Subgroups — C₆₇×#35118 #30714369

Order 17152.

2450 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2853	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2627	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2618	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2611	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2610	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2609	C₂	1	4	yes	maximal, complemented
12	C₆₇×#2601	C₂	1	4	yes	maximal, complemented
13	C₆₇×#2599	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
19	#529×C₆₇	—	2	8	no	—
20	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#120×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#117×C₆₇	—	2	8	no	—
32	C₂×#117×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂×#117×C₆₇	C₂²	1	2	yes	—
35	C₂×#117×C₆₇	C₂²	1	2	yes	—
36	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
43	#400×C₆₇	C₂²	1	2	yes	complemented
44	#399×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	2	yes	complemented
46	#398×C₆₇	C₂²	1	4	yes	complemented
47	#397×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	4	yes	—
49	#396×C₆₇	C₂²	1	4	yes	complemented
50	#395×C₆₇	C₂²	1	2	yes	complemented
51	#394×C₆₇	C₂²	1	4	yes	—
52	#394×C₆₇	C₂²	1	2	yes	complemented
53	#393×C₆₇	C₂²	1	2	yes	—
54	#392×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	4	yes	—
56	#389×C₆₇	C₂²	1	4	yes	complemented
57	#388×C₆₇	C₂²	1	4	yes	—
58	#388×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	4	yes	complemented
60	#388×C₆₇	C₂²	1	4	yes	complemented
61	#388×C₆₇	C₂²	1	4	yes	complemented
62	#387×C₆₇	C₂²	1	4	yes	complemented
63	#387×C₆₇	C₂²	1	4	yes	complemented
64	#387×C₆₇	C₂²	1	4	yes	complemented
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	4	yes	—
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	4	yes	—
69	#386×C₆₇	C₂²	1	4	yes	—
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	4	yes	—
73	#385×C₆₇	C₂²	1	4	yes	—
74	#385×C₆₇	C₂²	1	4	yes	complemented
75	#383×C₆₇	C₂²	1	2	yes	complemented
76	#382×C₆₇	C₂²	1	2	yes	complemented
77	#381×C₆₇	C₂²	1	2	yes	—
78	#381×C₆₇	C₂²	1	2	yes	—
79	#380×C₆₇	C₂²	1	1	yes	characteristic
80	#380×C₆₇	C₂²	1	1	yes	characteristic
81	#379×C₆₇	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
84	#376×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	—	2	4	no	—
91	C₂³×C₄×C₆₇	—	2	4	no	—
92	C₂³×C₄×C₆₇	—	2	4	no	—
93	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
94	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	#126×C₆₇	—	2	8	no	—
103	#125×C₆₇	—	2	4	no	—
104	#124×C₆₇	—	2	4	no	—
105	#123×C₆₇	—	2	8	no	—
106	#123×C₆₇	—	2	8	no	—
107	C₂²⋊Q₈×C₆₇	—	2	4	no	—
108	#121×C₆₇	—	2	4	no	—
109	#120×C₆₇	—	2	8	no	—
110	C₄×Q₈×C₆₇	—	2	4	no	—
111	C₄×D₄×C₆₇	—	2	8	no	—
112	C₄×D₄×C₆₇	—	2	4	no	—
113	#117×C₆₇	—	2	8	no	—
114	#117×C₆₇	—	2	8	no	—
115	#117×C₆₇	—	2	8	no	—
116	#117×C₆₇	—	2	8	no	—
117	#117×C₆₇	—	2	8	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
119	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
154	C₂×C₄²×C₆₇	—	2	4	no	—
155	C₂×C₄²×C₆₇	D₄	1	8	yes	complemented
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	#95×C₆₇	C₂³	1	2	yes	—
165	#95×C₆₇	C₂³	1	2	yes	—
166	#95×C₆₇	C₂³	1	4	yes	—
167	#95×C₆₇	C₂³	1	4	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	4	yes	—
170	#95×C₆₇	C₂³	1	4	yes	—
171	#95×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	C₂⁴×C₆₇	—	2	2	no	—
176	C₂⁴×C₆₇	—	2	2	no	—
