Subgroups — C₆₇×#61243 #30740494

Order 17152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3349	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3348	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3345	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3344	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3091	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3091	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3076	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
23	#556×C₆₇	C₂²	1	2	yes	—
24	#555×C₆₇	C₂²	1	2	yes	—
25	#554×C₆₇	C₂²	1	2	yes	—
26	#553×C₆₇	C₂²	1	2	yes	—
27	#553×C₆₇	C₂²	1	2	yes	—
28	#552×C₆₇	—	2	2	no	—
29	#552×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	C₂²	1	2	yes	—
31	#551×C₆₇	—	2	2	no	—
32	#551×C₆₇	—	2	2	no	—
33	#547×C₆₇	C₂²	1	2	yes	—
34	#546×C₆₇	—	2	2	no	—
35	#533×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	—	2	2	no	—
37	#529×C₆₇	—	2	2	no	—
38	#529×C₆₇	—	2	2	no	—
39	#525×C₆₇	C₂²	1	2	yes	—
40	#525×C₆₇	C₂²	1	2	yes	—
41	C₄×#41×C₆₇	—	2	2	no	—
42	C₄×#41×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₇	C₂²	1	2	yes	—
45	C₂×#117×C₆₇	C₂²	1	2	yes	—
46	#501×C₆₇	C₂²	1	2	yes	complemented
47	#501×C₆₇	C₂²	1	2	yes	complemented
48	#501×C₆₇	C₂²	1	2	yes	complemented
49	#501×C₆₇	C₂²	1	2	yes	complemented
50	#485×C₆₇	C₂²	1	2	yes	complemented
51	#485×C₆₇	C₂²	1	2	yes	complemented
52	#485×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	complemented
54	#484×C₆₇	C₂²	1	2	yes	complemented
55	#484×C₆₇	C₂²	1	2	yes	complemented
56	#483×C₆₇	C₂²	1	2	yes	complemented
57	#483×C₆₇	C₂²	1	2	yes	complemented
58	#482×C₆₇	C₂²	1	2	yes	complemented
59	#482×C₆₇	C₂²	1	2	yes	complemented
60	#482×C₆₇	C₂²	1	2	yes	complemented
61	#482×C₆₇	C₂²	1	2	yes	complemented
62	#481×C₆₇	C₂²	1	2	yes	complemented
63	#481×C₆₇	C₂²	1	2	yes	complemented
64	#480×C₆₇	C₂²	1	2	yes	complemented
65	#480×C₆₇	C₂²	1	2	yes	complemented
66	#479×C₆₇	C₂²	1	2	yes	complemented
67	#479×C₆₇	C₂²	1	2	yes	complemented
68	#478×C₆₇	C₂²	1	2	yes	complemented
69	#478×C₆₇	C₂²	1	2	yes	complemented
70	#477×C₆₇	C₂²	1	2	yes	complemented
71	#476×C₆₇	C₂²	1	2	yes	complemented
72	#475×C₆₇	C₂²	1	2	yes	complemented
73	#474×C₆₇	C₂²	1	2	yes	complemented
74	#470×C₆₇	C₂²	1	2	yes	complemented
75	#469×C₆₇	C₂²	1	2	yes	complemented
76	#468×C₆₇	C₂²	1	2	yes	complemented
77	#468×C₆₇	C₂²	1	2	yes	complemented
78	#467×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#467×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#466×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#466×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#465×C₆₇	C₂²	1	2	yes	complemented
83	#465×C₆₇	C₂²	1	2	yes	complemented
84	#442×C₆₇	C₂²	1	2	yes	complemented
85	#441×C₆₇	C₂²	1	2	yes	complemented
86	#440×C₆₇	C₂²	1	2	yes	complemented
87	#440×C₆₇	C₂²	1	2	yes	complemented
88	#435×C₆₇	C₂²	1	2	yes	—
89	#435×C₆₇	C₂²	1	2	yes	—
90	#435×C₆₇	C₂²	1	2	yes	—
91	#435×C₆₇	C₂²	1	2	yes	—
92	#428×C₆₇	C₂²	1	2	yes	complemented
93	#428×C₆₇	C₂²	1	2	yes	complemented
94	#428×C₆₇	C₂²	1	2	yes	complemented
95	#428×C₆₇	C₂²	1	2	yes	complemented
