	#532	C₂²×C₆₇	1	1	yes	characteristic
596	#532	C₂²×C₆₇	1	1	yes	characteristic
597	#529	C₂²×C₆₇	1	1	yes	characteristic
598	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
599	#497	C₂²×C₆₇	1	2	yes	—
600	#497	C₂²×C₆₇	1	1	yes	characteristic
601	#496	C₂²×C₆₇	1	1	yes	characteristic
602	#491	C₂²×C₆₇	1	1	yes	characteristic
603	#490	C₂²×C₆₇	1	1	yes	characteristic
604	#489	C₂²×C₆₇	1	2	yes	—
605	#485	C₂²×C₆₇	1	2	yes	—
606	#484	C₂²×C₆₇	1	1	yes	characteristic
607	#483	C₂²×C₆₇	1	2	yes	—
608	#483	C₂²×C₆₇	1	2	yes	—
609	#482	C₂²×C₆₇	1	2	yes	—
610	#481	C₂²×C₆₇	1	1	yes	characteristic
611	#481	C₂²×C₆₇	1	2	yes	—
612	#479	C₂²×C₆₇	1	2	yes	—
613	#475	C₂²×C₆₇	1	2	yes	—
614	#470	C₂²×C₆₇	1	2	yes	—
615	#470	C₂²×C₆₇	1	2	yes	—
616	#469	C₂²×C₆₇	1	2	yes	—
617	#468	C₂²×C₆₇	1	2	yes	—
618	#467	C₂²×C₆₇	1	2	yes	—
619	#465	C₂²×C₆₇	1	2	yes	—
620	#465	C₂²×C₆₇	1	2	yes	—
621	#465	C₂²×C₆₇	1	2	yes	—
622	#464	C₂²×C₆₇	1	2	yes	—
623	#464	C₂²×C₆₇	1	2	yes	—
624	#463	C₂²×C₆₇	1	2	yes	—
625	#462	C₂²×C₆₇	1	2	yes	—
626	#462	C₂²×C₆₇	1	2	yes	—
627	#460	C₂²×C₆₇	1	2	yes	—
628	#452	C₂²×C₆₇	1	2	yes	—
629	#452	C₂²×C₆₇	1	2	yes	—
630	#452	C₂²×C₆₇	1	2	yes	—
631	#452	C₂²×C₆₇	1	2	yes	—
632	#452	C₂²×C₆₇	1	2	yes	—
633	#452	C₂²×C₆₇	1	2	yes	—
634	#452	C₂²×C₆₇	1	2	yes	—
635	#451	C₂²×C₆₇	1	2	yes	—
636	#451	C₂²×C₆₇	1	1	yes	characteristic
637	#451	C₂²×C₆₇	1	2	yes	—
638	#451	C₂²×C₆₇	1	2	yes	—
639	#451	C₂²×C₆₇	1	2	yes	—
640	#451	C₂²×C₆₇	1	2	yes	—
641	#449	C₂²×C₆₇	1	2	yes	—
642	#449	C₂²×C₆₇	1	2	yes	—
643	#449	C₂²×C₆₇	1	2	yes	—
644	#448	C₂²×C₆₇	1	1	yes	characteristic
645	#448	C₂²×C₆₇	1	2	yes	—
646	#448	C₂²×C₆₇	1	2	yes	—
647	#441	C₂²×C₆₇	1	2	yes	—
648	#441	C₂²×C₆₇	1	2	yes	—
649	#441	C₂²×C₆₇	1	2	yes	—
650	#440	C₂²×C₆₇	1	2	yes	—
651	#435	C₂²×C₆₇	1	2	yes	—
652	#435	C₂²×C₆₇	1	2	yes	—
653	#435	C₂²×C₆₇	1	2	yes	—
654	#435	C₂²×C₆₇	1	2	yes	—
655	#432	C₂²×C₆₇	1	1	yes	characteristic
656	#432	C₂²×C₆₇	1	1	yes	characteristic
657	#419	C₂²×C₆₇	1	2	yes	—
658	#417	C₂²×C₆₇	1	2	yes	—
659	#416	C₂²×C₆₇	1	2	yes	—
660	C₂×#103	C₂²×C₆₇	1	2	yes	—
661	#408	C₂²×C₆₇	1	2	yes	—
662	#408	C₂²×C₆₇	1	2	yes	—
663	2₋¹⁺⁴	—	4	4	no	—
664	2₋¹⁺⁴	—	4	4	no	—
665	C₂×#41	—	2	2	no	—
666	C₂×#41	—	2	2	no	—
667	C₂×#41	—	2	2	no	—
668	C₂×#41	C₂³×C₆₇	1	2	yes	—
669	C₂×#41	C₂³×C₆₇	1	2	yes	—
670	C₂×#41	C₂³×C₆₇	1	2	yes	—
671	C₂×#41	C₂³×C₆₇	1	2	yes	—
672	C₂×#41	C₂³×C₆₇	1	2	yes	—
673	C₂²×Q₈	—	2	2	no	—
674	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
675	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
676	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
677	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
678	#137	—	4	4	no	—
679	#137	—	4	4	no	—
680	#135	—	4	4	no	—
681	C₂×Q₁₆	—	4	4	no	—
682	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
687	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
693	C₂×D₈	C₂³×C₆₇	1	2	yes	—
694	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
695	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
696	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
697	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	#127	—	2	2	no	—
706	#127	D₄×C₆₇	1	1	yes	characteristic
707	#127	C₂³×C₆₇	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	—	2	1	no	—
712	#125	—	2	1	no	—
713	#125	C₂³×C₆₇	1	1	yes	characteristic
714	#124	—	2	2	no	—
715	#124	—	2	2	no	—
716	#124	—	2	2	no	—
717	#124	—	2	2	no	—
718	#124	—	2	2	no	—
719	#124	D₄×C₆₇	1	2	yes	—
720	#124	C₂³×C₆₇	1	1	yes	characteristic