177	C₂⁴×C₆₇	—	4	2	no	—
178	C₂⁴×C₆₇	—	4	2	no	—
179	C₂⁴×C₆₇	#41	1	4	yes	—
180	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
181	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
182	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
183	C₂×Q₈×C₆₇	—	2	2	no	—
184	C₂×Q₈×C₆₇	—	4	2	no	—
185	C₂×D₄×C₆₇	—	2	4	no	—
186	C₂×D₄×C₆₇	—	2	4	no	—
187	C₂×D₄×C₆₇	—	2	4	no	—
188	C₂×D₄×C₆₇	—	2	8	no	—
189	C₂×D₄×C₆₇	—	2	2	no	—
190	C₂×D₄×C₆₇	—	4	2	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	4	no	—
193	C₂²×C₄×C₆₇	—	2	32	no	—
194	C₂²×C₄×C₆₇	—	2	2	no	—
195	C₂²×C₄×C₆₇	—	2	4	no	—
196	C₂²×C₄×C₆₇	—	2	4	no	—
197	C₂²×C₄×C₆₇	—	2	2	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	4	no	—
201	C₂²×C₄×C₆₇	—	2	4	no	—
202	C₂²×C₄×C₆₇	—	2	4	no	—
203	C₂²×C₄×C₆₇	—	2	4	no	—
204	C₂²×C₄×C₆₇	—	2	2	no	—
205	C₂²×C₄×C₆₇	—	2	2	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	4	2	no	—
208	C₂²×C₄×C₆₇	—	4	2	no	—
209	C₂²×C₄×C₆₇	—	4	4	no	—
210	C₂²×C₄×C₆₇	—	4	2	no	—
211	C₂²×C₄×C₆₇	—	4	2	no	—
212	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₆₇	#41	1	4	yes	—
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₄⋊C₄×C₆₇	—	2	4	no	—
231	C₄⋊C₄×C₆₇	—	2	4	no	—
232	C₄⋊C₄×C₆₇	—	2	4	no	—
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	8	no	—
241	C₄⋊C₄×C₆₇	—	4	2	no	—
242	C₄⋊C₄×C₆₇	—	4	2	no	—
243	C₄⋊C₄×C₆₇	—	4	4	no	—
244	C₄⋊C₄×C₆₇	—	4	4	no	—
245	C₂²⋊C₄×C₆₇	—	2	4	no	—
246	C₂²⋊C₄×C₆₇	—	2	8	no	—
247	C₂²⋊C₄×C₆₇	—	2	4	no	—
248	C₂²⋊C₄×C₆₇	—	2	4	no	—
249	C₂²⋊C₄×C₆₇	—	2	4	no	—
250	C₂²⋊C₄×C₆₇	—	2	4	no	—
251	C₂²⋊C₄×C₆₇	—	2	4	no	—
252	C₂²⋊C₄×C₆₇	—	2	4	no	—
253	C₂²⋊C₄×C₆₇	—	2	4	no	—
254	C₂²⋊C₄×C₆₇	—	2	4	no	—
255	C₂²⋊C₄×C₆₇	—	2	4	no	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	8	no	—
258	C₂²⋊C₄×C₆₇	—	4	4	no	—
259	C₂²⋊C₄×C₆₇	—	4	4	no	—
260	C₂²⋊C₄×C₆₇	—	4	4	no	—
261	C₂²⋊C₄×C₆₇	—	4	4	no	—
262	C₄²×C₆₇	—	2	4	no	—
263	C₄²×C₆₇	—	2	4	no	—
264	C₄²×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	4	4	no	—
266	C₄²×C₆₇	C₂×D₄	1	4	yes	—
267	C₄²×C₆₇	C₂×D₄	1	4	yes	—
268	C₄²×C₆₇	C₂×D₄	1	4	yes	—
269	C₄²×C₆₇	C₂×D₄	1	4	yes	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	2	no	—
272	C₂³×C₆₇	—	2	8	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	2	4	no	—
276	C₂³×C₆₇	—	2	4	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	4	no	—
281	C₂³×C₆₇	—	2	4	no	—
282	C₂³×C₆₇	—	4	8	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	4	4	no	—
285	C₂³×C₆₇	—	4	8	no	—
286	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
287	C₂³×C₆₇	C₂×#41	1	4	yes	—
288	C₂³×C₆₇	C₂×#41	1	2	yes	—
289	C₂³×C₆₇	C₂×#41	1	2	yes	—
290	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
291	Q₈×C₆₇	—	4	4	no	—
292	D₄×C₆₇	—	4	4	no	—
293	D₄×C₆₇	—	4	8	no	—
294	D₄×C₆₇	—	8	8	no	—
295	C₂×C₄×C₆₇	—	2	16	no	—
296	C₂×C₄×C₆₇	—	2	16	no	—
297	C₂×C₄×C₆₇	—	2	8	no	—
298	C₂×C₄×C₆₇	—	2	8	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	4	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	4	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	4	4	no	—
327	C₂×C₄×C₆₇	—	4	4	no	—
328	C₂×C₄×C₆₇	—	4	8	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	4	no	—
341	C₂²×C₆₇	—	2	4	no	—
342	C₂²×C₆₇	—	2	4	no	—
343	C₂²×C₆₇	—	2	8	no	—
344	C₂²×C₆₇	—	4	16	no	—
345	C₂²×C₆₇	—	4	2	no	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	4	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	4	no	—
352	C₂²×C₆₇	—	4	4	no	—
353	C₂²×C₆₇	#525	1	4	yes	—
354	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
