Subgroups — C₆₇×#61637 #30740888

Order 17152.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3309	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3222	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3220	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3191	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#135×C₆₇	C₂²	1	2	yes	—
24	C₂×#135×C₆₇	C₂²	1	2	yes	—
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	#560×C₆₇	—	2	2	no	—
27	#553×C₆₇	—	2	2	no	—
28	#553×C₆₇	C₂²	1	2	yes	complemented
29	#552×C₆₇	C₂²	1	2	yes	complemented
30	#550×C₆₇	—	2	2	no	—
31	#550×C₆₇	C₂²	1	2	yes	—
32	#550×C₆₇	C₂²	1	2	yes	—
33	#550×C₆₇	C₂²	1	2	yes	complemented
34	#548×C₆₇	—	2	2	no	—
35	#548×C₆₇	C₂²	1	2	yes	—
36	#548×C₆₇	C₂²	1	2	yes	—
37	#547×C₆₇	C₂²	1	2	yes	complemented
38	#541×C₆₇	C₂²	1	1	yes	characteristic
39	#540×C₆₇	—	2	2	no	—
40	#540×C₆₇	C₂²	1	1	yes	characteristic
41	#539×C₆₇	—	2	2	no	—
42	#537×C₆₇	C₂²	1	2	yes	—
43	#535×C₆₇	—	2	2	no	—
44	#535×C₆₇	C₂²	1	1	yes	characteristic
45	#535×C₆₇	C₂²	1	1	yes	characteristic
46	#525×C₆₇	—	2	2	no	—
47	#525×C₆₇	C₂²	1	2	yes	—
48	#525×C₆₇	C₂²	1	1	yes	characteristic
49	#525×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	C₂²	1	1	yes	characteristic
51	#497×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#496×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#490×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#490×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#488×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#488×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#485×C₆₇	C₂²	1	2	yes	—
60	#485×C₆₇	C₂²	1	2	yes	complemented
61	#482×C₆₇	C₂²	1	2	yes	—
62	#482×C₆₇	C₂²	1	2	yes	complemented
63	#481×C₆₇	C₂²	1	2	yes	complemented
64	#480×C₆₇	C₂²	1	2	yes	complemented
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#479×C₆₇	C₂²	1	2	yes	complemented
67	#469×C₆₇	C₂²	1	2	yes	complemented
68	#468×C₆₇	C₂²	1	2	yes	complemented
69	#467×C₆₇	C₂²	1	2	yes	complemented
70	#466×C₆₇	C₂²	1	2	yes	complemented
71	#466×C₆₇	C₂²	1	2	yes	complemented
72	#465×C₆₇	C₂²	1	2	yes	complemented
73	#465×C₆₇	C₂²	1	2	yes	complemented
74	#465×C₆₇	C₂²	1	2	yes	complemented
75	#464×C₆₇	C₂²	1	2	yes	complemented
76	#463×C₆₇	C₂²	1	2	yes	complemented
77	#462×C₆₇	C₂²	1	2	yes	complemented
78	#460×C₆₇	C₂²	1	2	yes	complemented
79	#460×C₆₇	C₂²	1	2	yes	complemented
80	#459×C₆₇	C₂²	1	2	yes	complemented
81	#452×C₆₇	C₂²	1	2	yes	—
82	#452×C₆₇	C₂²	1	2	yes	—
83	#452×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#451×C₆₇	C₂²	1	2	yes	—
87	#451×C₆₇	C₂²	1	2	yes	complemented
88	#450×C₆₇	C₂²	1	2	yes	—
89	#449×C₆₇	C₂²	1	2	yes	—
90	#449×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	—
92	#449×C₆₇	C₂²	1	2	yes	complemented
93	#449×C₆₇	C₂²	1	2	yes	complemented
94	#449×C₆₇	C₂²	1	2	yes	complemented
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#448×C₆₇	C₂²	1	2	yes	—
97	#448×C₆₇	C₂²	1	2	yes	complemented
98	#447×C₆₇	C₂²	1	2	yes	—
99	#441×C₆₇	C₂²	1	2	yes	complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	#435×C₆₇	C₂²	1	2	yes	complemented
104	#435×C₆₇	C₂²	1	2	yes	complemented
105	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
106	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
107	#433×C₆₇	C₂²	1	1	yes	characteristic
108	#433×C₆₇	C₂²	1	1	yes	characteristic
109	#417×C₆₇	C₂²	1	2	yes	complemented
110	#416×C₆₇	C₂²	1	2	yes	—
111	#416×C₆₇	C₂²	1	2	yes	—
112	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
