Subgroups — C₆₇×#35080 #30714331

Order 17152.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2847	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#2653	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2649	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2510	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2337	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₆₇	C₂²	1	2	yes	—
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
33	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#120×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#401×C₆₇	C₂²	1	2	yes	complemented
45	#400×C₆₇	C₂²	1	2	yes	complemented
46	#400×C₆₇	C₂²	1	2	yes	complemented
47	#399×C₆₇	C₂²	1	2	yes	—
48	#398×C₆₇	C₂²	1	2	yes	complemented
49	#397×C₆₇	C₂²	1	2	yes	—
50	#397×C₆₇	C₂²	1	2	yes	—
51	#397×C₆₇	C₂²	1	2	yes	complemented
52	#397×C₆₇	C₂²	1	2	yes	complemented
53	#396×C₆₇	C₂²	1	2	yes	complemented
54	#394×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	—
56	#394×C₆₇	C₂²	1	2	yes	—
57	#394×C₆₇	C₂²	1	2	yes	—
58	#393×C₆₇	C₂²	1	2	yes	—
59	#393×C₆₇	C₂²	1	2	yes	complemented
60	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#391×C₆₇	C₂²	1	2	yes	complemented
62	#391×C₆₇	C₂²	1	2	yes	complemented
63	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#390×C₆₇	C₂²	1	2	yes	—
65	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#389×C₆₇	C₂²	1	2	yes	complemented
70	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	complemented
77	#388×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#388×C₆₇	C₂²	1	2	yes	complemented
80	#388×C₆₇	C₂²	1	2	yes	complemented
81	#387×C₆₇	C₂²	1	2	yes	complemented
82	#387×C₆₇	C₂²	1	2	yes	complemented
83	#387×C₆₇	C₂²	1	2	yes	complemented
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	complemented
96	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#383×C₆₇	C₂²	1	2	yes	complemented
98	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#380×C₆₇	C₂²	1	2	yes	—
100	#380×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	#380×C₆₇	C₂²	1	1	yes	characteristic
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	1	yes	characteristic
106	#380×C₆₇	C₂²	1	2	yes	complemented
107	#379×C₆₇	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
123	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	—	2	4	no	—
131	C₂³×C₄×C₆₇	—	4	2	no	—
132	C₂³×C₄×C₆₇	—	4	2	no	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₆₇	—	4	2	no	—
145	#124×C₆₇	—	2	8	no	—
146	#124×C₆₇	—	4	2	no	—
147	#123×C₆₇	—	2	8	no	—
148	C₂²⋊Q₈×C₆₇	—	2	4	no	—
149	C₂²⋊Q₈×C₆₇	—	4	4	no	—
150	C₂²⋊Q₈×C₆₇	—	4	2	no	—
151	C₂²⋊Q₈×C₆₇	—	4	2	no	—
152	#121×C₆₇	—	2	4	no	—
153	#121×C₆₇	—	4	2	no	—
154	#121×C₆₇	—	4	2	no	—
155	#120×C₆₇	—	4	4	no	—
156	C₄×Q₈×C₆₇	—	4	2	no	—
157	C₄×D₄×C₆₇	—	4	2	no	—
158	C₄×D₄×C₆₇	—	4	4	no	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
177	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₇	—	4	2	no	—
206	C₂×C₄²×C₆₇	—	4	2	no	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	C₂⁴×C₆₇	—	2	2	no	—
245	C₂⁴×C₆₇	—	2	2	no	—
246	C₂⁴×C₆₇	—	2	2	no	—
247	C₂⁴×C₆₇	—	2	2	no	—
248	C₂⁴×C₆₇	—	2	2	no	—
249	C₂⁴×C₆₇	—	4	1	no	—
250	C₂⁴×C₆₇	—	4	1	no	—
251	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
252	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₆₇	—	2	2	no	—
256	C₂×Q₈×C₆₇	—	2	4	no	—
257	C₂×Q₈×C₆₇	—	2	2	no	—
258	C₂×Q₈×C₆₇	—	2	2	no	—
259	C₂×Q₈×C₆₇	—	4	2	no	—
260	C₂×Q₈×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	4	2	no	—
270	C₂×D₄×C₆₇	—	4	2	no	—
271	C₂×D₄×C₆₇	—	4	2	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
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	4	no	—
293	C₂²×C₄×C₆₇	—	4	1	no	—
294	C₂²×C₄×C₆₇	—	4	1	no	—
295	C₂²×C₄×C₆₇	—	4	1	no	—
296	C₂²×C₄×C₆₇	—	4	1	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	1	no	—