355	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
356	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
357	C₂²×C₆₇	#585	1	2	yes	—
358	C₂²×C₆₇	#585	1	2	yes	—
359	C₄×C₆₇	—	2	2	no	—
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	4	no	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	2	2	no	—
364	C₄×C₆₇	—	2	2	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	4	2	no	—
367	C₄×C₆₇	—	4	2	no	—
368	C₄×C₆₇	—	4	2	no	—
369	C₄×C₆₇	—	4	2	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	4	no	—
372	C₄×C₆₇	—	4	4	no	—
373	#35118	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₂×C₆₇	—	2	4	no	—
375	C₂×C₆₇	—	4	4	no	—
376	C₂×C₆₇	—	8	2	no	—
377	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
378	C₂×C₆₇	#3449	1	1	yes	characteristic
379	C₂×C₆₇	#3449	1	1	yes	characteristic
380	C₂×C₆₇	#3491	1	2	yes	—
381	C₂×C₆₇	#3493	1	2	yes	—
382	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
383	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
384	#2853	C₂×C₆₇	1	2	yes	complemented
385	#2849	C₂×C₆₇	1	2	yes	complemented
386	#2627	C₂×C₆₇	1	1	yes	characteristic, complemented
387	#2626	C₂×C₆₇	1	1	yes	characteristic, complemented
388	#2618	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#2617	C₂×C₆₇	1	1	yes	characteristic
390	#2611	C₂×C₆₇	1	2	yes	complemented
391	#2610	C₂×C₆₇	1	2	yes	complemented
392	#2609	C₂×C₆₇	1	4	yes	complemented
393	#2601	C₂×C₆₇	1	4	yes	complemented
394	#2599	C₂×C₆₇	1	2	yes	complemented
395	#2598	C₂×C₆₇	1	2	yes	complemented
396	#2322	C₂×C₆₇	1	2	yes	complemented
397	#2321	C₂×C₆₇	1	2	yes	complemented
398	#2283	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₆₇	#35118	1	1	yes	characteristic, direct product factor, Sylow
400	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
401	#529	—	2	8	no	—
402	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
403	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
405	C₂×#123	C₂²×C₆₇	1	2	yes	—
406	C₂×#123	C₂²×C₆₇	1	2	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×#120	C₂²×C₆₇	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
413	C₂×#117	—	2	8	no	—
414	C₂×#117	C₂²×C₆₇	1	2	yes	—
415	C₂×#117	C₂²×C₆₇	1	2	yes	—
416	C₂×#117	C₂²×C₆₇	1	2	yes	—
417	C₂×#117	C₂²×C₆₇	1	2	yes	—
418	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
419	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
425	#400	C₂²×C₆₇	1	2	yes	complemented
426	#399	C₂²×C₆₇	1	2	yes	—
427	#398	C₂²×C₆₇	1	2	yes	complemented
428	#398	C₂²×C₆₇	1	4	yes	complemented
429	#397	C₂²×C₆₇	1	2	yes	—
430	#396	C₂²×C₆₇	1	4	yes	—
431	#396	C₂²×C₆₇	1	4	yes	complemented
432	#395	C₂²×C₆₇	1	2	yes	complemented
433	#394	C₂²×C₆₇	1	4	yes	—
434	#394	C₂²×C₆₇	1	2	yes	complemented
435	#393	C₂²×C₆₇	1	2	yes	—
436	#392	C₂²×C₆₇	1	2	yes	—
437	#390	C₂²×C₆₇	1	4	yes	—
438	#389	C₂²×C₆₇	1	4	yes	complemented
439	#388	C₂²×C₆₇	1	4	yes	—
440	#388	C₂²×C₆₇	1	4	yes	—
441	#388	C₂²×C₆₇	1	4	yes	complemented
442	#388	C₂²×C₆₇	1	4	yes	complemented
443	#388	C₂²×C₆₇	1	4	yes	complemented
444	#387	C₂²×C₆₇	1	4	yes	complemented
445	#387	C₂²×C₆₇	1	4	yes	complemented
446	#387	C₂²×C₆₇	1	4	yes	complemented
447	#386	C₂²×C₆₇	1	2	yes	—
448	#386	C₂²×C₆₇	1	4	yes	—
449	#386	C₂²×C₆₇	1	2	yes	—
450	#386	C₂²×C₆₇	1	4	yes	—
451	#386	C₂²×C₆₇	1	4	yes	—
452	#385	C₂²×C₆₇	1	2	yes	—
453	#385	C₂²×C₆₇	1	2	yes	—
454	#385	C₂²×C₆₇	1	4	yes	—
455	#385	C₂²×C₆₇	1	4	yes	—
456	#385	C₂²×C₆₇	1	4	yes	complemented