113	#408×C₆₇	C₂²	1	2	yes	—
114	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
115	2₋¹⁺⁴×C₆₇	—	4	4	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	—	2	1	no	—
118	C₂×#41×C₆₇	—	2	2	no	—
119	C₂×#41×C₆₇	—	4	4	no	—
120	C₂×#41×C₆₇	C₂³	1	2	yes	—
121	C₂×#41×C₆₇	C₂³	1	2	yes	—
122	C₂×#41×C₆₇	C₂³	1	2	yes	—
123	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×#41×C₆₇	C₂³	1	2	yes	—
125	C₂×#41×C₆₇	C₂³	1	2	yes	—
126	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₆₇	—	2	1	no	—
128	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
130	C₂²×D₄×C₆₇	—	2	1	no	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	—	2	1	no	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	#137×C₆₇	—	4	4	no	—
135	#135×C₆₇	—	4	4	no	—
136	#135×C₆₇	—	4	4	no	—
137	#135×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×SD₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×SD₁₆×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×D₈×C₆₇	C₂³	1	2	yes	—
148	C₂×D₈×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂²×C₈×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	C₂³	1	1	yes	characteristic
155	#127×C₆₇	—	2	2	no	—
156	#127×C₆₇	—	2	2	no	—
157	#127×C₆₇	—	2	1	no	—
158	#127×C₆₇	—	2	2	no	—
159	#127×C₆₇	C₂³	1	1	yes	characteristic
160	#127×C₆₇	C₂³	1	1	yes	characteristic
161	#127×C₆₇	C₂³	1	1	yes	characteristic
162	#126×C₆₇	—	2	2	no	—
163	#126×C₆₇	—	2	2	no	—
164	#126×C₆₇	—	2	2	no	—
165	#125×C₆₇	—	2	2	no	—
166	#125×C₆₇	—	2	2	no	—
167	#125×C₆₇	C₂³	1	1	yes	characteristic
168	#125×C₆₇	C₂³	1	1	yes	characteristic
169	#124×C₆₇	—	2	1	no	—
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	C₂³	1	1	yes	characteristic
173	#124×C₆₇	C₂³	1	1	yes	characteristic
174	#123×C₆₇	—	2	2	no	—
175	#123×C₆₇	—	2	1	no	—
176	#123×C₆₇	—	2	2	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	D₄	1	2	yes	—
182	C₂²⋊Q₈×C₆₇	—	2	2	no	—
183	C₂²⋊Q₈×C₆₇	—	2	2	no	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
186	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
189	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
190	#121×C₆₇	—	2	2	no	—
191	#121×C₆₇	—	2	2	no	—
192	#121×C₆₇	—	2	2	no	—
193	#121×C₆₇	—	2	2	no	—
194	#121×C₆₇	—	2	2	no	—
195	#121×C₆₇	—	2	2	no	—
196	#121×C₆₇	—	2	2	no	—
197	#121×C₆₇	—	2	2	no	—
198	#121×C₆₇	—	2	2	no	—
199	#121×C₆₇	—	2	2	no	—
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	D₄	1	2	yes	—
206	#121×C₆₇	C₂³	1	2	yes	—
207	#121×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	C₂³	1	2	yes	—
209	#121×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#121×C₆₇	C₂³	1	2	yes	—
212	#120×C₆₇	—	2	1	no	—
213	#120×C₆₇	—	2	2	no	—
214	#120×C₆₇	—	2	2	no	—
215	#120×C₆₇	—	2	2	no	—
216	#120×C₆₇	D₄	1	2	yes	—
217	C₄×Q₈×C₆₇	—	2	2	no	—
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	#117×C₆₇	—	2	2	no	—
234	#117×C₆₇	—	2	2	no	—
235	#117×C₆₇	C₂³	1	1	yes	characteristic
236	#117×C₆₇	C₂³	1	2	yes	—
237	#117×C₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
240	#107×C₆₇	C₂³	1	2	yes	—
241	#107×C₆₇	C₂³	1	2	yes	—
242	#106×C₆₇	C₂³	1	2	yes	—
243	#106×C₆₇	C₂³	1	2	yes	—
244	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#103×C₆₇	C₂³	1	2	yes	—
249	#103×C₆₇	C₂³	1	2	yes	—
250	#103×C₆₇	C₂³	1	2	yes	—
251	#103×C₆₇	C₂³	1	2	yes	—
252	#103×C₆₇	C₂³	1	2	yes	—
253	#103×C₆₇	C₂³	1	2	yes	—
254	#102×C₆₇	C₂³	1	2	yes	—
255	#102×C₆₇	C₂³	1	2	yes	—
256	#102×C₆₇	C₂³	1	2	yes	—
257	#102×C₆₇	C₂³	1	2	yes	—
258	#102×C₆₇	C₂³	1	2	yes	—
259	#102×C₆₇	C₂³	1	2	yes	—
260	#102×C₆₇	C₂³	1	2	yes	—
