Subgroups — C₆₇×#59886 #30739137

Order 17152.

1930 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2806	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2805	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2804	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2732	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2569	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2520	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2465	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2409	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2364	C₂	1	2	yes	maximal
16	C₆₇×#2349	C₂	1	2	yes	maximal, complemented
17	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
19	C₂×#391×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#399×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#398×C₆₇	C₂²	1	2	yes	—
40	#396×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#395×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	2	yes	—
44	#395×C₆₇	C₂²	1	2	yes	—
45	#393×C₆₇	C₂²	1	2	yes	—
46	#393×C₆₇	C₂²	1	2	yes	—
47	#393×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	2	yes	—
49	#391×C₆₇	C₂²	1	2	yes	—
50	#391×C₆₇	C₂²	1	1	yes	characteristic
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#391×C₆₇	C₂²	1	1	yes	characteristic
54	#391×C₆₇	C₂²	1	2	yes	—
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#391×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	1	yes	characteristic
59	#389×C₆₇	C₂²	1	1	yes	characteristic
60	#389×C₆₇	C₂²	1	2	yes	—
61	#389×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	2	yes	—
66	#387×C₆₇	C₂²	1	2	yes	—
67	#387×C₆₇	C₂²	1	2	yes	—
68	#387×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	—
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#382×C₆₇	C₂²	1	2	yes	—
91	#380×C₆₇	C₂²	1	1	yes	characteristic
92	#380×C₆₇	C₂²	1	1	yes	characteristic
93	#380×C₆₇	C₂²	1	2	yes	—
94	#380×C₆₇	C₂²	1	2	yes	—
95	#380×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₂×#95×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₇	—	2	4	no	—
108	C₂²×Q₈×C₆₇	—	4	2	no	—
109	C₂²×Q₈×C₆₇	—	4	2	no	—
110	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²⋊Q₈×C₆₇	—	2	8	no	—
125	C₂²⋊Q₈×C₆₇	—	2	4	no	—
126	C₂²⋊Q₈×C₆₇	—	4	4	no	—
127	#121×C₆₇	Q₈	1	8	yes	complemented
128	C₄×Q₈×C₆₇	—	4	2	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	4	2	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	C₄×D₄×C₆₇	—	4	4	no	—
133	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	—	4	2	no	—
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
209	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂×Q₈×C₆₇	—	2	2	no	—
211	C₂×Q₈×C₆₇	—	2	4	no	—
212	C₂×Q₈×C₆₇	—	2	2	no	—
213	C₂×Q₈×C₆₇	—	2	4	no	—
214	C₂×Q₈×C₆₇	—	4	1	no	—
215	C₂×Q₈×C₆₇	—	4	1	no	—
216	C₂×Q₈×C₆₇	—	4	1	no	—
217	C₂×Q₈×C₆₇	—	4	1	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	—	4	1	no	—
220	C₂×Q₈×C₆₇	—	4	1	no	—
221	C₂×Q₈×C₆₇	—	4	16	no	—
222	C₂×Q₈×C₆₇	#41	1	4	yes	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	4	1	no	—
226	C₂×D₄×C₆₇	—	4	1	no	—
227	C₂×D₄×C₆₇	C₂×Q₈	1	8	yes	—
228	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	complemented
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	4	1	no	—
238	C₂²×C₄×C₆₇	—	4	1	no	—
239	C₂²×C₄×C₆₇	—	4	1	no	—
240	C₂²×C₄×C₆₇	—	4	1	no	—
241	C₂²×C₄×C₆₇	—	4	2	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	2	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	C₂×Q₈	1	4	yes	—
252	C₂²×C₄×C₆₇	#41	1	4	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	2	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	4	1	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	1	no	—
280	C₄⋊C₄×C₆₇	—	4	1	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	1	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	1	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	2	no	—
