Subgroups — C₆₇×#59361 #30738612

Order 17152.

1714 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2795	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2792	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2721	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2612	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2611	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2610	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2609	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2601	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2531	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2519	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2467	C₂	1	2	yes	maximal
14	C₆₇×#2454	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2371	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₇	C₂²	1	2	yes	—
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×#125×C₆₇	C₂²	1	2	yes	—
23	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×#117×C₆₇	C₂²	1	2	yes	—
27	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
30	#400×C₆₇	C₂²	1	1	yes	characteristic
31	#399×C₆₇	C₂²	1	2	yes	—
32	#399×C₆₇	C₂²	1	2	yes	—
33	#399×C₆₇	C₂²	1	1	yes	characteristic
34	#398×C₆₇	C₂²	1	2	yes	—
35	#398×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	1	yes	characteristic
37	#398×C₆₇	C₂²	1	2	yes	—
38	#397×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	1	yes	characteristic
40	#396×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#396×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	2	yes	—
44	#395×C₆₇	C₂²	1	1	yes	characteristic
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	1	yes	characteristic
48	#393×C₆₇	C₂²	1	1	yes	characteristic
49	#392×C₆₇	C₂²	1	1	yes	characteristic
50	#391×C₆₇	C₂²	1	2	yes	—
51	#390×C₆₇	C₂²	1	2	yes	—
52	#390×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	2	yes	—
56	#389×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×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	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×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	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#386×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	#384×C₆₇	C₂²	1	1	yes	characteristic
87	#384×C₆₇	C₂²	1	1	yes	characteristic
88	#382×C₆₇	C₂²	1	2	yes	—
89	#382×C₆₇	C₂²	1	1	yes	characteristic
90	#382×C₆₇	C₂²	1	1	yes	characteristic
91	#380×C₆₇	C₂²	1	2	yes	—
92	#380×C₆₇	C₂²	1	2	yes	—
93	#380×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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	2	yes	—
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	#376×C₆₇	C₂²	1	2	yes	—
104	#376×C₆₇	C₂²	1	2	yes	—
105	#376×C₆₇	C₂²	1	1	yes	characteristic
106	#376×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	#126×C₆₇	—	2	8	no	—
114	#126×C₆₇	—	4	4	no	—
115	#125×C₆₇	—	2	8	no	—
116	#125×C₆₇	—	4	2	no	—
117	#124×C₆₇	—	4	2	no	—
118	C₄×D₄×C₆₇	—	2	8	no	—
119	#117×C₆₇	—	2	8	no	—
120	#117×C₆₇	—	4	2	no	—
121	#117×C₆₇	—	4	2	no	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄²×C₆₇	—	2	4	no	—
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×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	1	yes	characteristic
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	1	yes	characteristic
187	#95×C₆₇	C₂³	1	1	yes	characteristic
188	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₆₇	—	4	1	no	—
207	C₂×Q₈×C₆₇	—	4	2	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	4	no	—
210	C₂×D₄×C₆₇	—	4	2	no	—
211	C₂×D₄×C₆₇	—	4	1	no	—
212	C₂×D₄×C₆₇	—	4	2	no	—
213	C₂²×C₄×C₆₇	—	2	2	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	4	no	—
220	C₂²×C₄×C₆₇	—	4	2	no	—
221	C₂²×C₄×C₆₇	—	4	2	no	—