299	C₂²×C₄×C₆₇	—	4	1	no	—
300	C₂²×C₄×C₆₇	—	4	1	no	—
301	C₂²×C₄×C₆₇	—	4	1	no	—
302	C₂²×C₄×C₆₇	—	4	1	no	—
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	16	no	—
306	C₂²×C₄×C₆₇	#41	1	4	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	4	no	—
329	C₄⋊C₄×C₆₇	—	2	4	no	—
330	C₄⋊C₄×C₆₇	—	2	4	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	—	4	2	no	—
336	C₄⋊C₄×C₆₇	—	4	2	no	—
337	C₄⋊C₄×C₆₇	—	4	2	no	—
338	C₄⋊C₄×C₆₇	—	4	2	no	—
339	C₄⋊C₄×C₆₇	—	4	2	no	—
340	C₄⋊C₄×C₆₇	—	4	2	no	—
341	C₄⋊C₄×C₆₇	—	4	2	no	—
342	C₄⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	4	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	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	4	no	—
356	C₂²⋊C₄×C₆₇	—	2	4	no	—
357	C₂²⋊C₄×C₆₇	—	2	4	no	—
358	C₂²⋊C₄×C₆₇	—	4	2	no	—
359	C₂²⋊C₄×C₆₇	—	4	2	no	—
360	C₂²⋊C₄×C₆₇	—	4	2	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	—	4	2	no	—
366	C₂²⋊C₄×C₆₇	—	4	2	no	—
367	C₂²⋊C₄×C₆₇	—	4	2	no	—
368	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
369	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
370	C₄²×C₆₇	—	2	4	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	—	4	1	no	—
376	C₄²×C₆₇	—	4	1	no	—
377	C₄²×C₆₇	—	4	1	no	—
378	C₄²×C₆₇	—	4	1	no	—
379	C₄²×C₆₇	—	4	2	no	—
380	C₄²×C₆₇	—	4	2	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	1	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	8	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	1	no	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	1	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	4	4	no	—
406	C₂³×C₆₇	—	4	4	no	—
407	C₂³×C₆₇	—	4	4	no	—
408	C₂³×C₆₇	—	4	4	no	—
409	C₂³×C₆₇	—	4	4	no	—
410	C₂³×C₆₇	—	4	4	no	—
411	C₂³×C₆₇	C₂×#41	1	2	yes	—
412	C₂³×C₆₇	C₂×#41	1	2	yes	—
413	C₂³×C₆₇	C₂×#41	1	2	yes	—
414	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
415	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
416	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
417	Q₈×C₆₇	—	4	4	no	—
418	Q₈×C₆₇	—	8	4	no	—
419	D₄×C₆₇	—	4	8	no	—
420	D₄×C₆₇	—	4	4	no	—
421	D₄×C₆₇	—	8	4	no	—
422	D₄×C₆₇	—	8	4	no	—
423	C₂×C₄×C₆₇	—	2	1	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	8	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	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	2	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	4	4	no	—
474	C₂×C₄×C₆₇	—	4	4	no	—
475	C₂×C₄×C₆₇	—	4	4	no	—
476	C₂×C₄×C₆₇	—	4	4	no	—
477	C₂×C₄×C₆₇	—	4	4	no	—
478	C₂×C₄×C₆₇	—	4	4	no	—
479	C₂×C₄×C₆₇	—	4	4	no	—
480	C₂×C₄×C₆₇	—	4	4	no	—
481	C₂×C₄×C₆₇	—	4	4	no	—
482	C₂×C₄×C₆₇	—	8	4	no	—
483	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
484	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
485	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
486	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
487	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
488	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
489	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
491	C₂²×C₆₇	—	2	2	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	2	2	no	—
495	C₂²×C₆₇	—	2	2	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	2	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	2	no	—
501	C₂²×C₆₇	—	2	2	no	—
502	C₂²×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	4	16	no	—
504	C₂²×C₆₇	—	4	1	no	—
505	C₂²×C₆₇	—	4	1	no	—
506	C₂²×C₆₇	—	4	1	no	—
507	C₂²×C₆₇	—	4	1	no	—
508	C₂²×C₆₇	—	4	1	no	—
509	C₂²×C₆₇	—	4	1	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	1	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	2	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	2	no	—
519	C₂²×C₆₇	#542	1	4	yes	—
520	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
521	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₄×C₆₇	—	2	2	no	—