96	#427×C₆₇	C₂²	1	1	yes	characteristic
97	#427×C₆₇	C₂²	1	1	yes	characteristic
98	#427×C₆₇	C₂²	1	2	yes	—
99	#427×C₆₇	C₂²	1	2	yes	—
100	#427×C₆₇	C₂²	1	2	yes	—
101	#427×C₆₇	C₂²	1	1	yes	characteristic
102	#427×C₆₇	C₂²	1	2	yes	complemented
103	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
108	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
109	#416×C₆₇	C₂²	1	2	yes	—
110	#416×C₆₇	C₂²	1	2	yes	—
111	#416×C₆₇	C₂²	1	2	yes	—
112	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	#135×C₆₇	—	2	4	no	—
121	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₆₇	—	2	4	no	—
125	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂²×C₈×C₆₇	—	2	4	no	—
128	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#125×C₆₇	—	2	2	no	—
145	#125×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	2	no	—
147	#125×C₆₇	C₂³	1	2	yes	—
148	#125×C₆₇	C₂³	1	2	yes	—
149	#124×C₆₇	—	2	2	no	—
150	#124×C₆₇	—	2	2	no	—
151	#124×C₆₇	—	2	2	no	—
152	#123×C₆₇	—	2	2	no	—
153	#123×C₆₇	—	2	2	no	—
154	#123×C₆₇	—	2	2	no	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	2	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	C₂²⋊Q₈×C₆₇	—	2	2	no	—
161	C₂²⋊Q₈×C₆₇	—	2	2	no	—
162	C₂²⋊Q₈×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	C₂³	1	2	yes	—
173	#121×C₆₇	C₂³	1	2	yes	—
174	#121×C₆₇	C₂³	1	2	yes	—
175	#121×C₆₇	C₂³	1	2	yes	—
176	#120×C₆₇	—	2	2	no	—
177	#120×C₆₇	—	2	2	no	—
178	C₄×Q₈×C₆₇	—	2	2	no	—
179	C₄×Q₈×C₆₇	—	2	2	no	—
180	C₄×Q₈×C₆₇	—	2	2	no	—
181	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
182	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
183	C₄×D₄×C₆₇	—	2	2	no	—
184	C₄×D₄×C₆₇	—	2	2	no	—
185	C₄×D₄×C₆₇	—	2	2	no	—
186	C₄×D₄×C₆₇	—	2	2	no	—
187	C₄×D₄×C₆₇	—	2	2	no	—
188	C₄×D₄×C₆₇	—	2	2	no	—
189	C₄×D₄×C₆₇	—	2	2	no	—
190	C₄×D₄×C₆₇	—	2	2	no	—
191	C₄×D₄×C₆₇	—	2	2	no	—
192	C₄×D₄×C₆₇	D₄	1	2	yes	—
193	C₄×D₄×C₆₇	D₄	1	2	yes	—
194	C₄×D₄×C₆₇	C₂³	1	2	yes	—
195	C₄×D₄×C₆₇	C₂³	1	2	yes	—
196	C₄×D₄×C₆₇	C₂³	1	2	yes	—
197	C₄×D₄×C₆₇	C₂³	1	2	yes	—
198	#117×C₆₇	—	2	2	no	—
199	#117×C₆₇	—	2	2	no	—
200	#117×C₆₇	—	2	2	no	—
201	#117×C₆₇	—	2	2	no	—
202	#117×C₆₇	—	2	2	no	—
203	#117×C₆₇	—	2	2	no	—
204	#117×C₆₇	—	2	2	no	—
205	#117×C₆₇	—	2	2	no	—
206	#117×C₆₇	C₂³	1	2	yes	—
207	#117×C₆₇	C₂³	1	2	yes	—
208	#117×C₆₇	C₂³	1	2	yes	—
209	#117×C₆₇	C₂³	1	2	yes	—
210	#117×C₆₇	C₂³	1	2	yes	—
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	—	2	2	no	—
223	C₂×C₄²×C₆₇	—	2	2	no	—
224	C₂×C₄²×C₆₇	—	2	2	no	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	#107×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	1	yes	characteristic
228	#107×C₆₇	C₂³	1	1	yes	characteristic
229	#107×C₆₇	C₂³	1	1	yes	characteristic
230	#107×C₆₇	C₂³	1	2	yes	—
231	#107×C₆₇	C₂³	1	2	yes	—
232	#107×C₆₇	C₂³	1	2	yes	—
233	#107×C₆₇	C₂³	1	2	yes	—
234	#107×C₆₇	C₂³	1	2	yes	—
235	#107×C₆₇	C₂³	1	2	yes	—
236	#107×C₆₇	C₂³	1	1	yes	characteristic
237	#107×C₆₇	C₂³	1	1	yes	characteristic
238	#106×C₆₇	C₂³	1	2	yes	—
239	#106×C₆₇	C₂³	1	2	yes	—
240	#106×C₆₇	C₂³	1	2	yes	—
241	#106×C₆₇	C₂³	1	2	yes	—
242	#106×C₆₇	C₂³	1	2	yes	—
243	#106×C₆₇	C₂³	1	2	yes	—
244	#106×C₆₇	C₂³	1	2	yes	—