261	#102×C₆₇	C₂³	1	2	yes	—
262	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
263	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
264	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
266	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
267	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
268	#97×C₆₇	C₂³	1	1	yes	characteristic
269	#97×C₆₇	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₂⁴×C₆₇	—	2	1	no	—
273	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
274	#41×C₆₇	—	2	4	no	—
275	#41×C₆₇	—	2	4	no	—
276	#41×C₆₇	—	2	4	no	—
277	#41×C₆₇	—	4	2	no	—
278	#41×C₆₇	—	4	2	no	—
279	#41×C₆₇	—	4	2	no	—
280	#41×C₆₇	—	4	2	no	—
281	#41×C₆₇	—	4	2	no	—
282	#41×C₆₇	—	4	8	no	—
283	#41×C₆₇	—	4	2	no	—
284	#41×C₆₇	—	4	2	no	—
285	#41×C₆₇	—	4	2	no	—
286	#41×C₆₇	—	4	2	no	—
287	#41×C₆₇	—	4	8	no	—
288	#41×C₆₇	—	4	4	no	—
289	C₂×Q₈×C₆₇	—	2	4	no	—
290	C₂×Q₈×C₆₇	—	2	1	no	—
291	C₂×Q₈×C₆₇	—	2	2	no	—
292	C₂×Q₈×C₆₇	—	2	4	no	—
293	C₂×Q₈×C₆₇	—	4	2	no	—
294	C₂×Q₈×C₆₇	—	4	4	no	—
295	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
299	C₂×D₄×C₆₇	—	2	1	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	2	no	—
302	C₂×D₄×C₆₇	—	2	2	no	—
303	C₂×D₄×C₆₇	—	2	2	no	—
304	C₂×D₄×C₆₇	—	2	2	no	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	2	2	no	—
307	C₂×D₄×C₆₇	—	2	2	no	—
308	C₂×D₄×C₆₇	—	2	2	no	—
309	C₂×D₄×C₆₇	—	2	2	no	—
310	C₂×D₄×C₆₇	—	2	2	no	—
311	C₂×D₄×C₆₇	—	2	1	no	—
312	C₂×D₄×C₆₇	—	2	2	no	—
313	C₂×D₄×C₆₇	—	2	2	no	—
314	C₂×D₄×C₆₇	—	2	2	no	—
315	C₂×D₄×C₆₇	—	4	2	no	—
316	C₂×D₄×C₆₇	—	4	4	no	—
317	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
319	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₆₇	—	2	1	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	1	no	—
330	C₂²×C₄×C₆₇	—	2	2	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	—	2	2	no	—
335	C₂²×C₄×C₆₇	—	4	2	no	—
336	C₂²×C₄×C₆₇	—	4	4	no	—
337	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
342	Q₁₆×C₆₇	—	2	4	no	—
343	Q₁₆×C₆₇	—	2	4	no	—
344	Q₁₆×C₆₇	—	4	2	no	—
345	SD₁₆×C₆₇	—	2	4	no	—
346	SD₁₆×C₆₇	—	2	4	no	—
347	SD₁₆×C₆₇	—	4	2	no	—
348	SD₁₆×C₆₇	—	4	2	no	—
349	SD₁₆×C₆₇	—	4	2	no	—
350	SD₁₆×C₆₇	—	4	2	no	—
351	D₈×C₆₇	—	4	2	no	—
352	D₈×C₆₇	—	4	2	no	—
353	D₈×C₆₇	—	4	2	no	—
354	M₁₆×C₆₇	—	4	2	no	—
355	C₂×C₈×C₆₇	—	4	2	no	—
356	C₂×C₈×C₆₇	—	4	2	no	—
357	C₂×C₈×C₆₇	—	4	2	no	—
358	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
359	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
360	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
361	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	2	no	—
364	C₄⋊C₄×C₆₇	—	2	2	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	2	no	—
367	C₄⋊C₄×C₆₇	—	2	2	no	—
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	2	no	—
372	C₄⋊C₄×C₆₇	—	2	2	no	—
373	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	2	no	—
384	C₂²⋊C₄×C₆₇	—	2	2	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	2	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	—	2	2	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₄²×C₆₇	—	2	2	no	—
400	C₄²×C₆₇	—	2	2	no	—
401	C₄²×C₆₇	—	2	2	no	—
402	C₄²×C₆₇	—	2	2	no	—
403	C₄²×C₆₇	—	2	1	no	—
404	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂³×C₆₇	—	2	2	no	—
407	C₂³×C₆₇	—	2	1	no	—
408	C₂³×C₆₇	—	2	1	no	—
409	C₂³×C₆₇	—	2	1	no	—
410	C₂³×C₆₇	—	4	1	no	—
411	C₂³×C₆₇	—	4	2	no	—
412	C₂³×C₆₇	—	4	2	no	—
413	C₂³×C₆₇	—	8	2	no	—
414	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
417	Q₈×C₆₇	—	2	4	no	—
