Subgroups — C₆₇×#59463 #30738714

Order 17152.

1680 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2790	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2788	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2587	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2566	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2556	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2497	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2452	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic
19	Q₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	#400×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	2	yes	—
39	#400×C₆₇	C₂²	1	2	yes	—
40	#400×C₆₇	C₂²	1	2	yes	—
41	#399×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	2	yes	—
49	#396×C₆₇	C₂²	1	2	yes	—
50	#395×C₆₇	C₂²	1	2	yes	—
51	#393×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#391×C₆₇	C₂²	1	1	yes	characteristic
57	#391×C₆₇	C₂²	1	1	yes	characteristic
58	#390×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	2	yes	—
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	2	yes	—
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	2	yes	—
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	1	yes	characteristic
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	1	yes	characteristic
87	#387×C₆₇	C₂²	1	1	yes	characteristic
88	#387×C₆₇	C₂²	1	1	yes	characteristic
89	#387×C₆₇	C₂²	1	2	yes	—
90	#385×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	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	2	yes	—
98	#384×C₆₇	C₂²	1	2	yes	—
99	#384×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	#382×C₆₇	C₂²	1	1	yes	characteristic
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	1	yes	characteristic
104	#380×C₆₇	C₂²	1	2	yes	—
105	#380×C₆₇	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₂×#95×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₇	—	4	2	no	—
130	#125×C₆₇	—	2	4	no	—
131	#125×C₆₇	—	2	4	no	—
132	#125×C₆₇	—	4	2	no	—
133	#124×C₆₇	Q₈	1	8	yes	complemented
134	C₂²⋊Q₈×C₆₇	—	2	8	no	—
135	C₄×Q₈×C₆₇	—	2	4	no	—
136	C₄×Q₈×C₆₇	—	4	2	no	—
137	C₄×Q₈×C₆₇	—	4	2	no	—
138	C₄×D₄×C₆₇	—	2	4	no	—
139	C₄×D₄×C₆₇	—	4	2	no	—
140	C₄×D₄×C₆₇	—	4	2	no	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	1	yes	characteristic
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	1	yes	characteristic
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	1	yes	characteristic
217	#95×C₆₇	C₂³	1	1	yes	characteristic
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	2	4	no	—
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	4	2	no	—
239	C₂×Q₈×C₆₇	—	4	2	no	—
240	C₂×Q₈×C₆₇	C₂×Q₈	1	4	yes	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	4	1	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	1	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	1	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	—	4	1	no	—
300	C₄⋊C₄×C₆₇	—	4	1	no	—
301	C₄⋊C₄×C₆₇	—	4	2	no	—
302	C₄⋊C₄×C₆₇	—	4	2	no	—
303	C₄⋊C₄×C₆₇	—	4	2	no	—
304	C₄⋊C₄×C₆₇	—	4	2	no	—
305	C₄⋊C₄×C₆₇	—	4	2	no	—
306	C₄⋊C₄×C₆₇	—	4	2	no	—
307	C₄⋊C₄×C₆₇	#41	1	4	yes	—
308	C₄⋊C₄×C₆₇	#41	1	4	yes	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
319	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	—	2	2	no	—
323	C₄²×C₆₇	—	2	2	no	—
324	C₄²×C₆₇	—	2	2	no	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₄²×C₆₇	—	4	1	no	—
330	C₄²×C₆₇	—	4	1	no	—
331	C₄²×C₆₇	—	4	2	no	—