245	#106×C₆₇	C₂³	1	2	yes	—
246	#106×C₆₇	C₂³	1	2	yes	—
247	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
248	C₄⋊C₈×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	#103×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	C₂²⋊C₈×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	#97×C₆₇	C₂³	1	2	yes	—
266	#97×C₆₇	C₂³	1	2	yes	—
267	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
269	#41×C₆₇	—	2	4	no	—
270	#41×C₆₇	—	2	4	no	—
271	#41×C₆₇	—	4	8	no	—
272	C₂×Q₈×C₆₇	—	2	2	no	—
273	C₂×Q₈×C₆₇	—	2	2	no	—
274	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	4	2	no	—
281	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	2	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	Q₁₆×C₆₇	—	2	2	no	—
307	SD₁₆×C₆₇	—	2	4	no	—
308	D₈×C₆₇	—	2	2	no	—
309	M₁₆×C₆₇	—	2	4	no	—
310	M₁₆×C₆₇	—	2	4	no	—
311	C₂×C₈×C₆₇	—	2	2	no	—
312	C₂×C₈×C₆₇	—	2	2	no	—
313	C₂×C₈×C₆₇	—	2	2	no	—
314	C₂×C₈×C₆₇	—	2	2	no	—
315	C₂×C₈×C₆₇	—	2	2	no	—
316	C₂×C₈×C₆₇	—	2	2	no	—
317	C₂×C₈×C₆₇	—	2	2	no	—
318	C₂×C₈×C₆₇	#41	1	4	yes	complemented
319	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
321	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	2	no	—
339	C₄⋊C₄×C₆₇	—	2	2	no	—
340	C₄⋊C₄×C₆₇	—	2	2	no	—
341	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	—	2	2	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	2	no	—
366	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	2	2	no	—
372	C₄²×C₆₇	—	2	2	no	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	—	2	2	no	—
375	C₄²×C₆₇	—	2	2	no	—
376	C₄²×C₆₇	—	2	2	no	—
377	C₄²×C₆₇	—	2	2	no	—
378	C₄²×C₆₇	—	2	2	no	—
379	C₄²×C₆₇	C₂×D₄	1	2	yes	—
380	C₄²×C₆₇	C₂⁴	1	2	yes	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	2	no	—
385	C₂³×C₆₇	—	4	1	no	—
386	C₂³×C₆₇	—	4	1	no	—
387	C₂³×C₆₇	—	4	1	no	—
388	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
390	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	Q₈×C₆₇	—	2	2	no	—
393	Q₈×C₆₇	—	2	2	no	—
394	Q₈×C₆₇	—	4	4	no	—
395	Q₈×C₆₇	—	8	2	no	—
396	D₄×C₆₇	—	2	4	no	—
397	D₄×C₆₇	—	2	2	no	—
398	D₄×C₆₇	—	2	2	no	—
399	D₄×C₆₇	—	4	2	no	—
400	D₄×C₆₇	—	4	4	no	—
401	D₄×C₆₇	—	4	4	no	—
402	D₄×C₆₇	—	4	4	no	—
403	D₄×C₆₇	—	8	2	no	—
404	D₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	4	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	4	1	no	—
424	C₂×C₄×C₆₇	—	4	1	no	—
425	C₂×C₄×C₆₇	—	4	4	no	—
426	C₂×C₄×C₆₇	—	4	4	no	—
427	C₂×C₄×C₆₇	—	4	4	no	—
428	C₂×C₄×C₆₇	—	4	4	no	—
429	C₂×C₄×C₆₇	—	8	2	no	—
430	C₂×C₄×C₆₇	—	8	2	no	—
431	C₂×C₄×C₆₇	—	8	2	no	—
432	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
439	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
440	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
441	C₈×C₆₇	—	2	1	no	—
442	C₈×C₆₇	—	2	1	no	—
443	C₈×C₆₇	—	2	2	no	—
444	C₈×C₆₇	—	2	2	no	—
445	C₈×C₆₇	C₂×#41	1	2	yes	—
446	C₈×C₆₇	C₂×#41	1	2	yes	—
447	C₂²×C₆₇	—	2	1	no	—
448	C₂²×C₆₇	—	2	1	no	—
449	C₂²×C₆₇	—	2	1	no	—
450	C₂²×C₆₇	—	2	1	no	—
451	C₂²×C₆₇	—	2	2	no	—
452	C₂²×C₆₇	—	2	1	no	—
453	C₂²×C₆₇	—	2	1	no	—
454	C₂²×C₆₇	—	2	2	no	—
455	C₂²×C₆₇	—	2	2	no	—
456	C₂²×C₆₇	—	2	1	no	—