457	#383	C₂²×C₆₇	1	2	yes	complemented
458	#382	C₂²×C₆₇	1	2	yes	complemented
459	#381	C₂²×C₆₇	1	2	yes	—
460	#381	C₂²×C₆₇	1	2	yes	—
461	#380	C₂²×C₆₇	1	1	yes	characteristic
462	#380	C₂²×C₆₇	1	1	yes	characteristic
463	#379	C₂²×C₆₇	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
465	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
466	#376	C₂²×C₆₇	1	2	yes	complemented
467	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
470	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
472	C₂³×C₄	—	2	4	no	—
473	C₂³×C₄	—	2	4	no	—
474	C₂³×C₄	—	2	4	no	—
475	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
476	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
477	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
482	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
484	#126	—	2	8	no	—
485	#125	—	2	4	no	—
486	#124	—	2	4	no	—
487	#123	—	2	8	no	—
488	#123	—	2	8	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	#121	—	2	4	no	—
491	#120	—	2	8	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×D₄	—	2	8	no	—
494	C₄×D₄	—	2	4	no	—
495	#117	—	2	8	no	—
496	#117	—	2	8	no	—
497	#117	—	2	8	no	—
498	#117	—	2	8	no	—
499	#117	—	2	8	no	—
500	C₂×C₄⋊C₄	—	2	4	no	—
501	C₂×C₄⋊C₄	—	2	4	no	—
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
517	C₂×C₂²⋊C₄	—	2	4	no	—
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
536	C₂×C₄²	—	2	4	no	—
537	C₂×C₄²	D₄×C₆₇	1	8	yes	complemented
538	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
540	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
541	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
542	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
546	#95	C₂³×C₆₇	1	2	yes	—
547	#95	C₂³×C₆₇	1	2	yes	—
548	#95	C₂³×C₆₇	1	4	yes	—
549	#95	C₂³×C₆₇	1	4	yes	—
550	#95	C₂³×C₆₇	1	4	yes	—
551	#95	C₂³×C₆₇	1	4	yes	—
552	#95	C₂³×C₆₇	1	4	yes	—
553	#95	C₂³×C₆₇	1	4	yes	—
554	#95	C₂³×C₆₇	1	4	yes	—
555	#95	C₂³×C₆₇	1	4	yes	—
556	#95	C₂³×C₆₇	1	4	yes	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	4	2	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	#41×C₆₇	1	4	yes	—
562	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
563	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
564	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	8	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂²×C₄	—	2	32	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
595	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
596	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
597	C₂²×C₄	#41×C₆₇	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	4	no	—
626	C₄⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	4	4	no	—
648	C₄²	C₂×D₄×C₆₇	1	4	yes	—
649	C₄²	C₂×D₄×C₆₇	1	4	yes	—
650	C₄²	C₂×D₄×C₆₇	1	4	yes	—
651	C₄²	C₂×D₄×C₆₇	1	4	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	8	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	4	8	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	8	no	—
668	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
669	C₂³	C₂×#41×C₆₇	1	4	yes	—
670	C₂³	C₂×#41×C₆₇	1	2	yes	—
671	C₂³	C₂×#41×C₆₇	1	2	yes	—
672	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
673	Q₈	—	4	4	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	D₄	—	8	8	no	—
677	C₂×C₄	—	2	16	no	—
678	C₂×C₄	—	2	16	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
719	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	8	no	—