332	C₄²×C₆₇	—	4	1	no	—
333	C₄²×C₆₇	—	4	2	no	—
334	C₄²×C₆₇	—	4	2	no	—
335	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
343	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
344	Q₈×C₆₇	—	2	8	no	—
345	Q₈×C₆₇	—	8	4	no	—
346	D₄×C₆₇	—	2	8	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	8	4	no	—
404	C₂×C₄×C₆₇	—	8	4	no	—
405	C₂×C₄×C₆₇	—	8	4	no	—
406	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
407	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
408	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
409	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
410	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
412	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
413	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
415	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	4	no	—
418	C₂²×C₆₇	—	2	4	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
424	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₆₇	#585	1	1	yes	characteristic
428	C₂²×C₆₇	#585	1	1	yes	characteristic
429	C₂²×C₆₇	#585	1	1	yes	characteristic
430	C₄×C₆₇	—	2	4	no	—
431	C₄×C₆₇	—	2	2	no	—
432	C₄×C₆₇	—	2	2	no	—
433	C₄×C₆₇	—	2	2	no	—
434	C₄×C₆₇	—	2	2	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	4	no	—
437	C₄×C₆₇	—	4	1	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₄×C₆₇	—	4	1	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	1	no	—
444	C₄×C₆₇	—	4	1	no	—
445	C₄×C₆₇	—	4	1	no	—
446	C₄×C₆₇	—	4	1	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	#554	1	4	yes	—
452	#59463	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂×C₆₇	—	4	4	no	—
454	C₂×C₆₇	C₂×#554	1	1	yes	characteristic
455	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
456	C₂×C₆₇	#3480	1	1	yes	characteristic
457	C₂×C₆₇	#3504	1	1	yes	characteristic
458	C₂×C₆₇	#3514	1	1	yes	characteristic
459	C₂×C₆₇	#3521	1	1	yes	characteristic
460	C₂×C₆₇	#3562	1	1	yes	characteristic
461	#2790	C₂×C₆₇	1	2	yes	complemented
462	#2788	C₂×C₆₇	1	2	yes	complemented
463	#2589	C₂×C₆₇	1	2	yes	complemented
464	#2587	C₂×C₆₇	1	2	yes	complemented
465	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#2568	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#2566	C₂×C₆₇	1	1	yes	characteristic
468	#2556	C₂×C₆₇	1	2	yes	complemented
469	#2550	C₂×C₆₇	1	1	yes	characteristic, complemented
470	#2505	C₂×C₆₇	1	2	yes	complemented
471	#2497	C₂×C₆₇	1	2	yes	complemented
472	#2454	C₂×C₆₇	1	1	yes	characteristic
473	#2453	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#2453	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#2452	C₂×C₆₇	1	1	yes	characteristic
476	#2368	C₂×C₆₇	1	2	yes	complemented
477	#2367	C₂×C₆₇	1	1	yes	characteristic
478	#2367	C₂×C₆₇	1	1	yes	characteristic
479	Q₈×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#2349	C₂×C₆₇	1	1	yes	characteristic
481	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
482	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
483	C₄×#124	C₂×C₆₇	1	1	yes	characteristic
484	C₆₇	#59463	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
486	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
497	#400	C₂²×C₆₇	1	2	yes	—
498	#400	C₂²×C₆₇	1	2	yes	—
499	#400	C₂²×C₆₇	1	2	yes	—
500	#400	C₂²×C₆₇	1	2	yes	—
501	#400	C₂²×C₆₇	1	2	yes	—
502	#399	C₂²×C₆₇	1	2	yes	—
503	#398	C₂²×C₆₇	1	2	yes	—
504	#398	C₂²×C₆₇	1	2	yes	—
505	#398	C₂²×C₆₇	1	2	yes	—
506	#398	C₂²×C₆₇	1	2	yes	—
507	#396	C₂²×C₆₇	1	2	yes	—