457	C₂²×C₆₇	—	4	4	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	8	2	no	—
462	C₂²×C₆₇	#547	1	2	yes	—
463	C₂²×C₆₇	#575	1	2	yes	—
464	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₆₇	—	2	2	no	—
466	C₄×C₆₇	—	2	1	no	—
467	C₄×C₆₇	—	2	1	no	—
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	2	no	—
470	C₄×C₆₇	—	4	2	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	2	no	—
473	C₄×C₆₇	—	4	2	no	—
474	C₄×C₆₇	—	4	2	no	—
475	C₄×C₆₇	—	4	2	no	—
476	C₄×C₆₇	—	4	2	no	—
477	C₄×C₆₇	#547	1	2	yes	—
478	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
479	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
480	#61243	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
481	C₂×C₆₇	—	2	2	no	—
482	C₂×C₆₇	—	2	2	no	—
483	C₂×C₆₇	—	4	1	no	—
484	C₂×C₆₇	—	4	2	no	—
485	C₂×C₆₇	—	8	2	no	—
486	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
487	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
488	C₂×C₆₇	#3584	1	1	yes	characteristic
489	#3475	C₂×C₆₇	1	2	yes	complemented
490	#3350	C₂×C₆₇	1	2	yes	complemented
491	#3349	C₂×C₆₇	1	2	yes	complemented
492	#3348	C₂×C₆₇	1	2	yes	complemented
493	#3347	C₂×C₆₇	1	2	yes	complemented
494	#3346	C₂×C₆₇	1	2	yes	complemented
495	#3345	C₂×C₆₇	1	2	yes	complemented
496	#3344	C₂×C₆₇	1	2	yes	complemented
497	#3343	C₂×C₆₇	1	2	yes	complemented
498	#3162	C₂×C₆₇	1	1	yes	characteristic, complemented
499	#3091	C₂×C₆₇	1	2	yes	complemented
500	#3091	C₂×C₆₇	1	2	yes	complemented
501	#3076	C₂×C₆₇	1	2	yes	complemented
502	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
503	#3050	C₂×C₆₇	1	1	yes	characteristic, complemented
504	#2943	C₂×C₆₇	1	1	yes	characteristic, complemented
505	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#2911	C₂×C₆₇	1	1	yes	characteristic, complemented
507	C₂×#427	C₂×C₆₇	1	1	yes	characteristic, complemented
508	C₆₇	#61243	1	1	yes	characteristic, direct product factor, Sylow
509	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
510	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
511	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
512	#556	C₂²×C₆₇	1	2	yes	—
513	#555	C₂²×C₆₇	1	2	yes	—
514	#554	C₂²×C₆₇	1	2	yes	—
515	#553	C₂²×C₆₇	1	2	yes	—
516	#553	C₂²×C₆₇	1	2	yes	—
517	#552	—	2	2	no	—
518	#552	C₂²×C₆₇	1	2	yes	—
519	#552	C₂²×C₆₇	1	2	yes	—
520	#551	—	2	2	no	—
521	#551	—	2	2	no	—
522	#547	C₂²×C₆₇	1	2	yes	—
523	#546	—	2	2	no	—
524	#533	C₂²×C₆₇	1	2	yes	—
525	#529	—	2	2	no	—
526	#529	—	2	2	no	—
527	#529	—	2	2	no	—
528	#525	C₂²×C₆₇	1	2	yes	—
529	#525	C₂²×C₆₇	1	2	yes	—
530	C₄×#41	—	2	2	no	—
531	C₄×#41	C₂²×C₆₇	1	2	yes	—
532	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
533	C₂×#117	C₂²×C₆₇	1	2	yes	—
534	C₂×#117	C₂²×C₆₇	1	2	yes	—
535	#501	C₂²×C₆₇	1	2	yes	complemented
536	#501	C₂²×C₆₇	1	2	yes	complemented
537	#501	C₂²×C₆₇	1	2	yes	complemented
538	#501	C₂²×C₆₇	1	2	yes	complemented
539	#485	C₂²×C₆₇	1	2	yes	complemented
540	#485	C₂²×C₆₇	1	2	yes	complemented
541	#485	C₂²×C₆₇	1	2	yes	complemented
542	#485	C₂²×C₆₇	1	2	yes	complemented
543	#484	C₂²×C₆₇	1	2	yes	complemented
544	#484	C₂²×C₆₇	1	2	yes	complemented