292	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	complemented
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	complemented
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	—	2	2	no	—
308	C₄²×C₆₇	—	2	2	no	—
309	C₄²×C₆₇	—	4	1	no	—
310	C₄²×C₆₇	—	4	1	no	—
311	C₄²×C₆₇	—	4	2	no	—
312	C₄²×C₆₇	—	4	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	2	no	—
315	C₂³×C₆₇	—	2	1	no	—
316	C₂³×C₆₇	—	2	1	no	—
317	C₂³×C₆₇	—	2	1	no	—
318	C₂³×C₆₇	—	2	1	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
326	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
327	C₂³×C₆₇	C₂×#41	1	2	yes	—
328	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
329	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
330	Q₈×C₆₇	—	4	4	no	—
331	Q₈×C₆₇	—	4	8	no	—
332	Q₈×C₆₇	—	4	4	no	—
333	Q₈×C₆₇	—	4	4	no	—
334	D₄×C₆₇	—	2	16	no	—
335	D₄×C₆₇	—	4	4	no	—
336	C₂×C₄×C₆₇	—	2	8	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	1	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	1	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	1	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	1	no	—
351	C₂×C₄×C₆₇	—	2	1	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	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	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	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	—	4	4	no	—
381	C₂×C₄×C₆₇	—	4	4	no	—
382	C₂×C₄×C₆₇	—	4	8	no	—
383	C₂×C₄×C₆₇	—	8	4	no	—
384	C₂×C₄×C₆₇	—	8	4	no	—
385	C₂×C₄×C₆₇	—	8	4	no	—
386	C₂×C₄×C₆₇	—	8	4	no	—
387	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
388	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
389	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
390	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
391	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
392	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
393	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
394	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₆₇	—	2	2	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	2	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	2	2	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	#554	1	4	yes	—
409	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
410	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₆₇	#585	1	1	yes	characteristic
415	C₂²×C₆₇	#585	1	1	yes	characteristic
416	C₄×C₆₇	—	2	4	no	—
417	C₄×C₆₇	—	2	2	no	—
418	C₄×C₆₇	—	2	2	no	—
419	C₄×C₆₇	—	2	4	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	#59886	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₆₇	—	2	4	no	—
435	C₂×C₆₇	—	4	4	no	—
436	C₂×C₆₇	C₂×#554	1	1	yes	characteristic
437	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
438	C₂×C₆₇	#3480	1	1	yes	characteristic
439	C₂×C₆₇	#3490	1	1	yes	characteristic
440	C₂×C₆₇	#3501	1	1	yes	characteristic
441	C₂×C₆₇	#3505	1	1	yes	characteristic
442	C₂×C₆₇	#3545	1	1	yes	characteristic
443	#2806	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#2805	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#2804	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#2732	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#2589	C₂×C₆₇	1	2	yes	complemented
448	#2579	C₂×C₆₇	1	2	yes	complemented
449	#2574	C₂×C₆₇	1	2	yes	complemented
450	#2569	C₂×C₆₇	1	2	yes	complemented
451	#2564	C₂×C₆₇	1	2	yes	complemented
452	#2520	C₂×C₆₇	1	2	yes	complemented
453	#2465	C₂×C₆₇	1	2	yes	complemented
454	#2450	C₂×C₆₇	1	2	yes	complemented
455	#2409	C₂×C₆₇	1	2	yes	complemented
456	#2368	C₂×C₆₇	1	2	yes	complemented
457	#2364	C₂×C₆₇	1	2	yes	—
458	#2349	C₂×C₆₇	1	2	yes	complemented
459	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
461	C₂×#391	C₂×C₆₇	1	1	yes	characteristic, complemented
462	C₆₇	#59886	1	1	yes	characteristic, direct product factor, Sylow