418	Q₈×C₆₇	—	2	2	no	—
419	Q₈×C₆₇	—	2	2	no	—
420	Q₈×C₆₇	—	2	2	no	—
421	Q₈×C₆₇	—	2	2	no	—
422	Q₈×C₆₇	—	4	1	no	—
423	Q₈×C₆₇	—	4	4	no	—
424	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
425	D₄×C₆₇	—	2	2	no	—
426	D₄×C₆₇	—	2	2	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	2	2	no	—
429	D₄×C₆₇	—	2	2	no	—
430	D₄×C₆₇	—	4	2	no	—
431	D₄×C₆₇	—	4	2	no	—
432	D₄×C₆₇	—	4	1	no	—
433	D₄×C₆₇	—	4	2	no	—
434	D₄×C₆₇	—	4	4	no	—
435	D₄×C₆₇	—	4	4	no	—
436	D₄×C₆₇	—	4	4	no	—
437	D₄×C₆₇	—	4	2	no	—
438	D₄×C₆₇	—	4	2	no	—
439	D₄×C₆₇	—	8	2	no	—
440	D₄×C₆₇	—	8	2	no	—
441	D₄×C₆₇	—	8	2	no	—
442	D₄×C₆₇	—	8	2	no	—
443	D₄×C₆₇	—	8	2	no	—
444	D₄×C₆₇	—	8	2	no	—
445	D₄×C₆₇	—	8	2	no	—
446	D₄×C₆₇	—	8	2	no	—
447	D₄×C₆₇	—	8	2	no	—
448	D₄×C₆₇	—	8	2	no	—
449	D₄×C₆₇	—	8	2	no	—
450	C₂×C₄×C₆₇	—	2	4	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	4	1	no	—
463	C₂×C₄×C₆₇	—	4	2	no	—
464	C₂×C₄×C₆₇	—	4	4	no	—
465	C₂×C₄×C₆₇	—	4	4	no	—
466	C₂×C₄×C₆₇	—	4	4	no	—
467	C₂×C₄×C₆₇	—	4	4	no	—
468	C₂×C₄×C₆₇	—	4	2	no	—
469	C₂×C₄×C₆₇	—	8	2	no	—
470	C₂×C₄×C₆₇	—	8	2	no	—
471	C₂×C₄×C₆₇	—	8	2	no	—
472	C₂×C₄×C₆₇	—	8	2	no	—
473	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
479	C₈×C₆₇	—	2	2	no	—
480	C₈×C₆₇	—	2	2	no	—
481	C₈×C₆₇	—	2	2	no	—
482	C₈×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	1	no	—
489	C₂²×C₆₇	—	2	2	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	—	4	2	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	4	1	no	—
497	C₂²×C₆₇	—	4	1	no	—
498	C₂²×C₆₇	—	4	1	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	8	2	no	—
501	C₂²×C₆₇	—	8	4	no	—
502	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	4	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	1	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	—	4	2	no	—
510	C₄×C₆₇	—	4	2	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	1	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
515	#61637	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
516	C₂×C₆₇	—	4	2	no	—
517	C₂×C₆₇	—	4	2	no	—
518	C₂×C₆₇	—	4	1	no	—
519	C₂×C₆₇	—	8	2	no	—
520	C₂×C₆₇	—	8	1	no	—
521	C₂×C₆₇	—	8	1	no	—
522	C₂×C₆₇	—	8	1	no	—
523	C₂×C₆₇	#3484	1	1	yes	characteristic
524	C₂×C₆₇	#3584	1	2	yes	—
525	#3539	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#3317	C₂×C₆₇	1	2	yes	complemented
528	#3309	C₂×C₆₇	1	2	yes	complemented
529	#3301	C₂×C₆₇	1	2	yes	complemented
530	#3300	C₂×C₆₇	1	2	yes	complemented
531	#3287	C₂×C₆₇	1	2	yes	complemented
532	#3284	C₂×C₆₇	1	2	yes	complemented
533	#3271	C₂×C₆₇	1	2	yes	complemented
534	#3269	C₂×C₆₇	1	2	yes	complemented
535	#3222	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#3220	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#3198	C₂×C₆₇	1	2	yes	complemented
538	#3191	C₂×C₆₇	1	2	yes	complemented
539	#3127	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#3126	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#3013	C₂×C₆₇	1	2	yes	complemented
542	#3002	C₂×C₆₇	1	2	yes	complemented
543	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₆₇	#61637	1	1	yes	characteristic, direct product factor, Sylow
545	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
546	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
547	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
548	C₂×#135	C₂²×C₆₇	1	2	yes	—
549	C₂×#135	C₂²×C₆₇	1	2	yes	—
550	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
551	#560	—	2	2	no	—
552	#553	—	2	2	no	—
553	#553	C₂²×C₆₇	1	2	yes	complemented
554	#552	C₂²×C₆₇	1	2	yes	complemented