545	#483	C₂²×C₆₇	1	2	yes	complemented
546	#483	C₂²×C₆₇	1	2	yes	complemented
547	#482	C₂²×C₆₇	1	2	yes	complemented
548	#482	C₂²×C₆₇	1	2	yes	complemented
549	#482	C₂²×C₆₇	1	2	yes	complemented
550	#482	C₂²×C₆₇	1	2	yes	complemented
551	#481	C₂²×C₆₇	1	2	yes	complemented
552	#481	C₂²×C₆₇	1	2	yes	complemented
553	#480	C₂²×C₆₇	1	2	yes	complemented
554	#480	C₂²×C₆₇	1	2	yes	complemented
555	#479	C₂²×C₆₇	1	2	yes	complemented
556	#479	C₂²×C₆₇	1	2	yes	complemented
557	#478	C₂²×C₆₇	1	2	yes	complemented
558	#478	C₂²×C₆₇	1	2	yes	complemented
559	#477	C₂²×C₆₇	1	2	yes	complemented
560	#476	C₂²×C₆₇	1	2	yes	complemented
561	#475	C₂²×C₆₇	1	2	yes	complemented
562	#474	C₂²×C₆₇	1	2	yes	complemented
563	#470	C₂²×C₆₇	1	2	yes	complemented
564	#469	C₂²×C₆₇	1	2	yes	complemented
565	#468	C₂²×C₆₇	1	2	yes	complemented
566	#468	C₂²×C₆₇	1	2	yes	complemented
567	#467	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#467	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	#466	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	#466	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	#465	C₂²×C₆₇	1	2	yes	complemented
572	#465	C₂²×C₆₇	1	2	yes	complemented
573	#442	C₂²×C₆₇	1	2	yes	complemented
574	#441	C₂²×C₆₇	1	2	yes	complemented
575	#440	C₂²×C₆₇	1	2	yes	complemented
576	#440	C₂²×C₆₇	1	2	yes	complemented
577	#435	C₂²×C₆₇	1	2	yes	—
578	#435	C₂²×C₆₇	1	2	yes	—
579	#435	C₂²×C₆₇	1	2	yes	—
580	#435	C₂²×C₆₇	1	2	yes	—
581	#428	C₂²×C₆₇	1	2	yes	complemented
582	#428	C₂²×C₆₇	1	2	yes	complemented
583	#428	C₂²×C₆₇	1	2	yes	complemented
584	#428	C₂²×C₆₇	1	2	yes	complemented
585	#427	C₂²×C₆₇	1	2	yes	—
586	#427	C₂²×C₆₇	1	2	yes	—
587	#427	C₂²×C₆₇	1	2	yes	—
588	#427	C₂²×C₆₇	1	1	yes	characteristic
589	#427	C₂²×C₆₇	1	1	yes	characteristic
590	#427	C₂²×C₆₇	1	1	yes	characteristic
591	#427	C₂²×C₆₇	1	2	yes	complemented
592	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
597	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
598	#416	C₂²×C₆₇	1	2	yes	—
599	#416	C₂²×C₆₇	1	2	yes	—
600	#416	C₂²×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#41	—	2	2	no	—
605	C₂×#41	C₂³×C₆₇	1	2	yes	—
606	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
609	#135	—	2	4	no	—
610	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
612	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×M₁₆	—	2	4	no	—
614	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
615	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
616	C₂²×C₈	—	2	4	no	—
617	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
620	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
621	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
624	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	C₂³×C₆₇	1	2	yes	—
637	#125	C₂³×C₆₇	1	2	yes	—
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
655	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
656	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
657	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	C₂³×C₆₇	1	2	yes	—
662	#121	C₂³×C₆₇	1	2	yes	—
663	#121	C₂³×C₆₇	1	2	yes	—
664	#121	C₂³×C₆₇	1	2	yes	—
665	#120	—	2	2	no	—