463	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
466	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
467	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
470	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
471	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
474	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
475	#400	C₂²×C₆₇	1	2	yes	—
476	#400	C₂²×C₆₇	1	2	yes	—
477	#400	C₂²×C₆₇	1	2	yes	—
478	#399	C₂²×C₆₇	1	2	yes	—
479	#398	C₂²×C₆₇	1	2	yes	—
480	#398	C₂²×C₆₇	1	2	yes	—
481	#398	C₂²×C₆₇	1	2	yes	—
482	#398	C₂²×C₆₇	1	2	yes	—
483	#396	C₂²×C₆₇	1	2	yes	—
484	#396	C₂²×C₆₇	1	2	yes	—
485	#395	C₂²×C₆₇	1	2	yes	—
486	#395	C₂²×C₆₇	1	2	yes	—
487	#395	C₂²×C₆₇	1	2	yes	—
488	#393	C₂²×C₆₇	1	2	yes	—
489	#393	C₂²×C₆₇	1	2	yes	—
490	#393	C₂²×C₆₇	1	2	yes	—
491	#391	C₂²×C₆₇	1	1	yes	characteristic
492	#391	C₂²×C₆₇	1	2	yes	—
493	#391	C₂²×C₆₇	1	2	yes	—
494	#391	C₂²×C₆₇	1	1	yes	characteristic
495	#391	C₂²×C₆₇	1	2	yes	—
496	#391	C₂²×C₆₇	1	2	yes	—
497	#391	C₂²×C₆₇	1	1	yes	characteristic
498	#391	C₂²×C₆₇	1	1	yes	characteristic
499	#391	C₂²×C₆₇	1	1	yes	characteristic
500	#390	C₂²×C₆₇	1	1	yes	characteristic
501	#389	C₂²×C₆₇	1	2	yes	—
502	#389	C₂²×C₆₇	1	2	yes	—
503	#389	C₂²×C₆₇	1	1	yes	characteristic
504	#389	C₂²×C₆₇	1	1	yes	characteristic
505	#388	C₂²×C₆₇	1	2	yes	—
506	#388	C₂²×C₆₇	1	2	yes	—
507	#388	C₂²×C₆₇	1	2	yes	—
508	#387	C₂²×C₆₇	1	2	yes	—
509	#387	C₂²×C₆₇	1	2	yes	—
510	#387	C₂²×C₆₇	1	2	yes	—
511	#387	C₂²×C₆₇	1	2	yes	—
512	#387	C₂²×C₆₇	1	2	yes	—
513	#387	C₂²×C₆₇	1	2	yes	—
514	#387	C₂²×C₆₇	1	2	yes	—
515	#387	C₂²×C₆₇	1	2	yes	—
516	#387	C₂²×C₆₇	1	2	yes	—
517	#387	C₂²×C₆₇	1	2	yes	—
518	#387	C₂²×C₆₇	1	2	yes	—
519	#386	C₂²×C₆₇	1	2	yes	—
520	#386	C₂²×C₆₇	1	2	yes	—
521	#386	C₂²×C₆₇	1	2	yes	—
522	#386	C₂²×C₆₇	1	2	yes	—
523	#386	C₂²×C₆₇	1	2	yes	—
524	#385	C₂²×C₆₇	1	2	yes	—
525	#385	C₂²×C₆₇	1	2	yes	—
526	#385	C₂²×C₆₇	1	2	yes	—
527	#385	C₂²×C₆₇	1	2	yes	—
528	#385	C₂²×C₆₇	1	2	yes	—
529	#385	C₂²×C₆₇	1	2	yes	—
530	#385	C₂²×C₆₇	1	2	yes	—
531	#385	C₂²×C₆₇	1	2	yes	—
532	#385	C₂²×C₆₇	1	2	yes	—
533	#382	C₂²×C₆₇	1	2	yes	—
534	#380	C₂²×C₆₇	1	2	yes	—
535	#380	C₂²×C₆₇	1	2	yes	—
536	#380	C₂²×C₆₇	1	1	yes	characteristic
537	#380	C₂²×C₆₇	1	2	yes	—
538	#380	C₂²×C₆₇	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
540	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
542	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
547	C₂×#95	C₂²×C₆₇	1	2	yes	—
548	C₂×#95	C₂²×C₆₇	1	2	yes	—
549	C₂×#95	C₂²×C₆₇	1	2	yes	—
550	C₂²×Q₈	—	2	4	no	—
551	C₂²×Q₈	—	4	2	no	—
552	C₂²×Q₈	—	4	2	no	—
553	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
554	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
561	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
562	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
563	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂²⋊Q₈	—	2	8	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	4	4	no	—
570	#121	Q₈×C₆₇	1	8	yes	complemented
571	C₄×Q₈	—	4	2	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	4	2	no	—
574	C₄×D₄	—	4	4	no	—
575	C₄×D₄	—	4	4	no	—
576	C₂×C₄⋊C₄	—	4	2	no	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄²	—	4	2	no	—
614	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
623	#95	C₂³×C₆₇	1	2	yes	—
624	#95	C₂³×C₆₇	1	2	yes	—
625	#95	C₂³×C₆₇	1	2	yes	—
626	#95	C₂³×C₆₇	1	2	yes	—
627	#95	C₂³×C₆₇	1	2	yes	—
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
652	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	1	no	—
659	C₂×Q₈	—	4	1	no	—
660	C₂×Q₈	—	4	1	no	—
661	C₂×Q₈	—	4	2	no	—
662	C₂×Q₈	—	4	1	no	—
663	C₂×Q₈	—	4	1	no	—
664	C₂×Q₈	—	4	16	no	—
665	C₂×Q₈	#41×C₆₇	1	4	yes	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	4	1	no	—
669	C₂×D₄	—	4	1	no	—
670	C₂×D₄	C₂×Q₈×C₆₇	1	8	yes	—
671	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	complemented