555	#550	—	2	2	no	—
556	#550	C₂²×C₆₇	1	2	yes	—
557	#550	C₂²×C₆₇	1	2	yes	—
558	#550	C₂²×C₆₇	1	2	yes	complemented
559	#548	—	2	2	no	—
560	#548	C₂²×C₆₇	1	2	yes	—
561	#548	C₂²×C₆₇	1	2	yes	—
562	#547	C₂²×C₆₇	1	2	yes	complemented
563	#541	C₂²×C₆₇	1	1	yes	characteristic
564	#540	—	2	2	no	—
565	#540	C₂²×C₆₇	1	1	yes	characteristic
566	#539	—	2	2	no	—
567	#537	C₂²×C₆₇	1	2	yes	—
568	#535	—	2	2	no	—
569	#535	C₂²×C₆₇	1	1	yes	characteristic
570	#535	C₂²×C₆₇	1	1	yes	characteristic
571	#525	—	2	2	no	—
572	#525	C₂²×C₆₇	1	1	yes	characteristic
573	#525	C₂²×C₆₇	1	2	yes	—
574	#525	C₂²×C₆₇	1	1	yes	characteristic
575	#519	C₂²×C₆₇	1	1	yes	characteristic
576	#497	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	#496	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#490	C₂²×C₆₇	1	1	yes	characteristic, complemented
581	#490	C₂²×C₆₇	1	1	yes	characteristic, complemented
582	#488	C₂²×C₆₇	1	1	yes	characteristic, complemented
583	#488	C₂²×C₆₇	1	1	yes	characteristic, complemented
584	#485	C₂²×C₆₇	1	2	yes	—
585	#485	C₂²×C₆₇	1	2	yes	complemented
586	#482	C₂²×C₆₇	1	2	yes	—
587	#482	C₂²×C₆₇	1	2	yes	complemented
588	#481	C₂²×C₆₇	1	2	yes	complemented
589	#480	C₂²×C₆₇	1	2	yes	complemented
590	#479	C₂²×C₆₇	1	2	yes	complemented
591	#479	C₂²×C₆₇	1	2	yes	complemented
592	#469	C₂²×C₆₇	1	2	yes	complemented
593	#468	C₂²×C₆₇	1	2	yes	complemented
594	#467	C₂²×C₆₇	1	2	yes	complemented
595	#466	C₂²×C₆₇	1	2	yes	complemented
596	#466	C₂²×C₆₇	1	2	yes	complemented
597	#465	C₂²×C₆₇	1	2	yes	complemented
598	#465	C₂²×C₆₇	1	2	yes	complemented
599	#465	C₂²×C₆₇	1	2	yes	complemented
600	#464	C₂²×C₆₇	1	2	yes	complemented
601	#463	C₂²×C₆₇	1	2	yes	complemented
602	#462	C₂²×C₆₇	1	2	yes	complemented
603	#460	C₂²×C₆₇	1	2	yes	complemented
604	#460	C₂²×C₆₇	1	2	yes	complemented
605	#459	C₂²×C₆₇	1	2	yes	complemented
606	#452	C₂²×C₆₇	1	2	yes	—
607	#452	C₂²×C₆₇	1	2	yes	—
608	#452	C₂²×C₆₇	1	2	yes	—
609	#452	C₂²×C₆₇	1	2	yes	complemented
610	#452	C₂²×C₆₇	1	2	yes	complemented
611	#451	C₂²×C₆₇	1	2	yes	—
612	#451	C₂²×C₆₇	1	2	yes	complemented
613	#450	C₂²×C₆₇	1	2	yes	—
614	#449	C₂²×C₆₇	1	2	yes	—
615	#449	C₂²×C₆₇	1	2	yes	—
616	#449	C₂²×C₆₇	1	2	yes	—
617	#449	C₂²×C₆₇	1	2	yes	complemented
618	#449	C₂²×C₆₇	1	2	yes	complemented
619	#449	C₂²×C₆₇	1	2	yes	complemented
620	#449	C₂²×C₆₇	1	2	yes	complemented
621	#448	C₂²×C₆₇	1	2	yes	—
622	#448	C₂²×C₆₇	1	2	yes	complemented
623	#447	C₂²×C₆₇	1	2	yes	—
624	#441	C₂²×C₆₇	1	2	yes	complemented
625	#440	C₂²×C₆₇	1	2	yes	complemented
626	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
627	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
628	#435	C₂²×C₆₇	1	2	yes	complemented
629	#435	C₂²×C₆₇	1	2	yes	complemented
630	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
631	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
632	#433	C₂²×C₆₇	1	1	yes	characteristic
633	#433	C₂²×C₆₇	1	1	yes	characteristic
634	#417	C₂²×C₆₇	1	2	yes	complemented
635	#416	C₂²×C₆₇	1	2	yes	—
636	#416	C₂²×C₆₇	1	2	yes	—
637	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
638	#408	C₂²×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
640	2₋¹⁺⁴	—	4	4	no	—
641	C₂×#41	—	2	2	no	—
642	C₂×#41	—	2	1	no	—
643	C₂×#41	—	2	2	no	—
644	C₂×#41	—	4	4	no	—
645	C₂×#41	C₂³×C₆₇	1	2	yes	—
646	C₂×#41	C₂³×C₆₇	1	2	yes	—
647	C₂×#41	C₂³×C₆₇	1	2	yes	—
648	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×#41	C₂³×C₆₇	1	2	yes	—
650	C₂×#41	C₂³×C₆₇	1	2	yes	—
651	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