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	2	4	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	4	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	4	2	no	—
250	C₄⋊C₄×C₆₇	—	4	2	no	—
251	C₄⋊C₄×C₆₇	—	4	2	no	—
252	C₄⋊C₄×C₆₇	—	4	2	no	—
253	C₄⋊C₄×C₆₇	—	4	1	no	—
254	C₄⋊C₄×C₆₇	—	4	1	no	—
255	C₄⋊C₄×C₆₇	—	4	1	no	—
256	C₄⋊C₄×C₆₇	—	4	1	no	—
257	C₄⋊C₄×C₆₇	—	4	2	no	—
258	C₄⋊C₄×C₆₇	—	4	1	no	—
259	C₄⋊C₄×C₆₇	—	4	1	no	—
260	C₄⋊C₄×C₆₇	—	4	2	no	—
261	C₄⋊C₄×C₆₇	—	4	2	no	—
262	C₄⋊C₄×C₆₇	#41	1	8	yes	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	4	2	no	—
273	C₂²⋊C₄×C₆₇	—	4	2	no	—
274	C₂²⋊C₄×C₆₇	—	4	2	no	—
275	C₂²⋊C₄×C₆₇	—	4	1	no	—
276	C₂²⋊C₄×C₆₇	—	4	2	no	—
277	C₂²⋊C₄×C₆₇	—	4	1	no	—
278	C₂²⋊C₄×C₆₇	—	4	2	no	—
279	C₂²⋊C₄×C₆₇	—	4	2	no	—
280	C₂²⋊C₄×C₆₇	—	4	2	no	—
281	C₄²×C₆₇	—	2	4	no	—
282	C₄²×C₆₇	—	2	2	no	—
283	C₄²×C₆₇	—	2	4	no	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	4	no	—
286	C₄²×C₆₇	—	2	4	no	—
287	C₄²×C₆₇	—	2	2	no	—
288	C₄²×C₆₇	—	2	2	no	—
289	C₄²×C₆₇	—	2	4	no	—
290	C₄²×C₆₇	—	4	2	no	—
291	C₄²×C₆₇	—	4	2	no	—
292	C₄²×C₆₇	—	4	2	no	—
293	C₄²×C₆₇	#41	1	4	yes	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	1	no	—
296	C₂³×C₆₇	—	2	1	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	2	2	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
306	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
307	Q₈×C₆₇	—	8	2	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	8	2	no	—
310	C₂×C₄×C₆₇	—	2	8	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	1	no	—
316	C₂×C₄×C₆₇	—	2	1	no	—
317	C₂×C₄×C₆₇	—	2	1	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	1	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	1	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	1	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	4	8	no	—
353	C₂×C₄×C₆₇	—	4	8	no	—
354	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
355	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
356	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
357	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
358	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
359	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
360	C₂²×C₆₇	—	2	2	no	—
361	C₂²×C₆₇	—	2	4	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	4	1	no	—
364	C₂²×C₆₇	—	4	1	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	2	no	—
370	C₂²×C₆₇	—	4	2	no	—
371	C₂²×C₆₇	—	4	2	no	—
372	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₆₇	C₂²×#41	1	2	yes	—
374	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂²×C₆₇	#585	1	2	yes	—
377	C₄×C₆₇	—	2	4	no	—
378	C₄×C₆₇	—	2	4	no	—
379	C₄×C₆₇	—	2	4	no	—
380	C₄×C₆₇	—	2	2	no	—
381	C₄×C₆₇	—	2	2	no	—
382	C₄×C₆₇	—	2	4	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	—	4	2	no	—
385	C₄×C₆₇	—	4	1	no	—
386	C₄×C₆₇	—	4	1	no	—
387	C₄×C₆₇	—	4	2	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	—	4	1	no	—
392	C₄×C₆₇	—	4	1	no	—
393	C₄×C₆₇	—	4	2	no	—
394	#59361	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂×C₆₇	—	4	2	no	—
396	C₂×C₆₇	—	8	2	no	—
397	C₂×C₆₇	#3475	1	2	yes	—
398	C₂×C₆₇	#3483	1	1	yes	characteristic
399	C₂×C₆₇	#3492	1	1	yes	characteristic
400	C₂×C₆₇	#3495	1	2	yes	—
401	C₂×C₆₇	#3551	1	1	yes	characteristic
402	#2795	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#2792	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#2721	C₂×C₆₇	1	2	yes	complemented
405	#2612	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#2611	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#2610	C₂×C₆₇	1	1	yes	characteristic
408	#2609	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#2601	C₂×C₆₇	1	2	yes	complemented
410	#2574	C₂×C₆₇	1	2	yes	complemented
411	#2531	C₂×C₆₇	1	2	yes	complemented