528	C₄×C₆₇	—	2	2	no	—
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	2	no	—
531	C₄×C₆₇	—	2	2	no	—
532	C₄×C₆₇	—	4	2	no	—
533	C₄×C₆₇	—	4	1	no	—
534	C₄×C₆₇	—	4	1	no	—
535	C₄×C₆₇	—	4	2	no	—
536	C₄×C₆₇	—	4	2	no	—
537	C₄×C₆₇	—	4	1	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	2	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	—	4	2	no	—
543	C₄×C₆₇	—	4	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	#538	1	4	yes	—
546	#35080	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
547	C₂×C₆₇	—	2	4	no	—
548	C₂×C₆₇	—	4	2	no	—
549	C₂×C₆₇	—	4	2	no	—
550	C₂×C₆₇	—	8	2	no	—
551	C₂×C₆₇	#3444	1	1	yes	characteristic
552	C₂×C₆₇	C₂×#538	1	1	yes	characteristic
553	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
554	C₂×C₆₇	#3519	1	1	yes	characteristic
555	C₂×C₆₇	#3519	1	1	yes	characteristic
556	C₂×C₆₇	#3520	1	1	yes	characteristic
557	C₂×C₆₇	#3520	1	1	yes	characteristic
558	#2857	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#2850	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#2848	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#2847	C₂×C₆₇	1	1	yes	characteristic
562	#2653	C₂×C₆₇	1	2	yes	complemented
563	#2649	C₂×C₆₇	1	2	yes	complemented
564	#2510	C₂×C₆₇	1	2	yes	complemented
565	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2494	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#2492	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2472	C₂×C₆₇	1	2	yes	complemented
570	#2450	C₂×C₆₇	1	2	yes	complemented
571	#2427	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2426	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2423	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2418	C₂×C₆₇	1	2	yes	complemented
576	#2337	C₂×C₆₇	1	2	yes	complemented
577	#2335	C₂×C₆₇	1	2	yes	complemented
578	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
579	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
580	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
581	C₆₇	#35080	1	1	yes	characteristic, direct product factor, Sylow
582	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
584	C₂×#124	C₂²×C₆₇	1	2	yes	—
585	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₂×#123	C₂²×C₆₇	1	2	yes	—
587	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
588	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
591	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
592	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
593	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
594	C₂×#120	C₂²×C₆₇	1	2	yes	—
595	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
597	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
598	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
599	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
600	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
601	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
602	#401	C₂²×C₆₇	1	2	yes	complemented
603	#400	C₂²×C₆₇	1	2	yes	complemented
604	#400	C₂²×C₆₇	1	2	yes	complemented
605	#399	C₂²×C₆₇	1	2	yes	—
606	#398	C₂²×C₆₇	1	2	yes	complemented
607	#397	C₂²×C₆₇	1	2	yes	—
608	#397	C₂²×C₆₇	1	2	yes	—
609	#397	C₂²×C₆₇	1	2	yes	complemented
610	#397	C₂²×C₆₇	1	2	yes	complemented
611	#396	C₂²×C₆₇	1	2	yes	complemented
612	#394	C₂²×C₆₇	1	2	yes	—
613	#394	C₂²×C₆₇	1	2	yes	—
614	#394	C₂²×C₆₇	1	2	yes	—
615	#394	C₂²×C₆₇	1	2	yes	—
616	#393	C₂²×C₆₇	1	2	yes	—
617	#393	C₂²×C₆₇	1	2	yes	complemented
618	#391	C₂²×C₆₇	1	2	yes	complemented
619	#391	C₂²×C₆₇	1	2	yes	complemented
620	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
622	#390	C₂²×C₆₇	1	2	yes	—
623	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#389	C₂²×C₆₇	1	2	yes	complemented
626	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#388	C₂²×C₆₇	1	2	yes	—