666	#120	—	2	2	no	—
667	C₄×Q₈	—	2	2	no	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	—	2	2	no	—
670	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
671	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	D₄×C₆₇	1	2	yes	—
682	C₄×D₄	D₄×C₆₇	1	2	yes	—
683	C₄×D₄	C₂³×C₆₇	1	2	yes	—
684	C₄×D₄	C₂³×C₆₇	1	2	yes	—
685	C₄×D₄	C₂³×C₆₇	1	2	yes	—
686	C₄×D₄	C₂³×C₆₇	1	2	yes	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	C₂³×C₆₇	1	2	yes	—
696	#117	C₂³×C₆₇	1	2	yes	—
697	#117	C₂³×C₆₇	1	2	yes	—
698	#117	C₂³×C₆₇	1	2	yes	—
699	#117	C₂³×C₆₇	1	2	yes	—
700	#117	C₂³×C₆₇	1	2	yes	—
701	#117	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	—	2	2	no	—
708	C₂×C₂²⋊C₄	—	2	2	no	—
709	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
711	C₂×C₄²	—	2	2	no	—
712	C₂×C₄²	—	2	2	no	—
713	C₂×C₄²	—	2	2	no	—
714	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
715	#107	C₂³×C₆₇	1	1	yes	characteristic
716	#107	C₂³×C₆₇	1	1	yes	characteristic
717	#107	C₂³×C₆₇	1	1	yes	characteristic
718	#107	C₂³×C₆₇	1	1	yes	characteristic
719	#107	C₂³×C₆₇	1	2	yes	—
720	#107	C₂³×C₆₇	1	2	yes	—
721	#107	C₂³×C₆₇	1	1	yes	characteristic
722	#107	C₂³×C₆₇	1	1	yes	characteristic
723	#107	C₂³×C₆₇	1	2	yes	—
724	#107	C₂³×C₆₇	1	2	yes	—
725	#107	C₂³×C₆₇	1	2	yes	—
726	#107	C₂³×C₆₇	1	2	yes	—
727	#106	C₂³×C₆₇	1	2	yes	—
728	#106	C₂³×C₆₇	1	2	yes	—
729	#106	C₂³×C₆₇	1	2	yes	—
730	#106	C₂³×C₆₇	1	2	yes	—
731	#106	C₂³×C₆₇	1	2	yes	—
732	#106	C₂³×C₆₇	1	2	yes	—
733	#106	C₂³×C₆₇	1	2	yes	—
734	#106	C₂³×C₆₇	1	2	yes	—
735	#106	C₂³×C₆₇	1	2	yes	—
736	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
737	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
738	#103	C₂³×C₆₇	1	2	yes	—
739	#103	C₂³×C₆₇	1	2	yes	—
740	#103	C₂³×C₆₇	1	2	yes	—
741	#103	C₂³×C₆₇	1	2	yes	—
742	#103	C₂³×C₆₇	1	2	yes	—
743	#103	C₂³×C₆₇	1	2	yes	—
744	#102	C₂³×C₆₇	1	2	yes	—
745	#102	C₂³×C₆₇	1	2	yes	—
746	#102	C₂³×C₆₇	1	2	yes	—
747	#102	C₂³×C₆₇	1	2	yes	—
748	#102	C₂³×C₆₇	1	2	yes	—
749	#102	C₂³×C₆₇	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
752	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
754	#97	C₂³×C₆₇	1	2	yes	—
755	#97	C₂³×C₆₇	1	2	yes	—
756	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
758	#41	—	2	4	no	—
759	#41	—	2	4	no	—
760	#41	—	4	8	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
771	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
772	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
786	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	Q₁₆	—	2	2	no	—
796	SD₁₆	—	2	4	no	—
797	D₈	—	2	2	no	—
798	M₁₆	—	2	4	no	—
799	M₁₆	—	2	4	no	—
800	C₂×C₈	—	2	2	no	—
801	C₂×C₈	—	2	2	no	—
802	C₂×C₈	—	2	2	no	—
803	C₂×C₈	—	2	2	no	—
804	C₂×C₈	—	2	2	no	—
805	C₂×C₈	—	2	2	no	—
806	C₂×C₈	—	2	2	no	—
807	C₂×C₈	#41×C₆₇	1	4	yes	complemented
808	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
809	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
810	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
811	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
832	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