652	C₂²×Q₈	—	2	1	no	—
653	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂³×C₄	—	2	1	no	—
658	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
659	#137	—	4	4	no	—
660	#135	—	4	4	no	—
661	#135	—	4	4	no	—
662	#135	—	4	4	no	—
663	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
666	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
672	C₂×D₈	C₂³×C₆₇	1	2	yes	—
673	C₂×D₈	C₂³×C₆₇	1	2	yes	—
674	C₂×D₈	C₂³×C₆₇	1	2	yes	—
675	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
676	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
678	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
679	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
680	#127	—	2	2	no	—
681	#127	—	2	2	no	—
682	#127	—	2	1	no	—
683	#127	—	2	2	no	—
684	#127	C₂³×C₆₇	1	1	yes	characteristic
685	#127	C₂³×C₆₇	1	1	yes	characteristic
686	#127	C₂³×C₆₇	1	1	yes	characteristic
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#125	—	2	2	no	—
691	#125	—	2	2	no	—
692	#125	C₂³×C₆₇	1	1	yes	characteristic
693	#125	C₂³×C₆₇	1	1	yes	characteristic
694	#124	—	2	1	no	—
695	#124	—	2	2	no	—
696	#124	—	2	2	no	—
697	#124	C₂³×C₆₇	1	1	yes	characteristic
698	#124	C₂³×C₆₇	1	1	yes	characteristic
699	#123	—	2	2	no	—
700	#123	—	2	1	no	—
701	#123	—	2	2	no	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	D₄×C₆₇	1	2	yes	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
713	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
714	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	2	no	—
730	#121	D₄×C₆₇	1	2	yes	—
731	#121	C₂³×C₆₇	1	2	yes	—
732	#121	C₂³×C₆₇	1	2	yes	—
733	#121	C₂³×C₆₇	1	2	yes	—
734	#121	C₂³×C₆₇	1	2	yes	—
735	#121	C₂³×C₆₇	1	2	yes	—
736	#121	C₂³×C₆₇	1	2	yes	—
737	#120	—	2	1	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	—	2	2	no	—
741	#120	D₄×C₆₇	1	2	yes	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
744	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
745	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	C₂³×C₆₇	1	2	yes	—
756	C₄×D₄	C₂³×C₆₇	1	2	yes	—
757	C₄×D₄	C₂³×C₆₇	1	2	yes	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	C₂³×C₆₇	1	1	yes	characteristic
761	#117	C₂³×C₆₇	1	2	yes	—
762	#117	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄⋊C₄	—	2	2	no	—
764	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
765	#107	C₂³×C₆₇	1	2	yes	—
766	#107	C₂³×C₆₇	1	2	yes	—
767	#106	C₂³×C₆₇	1	2	yes	—
768	#106	C₂³×C₆₇	1	2	yes	—
769	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
770	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
771	#103	C₂³×C₆₇	1	2	yes	—
772	#103	C₂³×C₆₇	1	2	yes	—
773	#103	C₂³×C₆₇	1	2	yes	—
774	#103	C₂³×C₆₇	1	2	yes	—
775	#103	C₂³×C₆₇	1	2	yes	—
776	#103	C₂³×C₆₇	1	2	yes	—
777	#103	C₂³×C₆₇	1	2	yes	—
778	#103	C₂³×C₆₇	1	2	yes	—
779	#102	C₂³×C₆₇	1	2	yes	—
780	#102	C₂³×C₆₇	1	2	yes	—
781	#102	C₂³×C₆₇	1	2	yes	—
782	#102	C₂³×C₆₇	1	2	yes	—
783	#102	C₂³×C₆₇	1	2	yes	—
784	#102	C₂³×C₆₇	1	2	yes	—
785	#102	C₂³×C₆₇	1	2	yes	—
786	#102	C₂³×C₆₇	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
793	#97	C₂³×C₆₇	1	1	yes	characteristic
794	#97	C₂³×C₆₇	1	1	yes	characteristic
795	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₂⁴	—	2	1	no	—
798	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
799	#41	—	2	4	no	—
800	#41	—	2	4	no	—
801	#41	—	2	4	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	4	8	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	4	8	no	—