631	#388	C₂²×C₆₇	1	2	yes	—
632	#388	C₂²×C₆₇	1	2	yes	—
633	#388	C₂²×C₆₇	1	2	yes	—
634	#388	C₂²×C₆₇	1	2	yes	complemented
635	#388	C₂²×C₆₇	1	2	yes	complemented
636	#388	C₂²×C₆₇	1	2	yes	complemented
637	#388	C₂²×C₆₇	1	2	yes	complemented
638	#388	C₂²×C₆₇	1	2	yes	complemented
639	#387	C₂²×C₆₇	1	2	yes	complemented
640	#387	C₂²×C₆₇	1	2	yes	complemented
641	#387	C₂²×C₆₇	1	2	yes	complemented
642	#386	C₂²×C₆₇	1	2	yes	—
643	#386	C₂²×C₆₇	1	2	yes	—
644	#386	C₂²×C₆₇	1	2	yes	—
645	#386	C₂²×C₆₇	1	2	yes	—
646	#386	C₂²×C₆₇	1	2	yes	—
647	#386	C₂²×C₆₇	1	2	yes	—
648	#386	C₂²×C₆₇	1	2	yes	—
649	#385	C₂²×C₆₇	1	2	yes	—
650	#385	C₂²×C₆₇	1	2	yes	—
651	#385	C₂²×C₆₇	1	2	yes	—
652	#385	C₂²×C₆₇	1	2	yes	—
653	#385	C₂²×C₆₇	1	2	yes	complemented
654	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#383	C₂²×C₆₇	1	2	yes	complemented
656	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#380	C₂²×C₆₇	1	1	yes	characteristic
658	#380	C₂²×C₆₇	1	1	yes	characteristic
659	#380	C₂²×C₆₇	1	1	yes	characteristic
660	#380	C₂²×C₆₇	1	1	yes	characteristic
661	#380	C₂²×C₆₇	1	1	yes	characteristic
662	#380	C₂²×C₆₇	1	1	yes	characteristic
663	#380	C₂²×C₆₇	1	2	yes	—
664	#380	C₂²×C₆₇	1	2	yes	complemented
665	#379	C₂²×C₆₇	1	2	yes	—
666	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
667	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
668	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
669	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
670	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
671	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
672	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
673	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
674	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
675	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
678	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
679	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
680	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
681	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
683	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
684	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
685	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
687	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
688	C₂³×C₄	—	2	4	no	—
689	C₂³×C₄	—	4	2	no	—
690	C₂³×C₄	—	4	2	no	—
691	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
699	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₄⋊Q₈	—	4	2	no	—
703	#124	—	2	8	no	—
704	#124	—	4	2	no	—
705	#123	—	2	8	no	—
706	C₂²⋊Q₈	—	2	4	no	—
707	C₂²⋊Q₈	—	4	4	no	—
708	C₂²⋊Q₈	—	4	2	no	—
709	C₂²⋊Q₈	—	4	2	no	—
710	#121	—	2	4	no	—
711	#121	—	4	2	no	—
712	#121	—	4	2	no	—
713	#120	—	4	4	no	—
714	C₄×Q₈	—	4	2	no	—
715	C₄×D₄	—	4	2	no	—
716	C₄×D₄	—	4	4	no	—
717	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	—	2	4	no	—
735	C₂×C₂²⋊C₄	—	2	4	no	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄²	—	4	2	no	—
764	C₂×C₄²	—	4	2	no	—
765	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
768	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
771	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
772	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
776	#95	C₂³×C₆₇	1	1	yes	characteristic
777	#95	C₂³×C₆₇	1	1	yes	characteristic
778	#95	C₂³×C₆₇	1	1	yes	characteristic
779	#95	C₂³×C₆₇	1	1	yes	characteristic
780	#95	C₂³×C₆₇	1	1	yes	characteristic
781	#95	C₂³×C₆₇	1	1	yes	characteristic
782	#95	C₂³×C₆₇	1	1	yes	characteristic
783	#95	C₂³×C₆₇	1	1	yes	characteristic
784	#95	C₂³×C₆₇	1	2	yes	—
785	#95	C₂³×C₆₇	1	2	yes	—
786	#95	C₂³×C₆₇	1	2	yes	—
787	#95	C₂³×C₆₇	1	2	yes	—
788	#95	C₂³×C₆₇	1	2	yes	—
789	#95	C₂³×C₆₇	1	2	yes	—
790	#95	C₂³×C₆₇	1	2	yes	—
791	#95	C₂³×C₆₇	1	2	yes	—