856	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
857	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	C₂×D₄×C₆₇	1	2	yes	—
869	C₄²	C₂⁴×C₆₇	1	2	yes	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	1	no	—
875	C₂³	—	4	1	no	—
876	C₂³	—	4	1	no	—
877	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
879	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
881	Q₈	—	2	2	no	—
882	Q₈	—	2	2	no	—
883	Q₈	—	4	4	no	—
884	Q₈	—	8	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	4	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	8	2	no	—
893	D₄	—	8	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
927	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
928	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
929	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
930	C₈	—	2	1	no	—
931	C₈	—	2	1	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	C₂×#41×C₆₇	1	2	yes	—
935	C₈	C₂×#41×C₆₇	1	2	yes	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	4	4	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	8	2	no	—
951	C₂²	#547×C₆₇	1	2	yes	—
952	C₂²	#575×C₆₇	1	2	yes	—
953	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	#547×C₆₇	1	2	yes	—
967	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
968	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
969	C₂	—	2	2	no	—
970	C₂	—	2	2	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	2	no	—
974	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
975	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
976	C₂	C₆₇×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3475	C₂	semidirect
2. C₆₇×#3350	C₂	semidirect
3. C₆₇×#3349	C₂	semidirect
4. C₆₇×#3348	C₂	semidirect
5. C₆₇×#3347	C₂	semidirect
6. C₆₇×#3346	C₂	semidirect
7. C₆₇×#3345	C₂	semidirect
8. C₆₇×#3344	C₂	semidirect
9. C₆₇×#3343	C₂	semidirect
10. C₆₇×#3162	C₂	semidirect
11. C₆₇×#3091	C₂	semidirect
12. C₆₇×#3091	C₂	semidirect
13. C₆₇×#3076	C₂	semidirect
14. C₆₇×#3054	C₂	semidirect
15. C₆₇×#3050	C₂	semidirect
16. C₆₇×#2943	C₂	semidirect
17. C₂×#435×C₆₇	C₂	semidirect
18. C₆₇×#2911	C₂	semidirect
19. C₂×#427×C₆₇	C₂	semidirect
46. #501×C₆₇	C₂²	semidirect
47. #501×C₆₇	C₂²	semidirect
48. #501×C₆₇	C₂²	semidirect
49. #501×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #485×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
55. #484×C₆₇	C₂²	semidirect
56. #483×C₆₇	C₂²	semidirect
57. #483×C₆₇	C₂²	semidirect
58. #482×C₆₇	C₂²	semidirect
59. #482×C₆₇	C₂²	semidirect
60. #482×C₆₇	C₂²	semidirect
61. #482×C₆₇	C₂²	semidirect
62. #481×C₆₇	C₂²	semidirect
63. #481×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #480×C₆₇	C₂²	semidirect
66. #479×C₆₇	C₂²	semidirect
67. #479×C₆₇	C₂²	semidirect
68. #478×C₆₇	C₂²	semidirect
69. #478×C₆₇	C₂²	semidirect
70. #477×C₆₇	C₂²	semidirect
71. #476×C₆₇	C₂²	semidirect
72. #475×C₆₇	C₂²	semidirect
73. #474×C₆₇	C₂²	semidirect
74. #470×C₆₇	C₂²	semidirect
75. #469×C₆₇	C₂²	semidirect
76. #468×C₆₇	C₂²	semidirect
77. #468×C₆₇	C₂²	semidirect
78. #467×C₆₇	C₂²	semidirect
79. #467×C₆₇	C₂²	semidirect
80. #466×C₆₇	C₂²	semidirect