813	#41	—	4	4	no	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	2	4	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×Q₈	—	4	4	no	—
820	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
823	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	4	no	—
842	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
843	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
844	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
848	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
849	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	4	no	—
862	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
863	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	2	4	no	—
869	Q₁₆	—	4	2	no	—
870	SD₁₆	—	2	4	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	D₈	—	4	2	no	—
877	D₈	—	4	2	no	—
878	D₈	—	4	2	no	—
879	M₁₆	—	4	2	no	—
880	C₂×C₈	—	4	2	no	—
881	C₂×C₈	—	4	2	no	—
882	C₂×C₈	—	4	2	no	—
883	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
884	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
885	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
886	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
900	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
903	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
904	C₂²⋊C₄	—	2	1	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	1	no	—
929	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
930	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	4	1	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	2	no	—
939	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
940	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
941	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
942	Q₈	—	2	4	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	4	1	no	—
948	Q₈	—	4	4	no	—
949	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
950	D₄	—	2	2	no	—
951	D₄	—	2	2	no	—
952	D₄	—	2	2	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	2	no	—
955	D₄	—	4	1	no	—
956	D₄	—	4	2	no	—
957	D₄	—	4	2	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	2	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	2	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	8	2	no	—
1026	C₂²	—	8	4	no	—
1027	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	8	1	no	—
1044	C₂	—	8	1	no	—
1045	C₂	—	8	2	no	—
1046	C₂	—	8	1	no	—
1047	C₂	C₆₇×#3484	1	1	yes	characteristic
1048	C₂	C₆₇×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3539	C₂	semidirect
2. C₆₇×#3487	C₂	semidirect
3. C₆₇×#3317	C₂	semidirect
4. C₆₇×#3309	C₂	semidirect
5. C₆₇×#3301	C₂	semidirect
6. C₆₇×#3300	C₂	semidirect
7. C₆₇×#3287	C₂	semidirect
8. C₆₇×#3284	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3269	C₂	semidirect
11. C₆₇×#3222	C₂	semidirect
12. C₆₇×#3220	C₂	semidirect
13. C₆₇×#3198	C₂	semidirect
14. C₆₇×#3191	C₂	semidirect
15. C₆₇×#3127	C₂	semidirect
16. C₆₇×#3126	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3002	C₂	semidirect
19. C₆₇×#2977	C₂	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
28. #553×C₆₇	C₂²	semidirect
29. #552×C₆₇	C₂²	semidirect
33. #550×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
51. #497×C₆₇	C₂²	semidirect
52. #496×C₆₇	C₂²	semidirect
53. #493×C₆₇	C₂²	semidirect
54. #492×C₆₇	C₂²	semidirect
55. #490×C₆₇	C₂²	semidirect
56. #490×C₆₇	C₂²	semidirect
57. #488×C₆₇	C₂²	semidirect
58. #488×C₆₇	C₂²	semidirect
60. #485×C₆₇	C₂²	semidirect
62. #482×C₆₇	C₂²	semidirect
63. #481×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #479×C₆₇	C₂²	semidirect