721	#124	C₂³×C₆₇	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	1	no	—
726	#123	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
738	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
739	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
740	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
741	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
742	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
743	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	—	2	2	no	—
747	#121	—	2	2	no	—
748	#121	—	2	2	no	—
749	#121	—	2	2	no	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	—	2	1	no	—
753	#121	—	2	2	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	D₄×C₆₇	1	2	yes	—
760	#121	D₄×C₆₇	1	1	yes	characteristic
761	#121	D₄×C₆₇	1	1	yes	characteristic
762	#121	C₂³×C₆₇	1	1	yes	characteristic
763	#121	C₂³×C₆₇	1	2	yes	—
764	#121	C₂³×C₆₇	1	2	yes	—
765	#121	C₂³×C₆₇	1	2	yes	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
770	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
771	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₆₇	1	2	yes	—
787	#117	—	2	1	no	—
788	#117	—	2	1	no	—
789	#117	—	2	2	no	—
790	#117	—	2	1	no	—
791	#117	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
798	#107	C₂³×C₆₇	1	2	yes	—
799	#106	C₂³×C₆₇	1	2	yes	—
800	#106	C₂³×C₆₇	1	2	yes	—
801	#106	C₂³×C₆₇	1	2	yes	—
802	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
804	#103	C₂³×C₆₇	1	2	yes	—
805	#103	C₂³×C₆₇	1	2	yes	—
806	#103	C₂³×C₆₇	1	2	yes	—
807	#103	C₂³×C₆₇	1	2	yes	—
808	#103	C₂³×C₆₇	1	2	yes	—
809	#103	C₂³×C₆₇	1	2	yes	—
810	#103	C₂³×C₆₇	1	2	yes	—
811	#103	C₂³×C₆₇	1	2	yes	—
812	#103	C₂³×C₆₇	1	2	yes	—
813	#103	C₂³×C₆₇	1	2	yes	—
814	#103	C₂³×C₆₇	1	2	yes	—
815	#102	C₂³×C₆₇	1	2	yes	—
816	#102	C₂³×C₆₇	1	2	yes	—
817	#102	C₂³×C₆₇	1	2	yes	—
818	#102	C₂³×C₆₇	1	2	yes	—
819	#102	C₂³×C₆₇	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
822	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
827	#97	C₂³×C₆₇	1	2	yes	—
828	#97	C₂³×C₆₇	1	1	yes	characteristic
829	#97	C₂³×C₆₇	1	1	yes	characteristic
830	#41	—	2	4	no	—
831	#41	—	2	4	no	—
832	#41	—	4	2	no	—
833	#41	—	4	2	no	—
834	#41	—	4	2	no	—
835	#41	—	4	2	no	—
836	#41	—	4	2	no	—
837	#41	—	4	2	no	—
838	#41	—	4	8	no	—
839	#41	—	4	8	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	#41	—	4	8	no	—
843	C₂×Q₈	—	2	4	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	—	2	4	no	—
850	C₂×Q₈	—	2	4	no	—
851	C₂×Q₈	—	4	2	no	—
852	C₂×Q₈	—	4	2	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	2	no	—
855	C₂×Q₈	—	4	8	no	—
856	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
858	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
859	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
860	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
872	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
873	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
874	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
875	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
877	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
878	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
895	Q₁₆	—	2	4	no	—
896	Q₁₆	—	2	4	no	—
897	Q₁₆	—	2	4	no	—
898	Q₁₆	—	4	2	no	—
899	Q₁₆	—	4	2	no	—
900	Q₁₆	—	4	2	no	—
901	SD₁₆	—	2	4	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	2	no	—
904	SD₁₆	—	4	2	no	—
905	SD₁₆	—	4	2	no	—
906	D₈	—	4	2	no	—
907	M₁₆	—	4	2	no	—