726	C₂²	—	4	16	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	4	no	—
735	C₂²	#525×C₆₇	1	4	yes	—
736	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
738	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
739	C₂²	#585×C₆₇	1	2	yes	—
740	C₂²	#585×C₆₇	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	4	no	—
755	C₂	—	2	4	no	—
756	C₂	—	4	4	no	—
757	C₂	—	8	2	no	—
758	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
759	C₂	C₆₇×#3449	1	1	yes	characteristic
760	C₂	C₆₇×#3449	1	1	yes	characteristic
761	C₂	C₆₇×#3491	1	2	yes	—
762	C₂	C₆₇×#3493	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2617	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#529×C₆₇	C₂	semidirect
2. C₂²×#117×C₆₇	C₂	semidirect
3. C₆₇×#2853	C₂	semidirect
4. C₆₇×#2849	C₂	semidirect
5. C₆₇×#2627	C₂	semidirect
6. C₆₇×#2626	C₂	semidirect
7. C₆₇×#2618	C₂	semidirect
9. C₆₇×#2611	C₂	semidirect
10. C₆₇×#2610	C₂	semidirect
11. C₆₇×#2609	C₂	semidirect
12. C₆₇×#2601	C₂	semidirect
13. C₆₇×#2599	C₂	semidirect
14. C₆₇×#2598	C₂	semidirect
15. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2321	C₂	semidirect
17. C₆₇×#2283	C₂	semidirect
20. C₂×#126×C₆₇	C₂²	semidirect
21. C₂×#125×C₆₇	C₂²	semidirect
22. C₂×#124×C₆₇	C₂²	semidirect
28. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×#117×C₆₇	C₂²	semidirect
43. #400×C₆₇	C₂²	semidirect
45. #398×C₆₇	C₂²	semidirect
46. #398×C₆₇	C₂²	semidirect
49. #396×C₆₇	C₂²	semidirect
50. #395×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
56. #389×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
74. #385×C₆₇	C₂²	semidirect
75. #383×C₆₇	C₂²	semidirect
76. #382×C₆₇	C₂²	semidirect
82. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
84. #376×C₆₇	C₂²	semidirect
155. C₂×C₄²×C₆₇	D₄	semidirect
373. #35118	C₆₇	direct (N × H)
382. C₂×#529	C₂×C₆₇	semidirect
383. C₂²×#117	C₂×C₆₇	semidirect
384. #2853	C₂×C₆₇	semidirect
385. #2849	C₂×C₆₇	semidirect
386. #2627	C₂×C₆₇	semidirect
387. #2626	C₂×C₆₇	semidirect
388. #2618	C₂×C₆₇	semidirect
390. #2611	C₂×C₆₇	semidirect
391. #2610	C₂×C₆₇	semidirect
392. #2609	C₂×C₆₇	semidirect
393. #2601	C₂×C₆₇	semidirect
394. #2599	C₂×C₆₇	semidirect
395. #2598	C₂×C₆₇	semidirect
396. #2322	C₂×C₆₇	semidirect
397. #2321	C₂×C₆₇	semidirect
398. #2283	C₂×C₆₇	semidirect
399. C₆₇	#35118	direct (N × H)
402. C₂×#126	C₂²×C₆₇	semidirect
403. C₂×#125	C₂²×C₆₇	semidirect
404. C₂×#124	C₂²×C₆₇	semidirect
410. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
412. C₂×C₄×D₄	C₂²×C₆₇	semidirect
418. C₂×#117	C₂²×C₆₇	semidirect
425. #400	C₂²×C₆₇	semidirect
427. #398	C₂²×C₆₇	semidirect
428. #398	C₂²×C₆₇	semidirect
431. #396	C₂²×C₆₇	semidirect
432. #395	C₂²×C₆₇	semidirect
434. #394	C₂²×C₆₇	semidirect
438. #389	C₂²×C₆₇	semidirect
441. #388	C₂²×C₆₇	semidirect
442. #388	C₂²×C₆₇	semidirect
443. #388	C₂²×C₆₇	semidirect
444. #387	C₂²×C₆₇	semidirect
445. #387	C₂²×C₆₇	semidirect
446. #387	C₂²×C₆₇	semidirect
456. #385	C₂²×C₆₇	semidirect
457. #383	C₂²×C₆₇	semidirect
458. #382	C₂²×C₆₇	semidirect
464. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
466. #376	C₂²×C₆₇	semidirect
537. C₂×C₄²	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2853	2
C₆₇×#2849	2
C₆₇×#2627	2
C₆₇×#2626	2
C₆₇×#2618	2
C₆₇×#2617	2
C₆₇×#2611	2
C₆₇×#2610	2
C₆₇×#2609	2
C₆₇×#2601	2
C₆₇×#2599	2
C₆₇×#2598	2
C₆₇×#2322	2
C₆₇×#2321	2
C₆₇×#2283	2
#35118	67

Subgroups — C67×#35118 #30714369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35118 #30714369