508	#396	C₂²×C₆₇	1	2	yes	—
509	#396	C₂²×C₆₇	1	2	yes	—
510	#396	C₂²×C₆₇	1	2	yes	—
511	#395	C₂²×C₆₇	1	2	yes	—
512	#393	C₂²×C₆₇	1	2	yes	—
513	#391	C₂²×C₆₇	1	2	yes	—
514	#391	C₂²×C₆₇	1	1	yes	characteristic
515	#391	C₂²×C₆₇	1	2	yes	—
516	#391	C₂²×C₆₇	1	1	yes	characteristic
517	#391	C₂²×C₆₇	1	2	yes	—
518	#391	C₂²×C₆₇	1	1	yes	characteristic
519	#390	C₂²×C₆₇	1	1	yes	characteristic
520	#390	C₂²×C₆₇	1	1	yes	characteristic
521	#390	C₂²×C₆₇	1	1	yes	characteristic
522	#389	C₂²×C₆₇	1	1	yes	characteristic
523	#389	C₂²×C₆₇	1	1	yes	characteristic
524	#389	C₂²×C₆₇	1	1	yes	characteristic
525	#389	C₂²×C₆₇	1	1	yes	characteristic
526	#389	C₂²×C₆₇	1	1	yes	characteristic
527	#389	C₂²×C₆₇	1	1	yes	characteristic
528	#389	C₂²×C₆₇	1	2	yes	—
529	#389	C₂²×C₆₇	1	2	yes	—
530	#389	C₂²×C₆₇	1	2	yes	—
531	#389	C₂²×C₆₇	1	2	yes	—
532	#389	C₂²×C₆₇	1	1	yes	characteristic
533	#389	C₂²×C₆₇	1	1	yes	characteristic
534	#389	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#388	C₂²×C₆₇	1	2	yes	—
537	#388	C₂²×C₆₇	1	2	yes	—
538	#388	C₂²×C₆₇	1	2	yes	—
539	#388	C₂²×C₆₇	1	2	yes	—
540	#388	C₂²×C₆₇	1	2	yes	—
541	#387	C₂²×C₆₇	1	1	yes	characteristic
542	#387	C₂²×C₆₇	1	1	yes	characteristic
543	#387	C₂²×C₆₇	1	1	yes	characteristic
544	#387	C₂²×C₆₇	1	1	yes	characteristic
545	#387	C₂²×C₆₇	1	2	yes	—
546	#387	C₂²×C₆₇	1	2	yes	—
547	#387	C₂²×C₆₇	1	2	yes	—
548	#387	C₂²×C₆₇	1	2	yes	—
549	#387	C₂²×C₆₇	1	2	yes	—
550	#387	C₂²×C₆₇	1	2	yes	—
551	#385	C₂²×C₆₇	1	2	yes	—
552	#385	C₂²×C₆₇	1	2	yes	—
553	#385	C₂²×C₆₇	1	2	yes	—
554	#385	C₂²×C₆₇	1	2	yes	—
555	#385	C₂²×C₆₇	1	2	yes	—
556	#385	C₂²×C₆₇	1	2	yes	—
557	#385	C₂²×C₆₇	1	2	yes	—
558	#385	C₂²×C₆₇	1	2	yes	—
559	#384	C₂²×C₆₇	1	1	yes	characteristic
560	#384	C₂²×C₆₇	1	2	yes	—
561	#382	C₂²×C₆₇	1	1	yes	characteristic
562	#382	C₂²×C₆₇	1	1	yes	characteristic
563	#382	C₂²×C₆₇	1	1	yes	characteristic
564	#382	C₂²×C₆₇	1	1	yes	characteristic
565	#380	C₂²×C₆₇	1	2	yes	—
566	#380	C₂²×C₆₇	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
573	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
578	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
582	C₂×#95	C₂²×C₆₇	1	2	yes	—
583	C₄³	C₂²×C₆₇	1	1	yes	characteristic
584	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
586	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
588	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
589	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
590	C₄⋊Q₈	—	4	2	no	—
591	#125	—	2	4	no	—
592	#125	—	2	4	no	—
593	#125	—	4	2	no	—
594	#124	Q₈×C₆₇	1	8	yes	complemented
595	C₂²⋊Q₈	—	2	8	no	—
596	C₄×Q₈	—	2	4	no	—
597	C₄×Q₈	—	4	2	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	4	2	no	—
601	C₄×D₄	—	4	2	no	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	#95	C₂³×C₆₇	1	1	yes	characteristic
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	1	yes	characteristic
668	#95	C₂³×C₆₇	1	1	yes	characteristic
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	#95	C₂³×C₆₇	1	1	yes	characteristic
676	#95	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	1	yes	characteristic
678	#95	C₂³×C₆₇	1	1	yes	characteristic
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	1	yes	characteristic
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	2	yes	—
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	1	yes	characteristic
686	#95	C₂³×C₆₇	1	1	yes	characteristic
687	#95	C₂³×C₆₇	1	1	yes	characteristic
688	#95	C₂³×C₆₇	1	2	yes	—