908	M₁₆	—	4	2	no	—
909	C₂×C₈	—	4	2	no	—
910	C₂×C₈	—	4	2	no	—
911	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
912	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
913	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
914	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
940	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
960	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
962	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
969	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
975	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
976	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
977	Q₈	—	2	4	no	—
978	Q₈	—	2	2	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	2	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	4	no	—
986	Q₈	—	4	4	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	1	no	—
989	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
990	D₄	—	2	2	no	—
991	D₄	—	2	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	4	2	no	—
994	D₄	—	4	2	no	—
995	D₄	—	4	2	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	1	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	2	no	—
1002	D₄	—	4	4	no	—
1003	D₄	—	8	1	no	—
1004	D₄	—	8	2	no	—
1005	D₄	—	8	1	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	2	no	—
1008	D₄	—	8	2	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	4	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	1	no	—
1035	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1042	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1043	C₈	—	2	2	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	2	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	8	1	no	—
1083	C₂	—	8	2	no	—
1084	C₂	C₆₇×#3484	1	1	yes	characteristic
1085	C₂	C₆₇×#3586	1	1	yes	characteristic
1086	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3547	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3321	C₂	semidirect
4. C₆₇×#3317	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3312	C₂	semidirect
7. C₆₇×#3271	C₂	semidirect
8. C₆₇×#3270	C₂	semidirect
9. C₆₇×#3270	C₂	semidirect
10. C₆₇×#3269	C₂	semidirect
11. C₆₇×#3219	C₂	semidirect
12. C₆₇×#3216	C₂	semidirect
13. C₆₇×#3204	C₂	semidirect
14. C₆₇×#3201	C₂	semidirect
15. C₆₇×#3117	C₂	semidirect
16. C₆₇×#3113	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3011	C₂	semidirect
19. C₆₇×#2980	C₂	semidirect
535. #61672	C₆₇	direct (N × H)
544. #3547	C₂×C₆₇	semidirect
545. #3497	C₂×C₆₇	semidirect
546. #3321	C₂×C₆₇	semidirect
547. #3317	C₂×C₆₇	semidirect
548. #3316	C₂×C₆₇	semidirect
549. #3312	C₂×C₆₇	semidirect
550. #3271	C₂×C₆₇	semidirect
551. #3270	C₂×C₆₇	semidirect
552. #3270	C₂×C₆₇	semidirect
553. #3269	C₂×C₆₇	semidirect
554. #3219	C₂×C₆₇	semidirect
555. #3216	C₂×C₆₇	semidirect
556. #3204	C₂×C₆₇	semidirect
557. #3201	C₂×C₆₇	semidirect
558. #3117	C₂×C₆₇	semidirect
559. #3113	C₂×C₆₇	semidirect
560. #3013	C₂×C₆₇	semidirect
561. #3011	C₂×C₆₇	semidirect
562. #2980	C₂×C₆₇	semidirect
563. C₆₇	#61672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3547	2
C₆₇×#3497	2
C₆₇×#3321	2
C₆₇×#3317	2
C₆₇×#3316	2
C₆₇×#3312	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3269	2
C₆₇×#3219	2
C₆₇×#3216	2
C₆₇×#3204	2
C₆₇×#3201	2
C₆₇×#3117	2
C₆₇×#3113	2
C₆₇×#3013	2
C₆₇×#3011	2
C₆₇×#2980	2
#61672	67

Subgroups — C67×#61672 #30740923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61672 #30740923