81. #466×C₆₇	C₂²	semidirect
82. #465×C₆₇	C₂²	semidirect
83. #465×C₆₇	C₂²	semidirect
84. #442×C₆₇	C₂²	semidirect
85. #441×C₆₇	C₂²	semidirect
86. #440×C₆₇	C₂²	semidirect
87. #440×C₆₇	C₂²	semidirect
92. #428×C₆₇	C₂²	semidirect
93. #428×C₆₇	C₂²	semidirect
94. #428×C₆₇	C₂²	semidirect
95. #428×C₆₇	C₂²	semidirect
102. #427×C₆₇	C₂²	semidirect
103. #427×C₆₇	C₂²	semidirect
104. #427×C₆₇	C₂²	semidirect
105. C₂×#107×C₆₇	C₂²	semidirect
106. C₂×#107×C₆₇	C₂²	semidirect
107. C₂×#106×C₆₇	C₂²	semidirect
318. C₂×C₈×C₆₇	#41	semidirect
480. #61243	C₆₇	direct (N × H)
489. #3475	C₂×C₆₇	semidirect
490. #3350	C₂×C₆₇	semidirect
491. #3349	C₂×C₆₇	semidirect
492. #3348	C₂×C₆₇	semidirect
493. #3347	C₂×C₆₇	semidirect
494. #3346	C₂×C₆₇	semidirect
495. #3345	C₂×C₆₇	semidirect
496. #3344	C₂×C₆₇	semidirect
497. #3343	C₂×C₆₇	semidirect
498. #3162	C₂×C₆₇	semidirect
499. #3091	C₂×C₆₇	semidirect
500. #3091	C₂×C₆₇	semidirect
501. #3076	C₂×C₆₇	semidirect
502. #3054	C₂×C₆₇	semidirect
503. #3050	C₂×C₆₇	semidirect
504. #2943	C₂×C₆₇	semidirect
505. C₂×#435	C₂×C₆₇	semidirect
506. #2911	C₂×C₆₇	semidirect
507. C₂×#427	C₂×C₆₇	semidirect
508. C₆₇	#61243	direct (N × H)
535. #501	C₂²×C₆₇	semidirect
536. #501	C₂²×C₆₇	semidirect
537. #501	C₂²×C₆₇	semidirect
538. #501	C₂²×C₆₇	semidirect
539. #485	C₂²×C₆₇	semidirect
540. #485	C₂²×C₆₇	semidirect
541. #485	C₂²×C₆₇	semidirect
542. #485	C₂²×C₆₇	semidirect
543. #484	C₂²×C₆₇	semidirect
544. #484	C₂²×C₆₇	semidirect
545. #483	C₂²×C₆₇	semidirect
546. #483	C₂²×C₆₇	semidirect
547. #482	C₂²×C₆₇	semidirect
548. #482	C₂²×C₆₇	semidirect
549. #482	C₂²×C₆₇	semidirect
550. #482	C₂²×C₆₇	semidirect
551. #481	C₂²×C₆₇	semidirect
552. #481	C₂²×C₆₇	semidirect
553. #480	C₂²×C₆₇	semidirect
554. #480	C₂²×C₆₇	semidirect
555. #479	C₂²×C₆₇	semidirect
556. #479	C₂²×C₆₇	semidirect
557. #478	C₂²×C₆₇	semidirect
558. #478	C₂²×C₆₇	semidirect
559. #477	C₂²×C₆₇	semidirect
560. #476	C₂²×C₆₇	semidirect
561. #475	C₂²×C₆₇	semidirect
562. #474	C₂²×C₆₇	semidirect
563. #470	C₂²×C₆₇	semidirect
564. #469	C₂²×C₆₇	semidirect
565. #468	C₂²×C₆₇	semidirect
566. #468	C₂²×C₆₇	semidirect
567. #467	C₂²×C₆₇	semidirect
568. #467	C₂²×C₆₇	semidirect
569. #466	C₂²×C₆₇	semidirect
570. #466	C₂²×C₆₇	semidirect
571. #465	C₂²×C₆₇	semidirect
572. #465	C₂²×C₆₇	semidirect
573. #442	C₂²×C₆₇	semidirect
574. #441	C₂²×C₆₇	semidirect
575. #440	C₂²×C₆₇	semidirect
576. #440	C₂²×C₆₇	semidirect
581. #428	C₂²×C₆₇	semidirect
582. #428	C₂²×C₆₇	semidirect
583. #428	C₂²×C₆₇	semidirect
584. #428	C₂²×C₆₇	semidirect
591. #427	C₂²×C₆₇	semidirect
592. #427	C₂²×C₆₇	semidirect
593. #427	C₂²×C₆₇	semidirect
594. C₂×#107	C₂²×C₆₇	semidirect
595. C₂×#107	C₂²×C₆₇	semidirect
596. C₂×#106	C₂²×C₆₇	semidirect
807. C₂×C₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₆₇×#3350	2
C₆₇×#3349	2
C₆₇×#3348	2
C₆₇×#3347	2
C₆₇×#3346	2
C₆₇×#3345	2
C₆₇×#3344	2
C₆₇×#3343	2
C₆₇×#3162	2
C₆₇×#3091	2
C₆₇×#3076	2
C₆₇×#3054	2
C₆₇×#3050	2
C₆₇×#2943	2
C₂×#435×C₆₇	2
C₆₇×#2911	2
C₂×#427×C₆₇	2
#61243	67

Subgroups — C67×#61243 #30740494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61243 #30740494