792	#95	C₂³×C₆₇	1	2	yes	—
793	#95	C₂³×C₆₇	1	2	yes	—
794	#95	C₂³×C₆₇	1	2	yes	—
795	#95	C₂³×C₆₇	1	2	yes	—
796	#95	C₂³×C₆₇	1	2	yes	—
797	#95	C₂³×C₆₇	1	2	yes	—
798	#95	C₂³×C₆₇	1	2	yes	—
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	2	yes	—
801	#95	C₂³×C₆₇	1	2	yes	—
802	C₂⁴	—	2	2	no	—
803	C₂⁴	—	2	2	no	—
804	C₂⁴	—	2	2	no	—
805	C₂⁴	—	2	2	no	—
806	C₂⁴	—	2	2	no	—
807	C₂⁴	—	4	1	no	—
808	C₂⁴	—	4	1	no	—
809	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
810	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
811	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
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	4	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	16	no	—
864	C₂²×C₄	#41×C₆₇	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	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	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	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	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
927	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
928	C₄²	—	2	4	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	4	1	no	—
934	C₄²	—	4	1	no	—
935	C₄²	—	4	1	no	—
936	C₄²	—	4	1	no	—
937	C₄²	—	4	2	no	—
938	C₄²	—	4	2	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	8	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	4	4	no	—
966	C₂³	—	4	4	no	—
967	C₂³	—	4	4	no	—
968	C₂³	—	4	4	no	—
969	C₂³	C₂×#41×C₆₇	1	2	yes	—
970	C₂³	C₂×#41×C₆₇	1	2	yes	—
971	C₂³	C₂×#41×C₆₇	1	2	yes	—
972	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
973	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
974	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
975	Q₈	—	4	4	no	—
976	Q₈	—	8	4	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	8	4	no	—
1041	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1042	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1043	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1044	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1045	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1046	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1047	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1048	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	4	16	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	#542×C₆₇	1	4	yes	—
1078	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1079	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1080	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1081	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1082	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1083	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1084	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	#538×C₆₇	1	4	yes	—
1104	C₂	—	2	4	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	C₆₇×#3444	1	1	yes	characteristic
1109	C₂	C₂×#538×C₆₇	1	1	yes	characteristic
1110	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
1111	C₂	C₆₇×#3519	1	1	yes	characteristic
1112	C₂	C₆₇×#3519	1	1	yes	characteristic
1113	C₂	C₆₇×#3520	1	1	yes	characteristic
1114	C₂	C₆₇×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2847	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. C₆₇×#2857	C₂	semidirect
2. C₆₇×#2850	C₂	semidirect
3. C₆₇×#2848	C₂	semidirect
5. C₆₇×#2653	C₂	semidirect
6. C₆₇×#2649	C₂	semidirect
7. C₆₇×#2510	C₂	semidirect
8. C₆₇×#2495	C₂	semidirect
9. C₆₇×#2494	C₂	semidirect
10. C₆₇×#2492	C₂	semidirect
11. C₆₇×#2491	C₂	semidirect
12. C₆₇×#2472	C₂	semidirect
13. C₆₇×#2450	C₂	semidirect
14. C₆₇×#2427	C₂	semidirect
15. C₆₇×#2426	C₂	semidirect
16. C₆₇×#2423	C₂	semidirect
17. C₆₇×#2422	C₂	semidirect
18. C₆₇×#2418	C₂	semidirect
19. C₆₇×#2337	C₂	semidirect
20. C₆₇×#2335	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
25. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
27. C₂×#124×C₆₇	C₂²	semidirect
37. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
44. #401×C₆₇	C₂²	semidirect
45. #400×C₆₇	C₂²	semidirect
46. #400×C₆₇	C₂²	semidirect
48. #398×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #397×C₆₇	C₂²	semidirect
53. #396×C₆₇	C₂²	semidirect
59. #393×C₆₇	C₂²	semidirect
60. #391×C₆₇	C₂²	semidirect
61. #391×C₆₇	C₂²	semidirect
62. #391×C₆₇	C₂²	semidirect
63. #391×C₆₇	C₂²	semidirect
65. #390×C₆₇	C₂²	semidirect
66. #390×C₆₇	C₂²	semidirect
67. #389×C₆₇	C₂²	semidirect
68. #389×C₆₇	C₂²	semidirect
69. #389×C₆₇	C₂²	semidirect
70. #389×C₆₇	C₂²	semidirect
71. #389×C₆₇	C₂²	semidirect
76. #388×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #388×C₆₇	C₂²	semidirect
81. #387×C₆₇	C₂²	semidirect
82. #387×C₆₇	C₂²	semidirect
83. #387×C₆₇	C₂²	semidirect
95. #385×C₆₇	C₂²	semidirect
96. #384×C₆₇	C₂²	semidirect
97. #383×C₆₇	C₂²	semidirect
98. #382×C₆₇	C₂²	semidirect
106. #380×C₆₇	C₂²	semidirect
108. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
109. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
110. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
546. #35080	C₆₇	direct (N × H)
558. #2857	C₂×C₆₇	semidirect
559. #2850	C₂×C₆₇	semidirect
560. #2848	C₂×C₆₇	semidirect
562. #2653	C₂×C₆₇	semidirect
563. #2649	C₂×C₆₇	semidirect
564. #2510	C₂×C₆₇	semidirect
565. #2495	C₂×C₆₇	semidirect
566. #2494	C₂×C₆₇	semidirect
567. #2492	C₂×C₆₇	semidirect
568. #2491	C₂×C₆₇	semidirect
569. #2472	C₂×C₆₇	semidirect
570. #2450	C₂×C₆₇	semidirect
571. #2427	C₂×C₆₇	semidirect
572. #2426	C₂×C₆₇	semidirect
573. #2423	C₂×C₆₇	semidirect
574. #2422	C₂×C₆₇	semidirect
575. #2418	C₂×C₆₇	semidirect
576. #2337	C₂×C₆₇	semidirect
577. #2335	C₂×C₆₇	semidirect
578. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
579. C₄×#121	C₂×C₆₇	semidirect
580. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
581. C₆₇	#35080	direct (N × H)
583. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
585. C₂×#124	C₂²×C₆₇	semidirect
595. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
597. C₂×C₄×D₄	C₂²×C₆₇	semidirect
602. #401	C₂²×C₆₇	semidirect
603. #400	C₂²×C₆₇	semidirect
604. #400	C₂²×C₆₇	semidirect
606. #398	C₂²×C₆₇	semidirect
609. #397	C₂²×C₆₇	semidirect
610. #397	C₂²×C₆₇	semidirect
611. #396	C₂²×C₆₇	semidirect
617. #393	C₂²×C₆₇	semidirect
618. #391	C₂²×C₆₇	semidirect
619. #391	C₂²×C₆₇	semidirect
620. #391	C₂²×C₆₇	semidirect
621. #391	C₂²×C₆₇	semidirect
623. #390	C₂²×C₆₇	semidirect
624. #390	C₂²×C₆₇	semidirect
625. #389	C₂²×C₆₇	semidirect
626. #389	C₂²×C₆₇	semidirect
627. #389	C₂²×C₆₇	semidirect
628. #389	C₂²×C₆₇	semidirect
629. #389	C₂²×C₆₇	semidirect
634. #388	C₂²×C₆₇	semidirect
635. #388	C₂²×C₆₇	semidirect
636. #388	C₂²×C₆₇	semidirect
637. #388	C₂²×C₆₇	semidirect
638. #388	C₂²×C₆₇	semidirect
639. #387	C₂²×C₆₇	semidirect
640. #387	C₂²×C₆₇	semidirect
641. #387	C₂²×C₆₇	semidirect
653. #385	C₂²×C₆₇	semidirect
654. #384	C₂²×C₆₇	semidirect
655. #383	C₂²×C₆₇	semidirect
656. #382	C₂²×C₆₇	semidirect
664. #380	C₂²×C₆₇	semidirect
666. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
667. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
668. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
678. C₄×C₂²⋊C₄	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×#2857	2
C₆₇×#2850	2
C₆₇×#2848	2
C₆₇×#2847	2
C₆₇×#2653	2
C₆₇×#2649	2
C₆₇×#2510	2
C₆₇×#2495	2
C₆₇×#2494	2
C₆₇×#2492	2
C₆₇×#2491	2
C₆₇×#2472	2
C₆₇×#2450	2
C₆₇×#2427	2
C₆₇×#2426	2
C₆₇×#2423	2
C₆₇×#2422	2
C₆₇×#2418	2
C₆₇×#2337	2
C₆₇×#2335	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
#35080	67

Subgroups — C67×#35080 #30714331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35080 #30714331