412	#2521	C₂×C₆₇	1	2	yes	complemented
413	#2519	C₂×C₆₇	1	2	yes	complemented
414	#2467	C₂×C₆₇	1	2	yes	—
415	#2454	C₂×C₆₇	1	2	yes	complemented
416	#2373	C₂×C₆₇	1	2	yes	complemented
417	#2371	C₂×C₆₇	1	2	yes	complemented
418	#2346	C₂×C₆₇	1	2	yes	complemented
419	#2290	C₂×C₆₇	1	2	yes	complemented
420	#2285	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₆₇	#59361	1	1	yes	characteristic, direct product factor, Sylow
422	C₂×#126	C₂²×C₆₇	1	2	yes	—
423	C₂×#126	C₂²×C₆₇	1	2	yes	—
424	C₂×#125	C₂²×C₆₇	1	2	yes	—
425	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
428	C₂×#117	C₂²×C₆₇	1	2	yes	—
429	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
431	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
432	#400	C₂²×C₆₇	1	1	yes	characteristic
433	#399	C₂²×C₆₇	1	1	yes	characteristic
434	#399	C₂²×C₆₇	1	2	yes	—
435	#399	C₂²×C₆₇	1	2	yes	—
436	#398	C₂²×C₆₇	1	2	yes	—
437	#398	C₂²×C₆₇	1	2	yes	—
438	#398	C₂²×C₆₇	1	1	yes	characteristic
439	#398	C₂²×C₆₇	1	2	yes	—
440	#397	C₂²×C₆₇	1	1	yes	characteristic
441	#397	C₂²×C₆₇	1	2	yes	—
442	#396	C₂²×C₆₇	1	2	yes	—
443	#396	C₂²×C₆₇	1	2	yes	—
444	#396	C₂²×C₆₇	1	2	yes	—
445	#395	C₂²×C₆₇	1	2	yes	—
446	#395	C₂²×C₆₇	1	1	yes	characteristic
447	#394	C₂²×C₆₇	1	2	yes	—
448	#394	C₂²×C₆₇	1	1	yes	characteristic
449	#394	C₂²×C₆₇	1	2	yes	—
450	#393	C₂²×C₆₇	1	1	yes	characteristic
451	#392	C₂²×C₆₇	1	1	yes	characteristic
452	#391	C₂²×C₆₇	1	2	yes	—
453	#390	C₂²×C₆₇	1	2	yes	—
454	#390	C₂²×C₆₇	1	2	yes	—
455	#389	C₂²×C₆₇	1	2	yes	—
456	#389	C₂²×C₆₇	1	2	yes	—
457	#389	C₂²×C₆₇	1	2	yes	—
458	#389	C₂²×C₆₇	1	2	yes	—
459	#388	C₂²×C₆₇	1	2	yes	—
460	#388	C₂²×C₆₇	1	2	yes	—
461	#388	C₂²×C₆₇	1	2	yes	—
462	#388	C₂²×C₆₇	1	2	yes	—
463	#388	C₂²×C₆₇	1	2	yes	—
464	#388	C₂²×C₆₇	1	2	yes	—
465	#388	C₂²×C₆₇	1	2	yes	—
466	#388	C₂²×C₆₇	1	2	yes	—
467	#388	C₂²×C₆₇	1	2	yes	—
468	#388	C₂²×C₆₇	1	2	yes	—
469	#388	C₂²×C₆₇	1	2	yes	—
470	#388	C₂²×C₆₇	1	2	yes	—
471	#387	C₂²×C₆₇	1	2	yes	—
472	#387	C₂²×C₆₇	1	2	yes	—
473	#387	C₂²×C₆₇	1	2	yes	—
474	#387	C₂²×C₆₇	1	2	yes	—
475	#387	C₂²×C₆₇	1	2	yes	—
476	#387	C₂²×C₆₇	1	2	yes	—
477	#387	C₂²×C₆₇	1	2	yes	—
478	#387	C₂²×C₆₇	1	2	yes	—
479	#387	C₂²×C₆₇	1	2	yes	—
480	#387	C₂²×C₆₇	1	2	yes	—
481	#387	C₂²×C₆₇	1	2	yes	—
482	#386	C₂²×C₆₇	1	2	yes	—
483	#386	C₂²×C₆₇	1	2	yes	—
484	#386	C₂²×C₆₇	1	2	yes	—
485	#385	C₂²×C₆₇	1	2	yes	—
486	#385	C₂²×C₆₇	1	2	yes	—
487	#385	C₂²×C₆₇	1	2	yes	—
488	#384	C₂²×C₆₇	1	1	yes	characteristic
489	#384	C₂²×C₆₇	1	1	yes	characteristic
490	#382	C₂²×C₆₇	1	2	yes	—
491	#382	C₂²×C₆₇	1	1	yes	characteristic
492	#382	C₂²×C₆₇	1	1	yes	characteristic
493	#380	C₂²×C₆₇	1	2	yes	—
494	#380	C₂²×C₆₇	1	2	yes	—
495	#380	C₂²×C₆₇	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
498	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
505	#376	C₂²×C₆₇	1	2	yes	—
506	#376	C₂²×C₆₇	1	2	yes	—
507	#376	C₂²×C₆₇	1	1	yes	characteristic
508	#376	C₂²×C₆₇	1	1	yes	characteristic
509	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
511	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
515	#126	—	2	8	no	—
516	#126	—	4	4	no	—
517	#125	—	2	8	no	—
518	#125	—	4	2	no	—
519	#124	—	4	2	no	—
520	C₄×D₄	—	2	8	no	—
521	#117	—	2	8	no	—
522	#117	—	4	2	no	—
523	#117	—	4	2	no	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄²	—	2	4	no	—
567	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
570	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
571	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
572	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
573	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
574	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
575	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
577	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