689	#95	C₂³×C₆₇	1	1	yes	characteristic
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	C₂×Q₈×C₆₇	1	4	yes	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	#41×C₆₇	1	4	yes	—
769	C₄⋊C₄	#41×C₆₇	1	4	yes	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
780	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	1	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	1	no	—
796	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
804	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
805	Q₈	—	2	8	no	—
806	Q₈	—	8	4	no	—
807	D₄	—	2	8	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	—	8	4	no	—
866	C₂×C₄	—	8	4	no	—
867	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
868	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
869	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
870	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
871	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
872	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
873	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
874	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
875	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
876	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
886	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
887	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
888	C₂²	#585×C₆₇	1	1	yes	characteristic
889	C₂²	#585×C₆₇	1	1	yes	characteristic
890	C₂²	#585×C₆₇	1	1	yes	characteristic
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	1	no	—
912	C₄	#554×C₆₇	1	4	yes	—
913	C₂	—	4	4	no	—
914	C₂	C₂×#554×C₆₇	1	1	yes	characteristic
915	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
916	C₂	C₆₇×#3480	1	1	yes	characteristic
917	C₂	C₆₇×#3504	1	1	yes	characteristic
918	C₂	C₆₇×#3514	1	1	yes	characteristic
919	C₂	C₆₇×#3521	1	1	yes	characteristic
920	C₂	C₆₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
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×#2790	C₂	semidirect
2. C₆₇×#2788	C₂	semidirect
3. C₆₇×#2589	C₂	semidirect
4. C₆₇×#2587	C₂	semidirect
5. C₆₇×#2570	C₂	semidirect
6. C₆₇×#2568	C₂	semidirect
8. C₆₇×#2556	C₂	semidirect
9. C₆₇×#2550	C₂	semidirect
10. C₆₇×#2505	C₂	semidirect
11. C₆₇×#2497	C₂	semidirect
13. C₆₇×#2453	C₂	semidirect
14. C₆₇×#2453	C₂	semidirect
16. C₆₇×#2368	C₂	semidirect
19. Q₈×C₄⋊C₄×C₆₇	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
22. C₄×#125×C₆₇	C₂	semidirect
133. #124×C₆₇	Q₈	semidirect
452. #59463	C₆₇	direct (N × H)
461. #2790	C₂×C₆₇	semidirect
462. #2788	C₂×C₆₇	semidirect
463. #2589	C₂×C₆₇	semidirect
464. #2587	C₂×C₆₇	semidirect
465. #2570	C₂×C₆₇	semidirect
466. #2568	C₂×C₆₇	semidirect
468. #2556	C₂×C₆₇	semidirect
469. #2550	C₂×C₆₇	semidirect
470. #2505	C₂×C₆₇	semidirect
471. #2497	C₂×C₆₇	semidirect
473. #2453	C₂×C₆₇	semidirect
474. #2453	C₂×C₆₇	semidirect
476. #2368	C₂×C₆₇	semidirect
479. Q₈×C₄⋊C₄	C₂×C₆₇	semidirect
481. C₄×#125	C₂×C₆₇	semidirect
482. C₄×#125	C₂×C₆₇	semidirect
484. C₆₇	#59463	direct (N × H)
594. #124	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2790	2
C₆₇×#2788	2
C₆₇×#2589	2
C₆₇×#2587	2
C₆₇×#2570	2
C₆₇×#2568	2
C₆₇×#2566	2
C₆₇×#2556	2
C₆₇×#2550	2
C₆₇×#2505	2
C₆₇×#2497	2
C₆₇×#2454	2
C₆₇×#2453	2
C₆₇×#2452	2
C₆₇×#2368	2
C₆₇×#2367	2
Q₈×C₄⋊C₄×C₆₇	2
C₆₇×#2349	2
C₄×#125×C₆₇	2
C₄×#124×C₆₇	2
#59463	67

Subgroups — C67×#59463 #30738714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59463 #30738714