67. #469×C₆₇	C₂²	semidirect
68. #468×C₆₇	C₂²	semidirect
69. #467×C₆₇	C₂²	semidirect
70. #466×C₆₇	C₂²	semidirect
71. #466×C₆₇	C₂²	semidirect
72. #465×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #465×C₆₇	C₂²	semidirect
75. #464×C₆₇	C₂²	semidirect
76. #463×C₆₇	C₂²	semidirect
77. #462×C₆₇	C₂²	semidirect
78. #460×C₆₇	C₂²	semidirect
79. #460×C₆₇	C₂²	semidirect
80. #459×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
87. #451×C₆₇	C₂²	semidirect
92. #449×C₆₇	C₂²	semidirect
93. #449×C₆₇	C₂²	semidirect
94. #449×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
97. #448×C₆₇	C₂²	semidirect
99. #441×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. #435×C₆₇	C₂²	semidirect
104. #435×C₆₇	C₂²	semidirect
105. C₈×D₄×C₆₇	C₂²	semidirect
106. C₈×D₄×C₆₇	C₂²	semidirect
109. #417×C₆₇	C₂²	semidirect
112. C₂×#103×C₆₇	C₂²	semidirect
515. #61637	C₆₇	direct (N × H)
525. #3539	C₂×C₆₇	semidirect
526. #3487	C₂×C₆₇	semidirect
527. #3317	C₂×C₆₇	semidirect
528. #3309	C₂×C₆₇	semidirect
529. #3301	C₂×C₆₇	semidirect
530. #3300	C₂×C₆₇	semidirect
531. #3287	C₂×C₆₇	semidirect
532. #3284	C₂×C₆₇	semidirect
533. #3271	C₂×C₆₇	semidirect
534. #3269	C₂×C₆₇	semidirect
535. #3222	C₂×C₆₇	semidirect
536. #3220	C₂×C₆₇	semidirect
537. #3198	C₂×C₆₇	semidirect
538. #3191	C₂×C₆₇	semidirect
539. #3127	C₂×C₆₇	semidirect
540. #3126	C₂×C₆₇	semidirect
541. #3013	C₂×C₆₇	semidirect
542. #3002	C₂×C₆₇	semidirect
543. #2977	C₂×C₆₇	semidirect
544. C₆₇	#61637	direct (N × H)
547. C₂×#137	C₂²×C₆₇	semidirect
550. C₂×#135	C₂²×C₆₇	semidirect
553. #553	C₂²×C₆₇	semidirect
554. #552	C₂²×C₆₇	semidirect
558. #550	C₂²×C₆₇	semidirect
562. #547	C₂²×C₆₇	semidirect
576. #497	C₂²×C₆₇	semidirect
577. #496	C₂²×C₆₇	semidirect
578. #493	C₂²×C₆₇	semidirect
579. #492	C₂²×C₆₇	semidirect
580. #490	C₂²×C₆₇	semidirect
581. #490	C₂²×C₆₇	semidirect
582. #488	C₂²×C₆₇	semidirect
583. #488	C₂²×C₆₇	semidirect
585. #485	C₂²×C₆₇	semidirect
587. #482	C₂²×C₆₇	semidirect
588. #481	C₂²×C₆₇	semidirect
589. #480	C₂²×C₆₇	semidirect
590. #479	C₂²×C₆₇	semidirect
591. #479	C₂²×C₆₇	semidirect
592. #469	C₂²×C₆₇	semidirect
593. #468	C₂²×C₆₇	semidirect
594. #467	C₂²×C₆₇	semidirect
595. #466	C₂²×C₆₇	semidirect
596. #466	C₂²×C₆₇	semidirect
597. #465	C₂²×C₆₇	semidirect
598. #465	C₂²×C₆₇	semidirect
599. #465	C₂²×C₆₇	semidirect
600. #464	C₂²×C₆₇	semidirect
601. #463	C₂²×C₆₇	semidirect
602. #462	C₂²×C₆₇	semidirect
603. #460	C₂²×C₆₇	semidirect
604. #460	C₂²×C₆₇	semidirect
605. #459	C₂²×C₆₇	semidirect
609. #452	C₂²×C₆₇	semidirect
610. #452	C₂²×C₆₇	semidirect
612. #451	C₂²×C₆₇	semidirect
617. #449	C₂²×C₆₇	semidirect
618. #449	C₂²×C₆₇	semidirect
619. #449	C₂²×C₆₇	semidirect
620. #449	C₂²×C₆₇	semidirect
622. #448	C₂²×C₆₇	semidirect
624. #441	C₂²×C₆₇	semidirect
625. #440	C₂²×C₆₇	semidirect
626. C₄×Q₁₆	C₂²×C₆₇	semidirect
627. C₄×SD₁₆	C₂²×C₆₇	semidirect
628. #435	C₂²×C₆₇	semidirect
629. #435	C₂²×C₆₇	semidirect
630. C₈×D₄	C₂²×C₆₇	semidirect
631. C₈×D₄	C₂²×C₆₇	semidirect
634. #417	C₂²×C₆₇	semidirect
637. C₂×#103	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×#3539	2
C₆₇×#3487	2
C₆₇×#3317	2
C₆₇×#3309	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3287	2
C₆₇×#3284	2
C₆₇×#3271	2
C₆₇×#3269	2
C₆₇×#3222	2
C₆₇×#3220	2
C₆₇×#3198	2
C₆₇×#3191	2
C₆₇×#3127	2
C₆₇×#3126	2
C₆₇×#3013	2
C₆₇×#3002	2
C₆₇×#2977	2
#61637	67

Subgroups — C67×#61637 #30740888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61637 #30740888