579	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
580	#95	C₂³×C₆₇	1	2	yes	—
581	#95	C₂³×C₆₇	1	2	yes	—
582	#95	C₂³×C₆₇	1	2	yes	—
583	#95	C₂³×C₆₇	1	2	yes	—
584	#95	C₂³×C₆₇	1	2	yes	—
585	#95	C₂³×C₆₇	1	1	yes	characteristic
586	#95	C₂³×C₆₇	1	2	yes	—
587	#95	C₂³×C₆₇	1	2	yes	—
588	#95	C₂³×C₆₇	1	1	yes	characteristic
589	#95	C₂³×C₆₇	1	1	yes	characteristic
590	#95	C₂³×C₆₇	1	1	yes	characteristic
591	#95	C₂³×C₆₇	1	2	yes	—
592	#95	C₂³×C₆₇	1	2	yes	—
593	#95	C₂³×C₆₇	1	2	yes	—
594	#95	C₂³×C₆₇	1	2	yes	—
595	#95	C₂³×C₆₇	1	2	yes	—
596	#95	C₂³×C₆₇	1	2	yes	—
597	#95	C₂³×C₆₇	1	2	yes	—
598	#95	C₂³×C₆₇	1	2	yes	—
599	#95	C₂³×C₆₇	1	2	yes	—
600	#95	C₂³×C₆₇	1	2	yes	—
601	#95	C₂³×C₆₇	1	2	yes	—
602	#95	C₂³×C₆₇	1	2	yes	—
603	#95	C₂³×C₆₇	1	2	yes	—
604	#95	C₂³×C₆₇	1	2	yes	—
605	#95	C₂³×C₆₇	1	2	yes	—
606	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
607	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	1	no	—
657	C₄⋊C₄	—	4	1	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	#41×C₆₇	1	8	yes	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	4	1	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	#41×C₆₇	1	4	yes	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
708	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
709	Q₈	—	8	2	no	—
710	D₄	—	4	8	no	—
711	D₄	—	8	2	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
757	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
758	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
759	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
760	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
761	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
775	C₂²	C₂²×#41×C₆₇	1	2	yes	—
776	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
777	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
778	C₂²	#585×C₆₇	1	2	yes	—
779	C₄	—	2	4	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	4	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₂	—	4	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₆₇×#3475	1	2	yes	—
799	C₂	C₆₇×#3483	1	1	yes	characteristic
800	C₂	C₆₇×#3492	1	1	yes	characteristic
801	C₂	C₆₇×#3495	1	2	yes	—
802	C₂	C₆₇×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	#392×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×#2795	C₂	semidirect
2. C₆₇×#2792	C₂	semidirect
3. C₆₇×#2721	C₂	semidirect
4. C₆₇×#2612	C₂	semidirect
5. C₆₇×#2611	C₂	semidirect
7. C₆₇×#2609	C₂	semidirect
8. C₆₇×#2601	C₂	semidirect
9. C₆₇×#2574	C₂	semidirect
10. C₆₇×#2531	C₂	semidirect
11. C₆₇×#2521	C₂	semidirect
12. C₆₇×#2519	C₂	semidirect
14. C₆₇×#2454	C₂	semidirect
15. C₆₇×#2373	C₂	semidirect
16. C₆₇×#2371	C₂	semidirect
17. C₆₇×#2346	C₂	semidirect
18. C₆₇×#2290	C₂	semidirect
19. C₆₇×#2285	C₂	semidirect
394. #59361	C₆₇	direct (N × H)
402. #2795	C₂×C₆₇	semidirect
403. #2792	C₂×C₆₇	semidirect
404. #2721	C₂×C₆₇	semidirect
405. #2612	C₂×C₆₇	semidirect
406. #2611	C₂×C₆₇	semidirect
408. #2609	C₂×C₆₇	semidirect
409. #2601	C₂×C₆₇	semidirect
410. #2574	C₂×C₆₇	semidirect
411. #2531	C₂×C₆₇	semidirect
412. #2521	C₂×C₆₇	semidirect
413. #2519	C₂×C₆₇	semidirect
415. #2454	C₂×C₆₇	semidirect
416. #2373	C₂×C₆₇	semidirect
417. #2371	C₂×C₆₇	semidirect
418. #2346	C₂×C₆₇	semidirect
419. #2290	C₂×C₆₇	semidirect
420. #2285	C₂×C₆₇	semidirect
421. C₆₇	#59361	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2795	2
C₆₇×#2792	2
C₆₇×#2721	2
C₆₇×#2612	2
C₆₇×#2611	2
C₆₇×#2610	2
C₆₇×#2609	2
C₆₇×#2601	2
C₆₇×#2574	2
C₆₇×#2531	2
C₆₇×#2521	2
C₆₇×#2519	2
C₆₇×#2467	2
C₆₇×#2454	2
C₆₇×#2373	2
C₆₇×#2371	2
C₆₇×#2346	2
C₆₇×#2290	2
C₆₇×#2285	2
#59361	67

Subgroups — C67×#59361 #30738612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59361 #30738612