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
695	C₂²×C₄	#41×C₆₇	1	4	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	complemented
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	complemented
749	C₄²	—	2	4	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	4	1	no	—
753	C₄²	—	4	1	no	—
754	C₄²	—	4	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
769	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
770	C₂³	C₂×#41×C₆₇	1	2	yes	—
771	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
772	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
773	Q₈	—	4	4	no	—
774	Q₈	—	4	8	no	—
775	Q₈	—	4	4	no	—
776	Q₈	—	4	4	no	—
777	D₄	—	2	16	no	—
778	D₄	—	4	4	no	—
779	C₂×C₄	—	2	8	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	8	4	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
831	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
832	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
833	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
834	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
835	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
836	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
837	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	#554×C₆₇	1	4	yes	—
852	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
853	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
854	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
855	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
856	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
857	C₂²	#585×C₆₇	1	1	yes	characteristic
858	C₂²	#585×C₆₇	1	1	yes	characteristic
859	C₄	—	2	4	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₂	—	2	4	no	—
877	C₂	—	4	4	no	—
878	C₂	C₂×#554×C₆₇	1	1	yes	characteristic
879	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
880	C₂	C₆₇×#3480	1	1	yes	characteristic
881	C₂	C₆₇×#3490	1	1	yes	characteristic
882	C₂	C₆₇×#3501	1	1	yes	characteristic
883	C₂	C₆₇×#3505	1	1	yes	characteristic
884	C₂	C₆₇×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
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×#2806	C₂	semidirect
2. C₆₇×#2805	C₂	semidirect
3. C₆₇×#2804	C₂	semidirect
4. C₆₇×#2732	C₂	semidirect
5. C₆₇×#2589	C₂	semidirect
6. C₆₇×#2579	C₂	semidirect
7. C₆₇×#2574	C₂	semidirect
8. C₆₇×#2569	C₂	semidirect
9. C₆₇×#2564	C₂	semidirect
10. C₆₇×#2520	C₂	semidirect
11. C₆₇×#2465	C₂	semidirect
12. C₆₇×#2450	C₂	semidirect
13. C₆₇×#2409	C₂	semidirect
14. C₆₇×#2368	C₂	semidirect
16. C₆₇×#2349	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
19. C₂×#391×C₆₇	C₂	semidirect
127. #121×C₆₇	Q₈	semidirect
228. C₂×D₄×C₆₇	C₂×Q₈	semidirect
292. C₄⋊C₄×C₆₇	C₂×Q₈	semidirect
305. C₂²⋊C₄×C₆₇	C₂×Q₈	semidirect
433. #59886	C₆₇	direct (N × H)
443. #2806	C₂×C₆₇	semidirect
444. #2805	C₂×C₆₇	semidirect
445. #2804	C₂×C₆₇	semidirect
446. #2732	C₂×C₆₇	semidirect
447. #2589	C₂×C₆₇	semidirect
448. #2579	C₂×C₆₇	semidirect
449. #2574	C₂×C₆₇	semidirect
450. #2569	C₂×C₆₇	semidirect
451. #2564	C₂×C₆₇	semidirect
452. #2520	C₂×C₆₇	semidirect
453. #2465	C₂×C₆₇	semidirect
454. #2450	C₂×C₆₇	semidirect
455. #2409	C₂×C₆₇	semidirect
456. #2368	C₂×C₆₇	semidirect
458. #2349	C₂×C₆₇	semidirect
459. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
461. C₂×#391	C₂×C₆₇	semidirect
462. C₆₇	#59886	direct (N × H)
570. #121	Q₈×C₆₇	semidirect
671. C₂×D₄	C₂×Q₈×C₆₇	semidirect
735. C₄⋊C₄	C₂×Q₈×C₆₇	semidirect
748. C₂²⋊C₄	C₂×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×#2806	2
C₆₇×#2805	2
C₆₇×#2804	2
C₆₇×#2732	2
C₆₇×#2589	2
C₆₇×#2579	2
C₆₇×#2574	2
C₆₇×#2569	2
C₆₇×#2564	2
C₆₇×#2520	2
C₆₇×#2465	2
C₆₇×#2450	2
C₆₇×#2409	2
C₆₇×#2368	2
C₆₇×#2364	2
C₆₇×#2349	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#391×C₆₇	2
#59886	67

Subgroups — C67×#59886 #30739137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59886 #30739137