Subgroups — C₆₇×#22472 #30701723

Order 17152.

1162 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	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	#529×C₆₇	—	2	4	no	—
21	#529×C₆₇	—	2	4	no	—
22	C₂×#126×C₆₇	C₄	1	1	yes	characteristic
23	C₂×#126×C₆₇	C₄	1	1	yes	characteristic
24	C₂×#125×C₆₇	C₄	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₄	1	1	yes	characteristic
26	C₂×#123×C₆₇	C₄	1	1	yes	characteristic
27	C₂×#123×C₆₇	C₄	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₄	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
37	#436×C₆₇	—	2	4	no	—
38	#435×C₆₇	—	2	4	no	—
39	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
51	#336×C₆₇	C₂²	1	1	yes	characteristic
52	#336×C₆₇	C₂²	1	1	yes	characteristic
53	#336×C₆₇	C₂²	1	1	yes	characteristic
54	#336×C₆₇	C₂²	1	1	yes	characteristic
55	#336×C₆₇	C₂²	1	1	yes	characteristic
56	#336×C₆₇	C₂²	1	1	yes	characteristic
57	#336×C₆₇	C₂²	1	1	yes	characteristic
58	#336×C₆₇	C₂²	1	1	yes	characteristic
59	#336×C₆₇	C₂²	1	1	yes	characteristic
60	#336×C₆₇	C₂²	1	1	yes	characteristic
61	#336×C₆₇	C₂²	1	1	yes	characteristic
62	#336×C₆₇	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₆₇	—	2	2	no	—
73	C₂×M₁₆×C₆₇	—	2	2	no	—
74	C₂×M₁₆×C₆₇	—	2	2	no	—
75	C₂×M₁₆×C₆₇	—	2	2	no	—
76	C₂×M₁₆×C₆₇	—	2	2	no	—
77	C₂×M₁₆×C₆₇	—	2	2	no	—
78	C₂×M₁₆×C₆₇	—	4	1	no	—
79	C₂×M₁₆×C₆₇	—	4	1	no	—
80	C₂×M₁₆×C₆₇	—	4	1	no	—
81	C₂²×C₈×C₆₇	—	2	2	no	—
82	C₂²×C₈×C₆₇	—	2	2	no	—
83	C₂²×C₈×C₆₇	—	4	1	no	—
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	#126×C₆₇	—	2	4	no	—
93	#126×C₆₇	—	2	4	no	—
94	#125×C₆₇	—	2	4	no	—
95	#124×C₆₇	—	2	4	no	—
96	#123×C₆₇	—	2	4	no	—
97	#123×C₆₇	—	2	4	no	—
98	C₂²⋊Q₈×C₆₇	—	2	4	no	—
99	#121×C₆₇	—	2	4	no	—
100	C₄×Q₈×C₆₇	—	2	2	no	—
101	C₄×Q₈×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	C₄×D₄×C₆₇	—	2	2	no	—
104	C₄×D₄×C₆₇	—	2	2	no	—
105	C₄×D₄×C₆₇	—	2	2	no	—
106	C₄×D₄×C₆₇	D₄	1	4	yes	—
107	C₄×D₄×C₆₇	D₄	1	4	yes	—
108	#117×C₆₇	—	2	2	no	—
109	#117×C₆₇	—	2	2	no	—
110	#117×C₆₇	—	2	2	no	—
111	#117×C₆₇	—	2	2	no	—
112	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₇	—	2	2	no	—
133	C₂×C₄²×C₆₇	—	2	2	no	—
134	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₄⋊C₈×C₆₇	—	2	2	no	—
141	C₄⋊C₈×C₆₇	—	2	2	no	—
142	C₂²⋊C₈×C₆₇	—	2	2	no	—
143	C₂²⋊C₈×C₆₇	—	2	2	no	—
144	C₂²⋊C₈×C₆₇	—	2	2	no	—
145	C₂²⋊C₈×C₆₇	—	2	2	no	—
146	C₂²⋊C₈×C₆₇	—	2	2	no	—
147	C₂²⋊C₈×C₆₇	—	2	2	no	—
148	C₂²⋊C₈×C₆₇	—	4	1	no	—
149	C₂²⋊C₈×C₆₇	—	4	1	no	—
150	#97×C₆₇	—	2	2	no	—
151	C₄×C₈×C₆₇	—	2	2	no	—
152	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
154	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₆₇	—	2	2	no	—
156	C₂×Q₈×C₆₇	—	2	2	no	—
157	C₂×Q₈×C₆₇	—	4	1	no	—
158	C₂×D₄×C₆₇	—	2	2	no	—
159	C₂×D₄×C₆₇	—	2	2	no	—
160	C₂×D₄×C₆₇	—	2	2	no	—
161	C₂×D₄×C₆₇	—	4	1	no	—
162	C₂×D₄×C₆₇	—	4	1	no	—
163	C₂×D₄×C₆₇	—	4	1	no	—
164	C₂×D₄×C₆₇	—	4	1	no	—
165	C₂×D₄×C₆₇	—	4	1	no	—
166	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
167	C₂²×C₄×C₆₇	—	2	1	no	—
168	C₂²×C₄×C₆₇	—	2	1	no	—
169	C₂²×C₄×C₆₇	—	2	1	no	—
170	C₂²×C₄×C₆₇	—	2	1	no	—
171	C₂²×C₄×C₆₇	—	2	1	no	—
172	C₂²×C₄×C₆₇	—	2	1	no	—
173	C₂²×C₄×C₆₇	—	2	1	no	—
174	C₂²×C₄×C₆₇	—	2	1	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	2	no	—
177	C₂²×C₄×C₆₇	—	2	2	no	—
178	C₂²×C₄×C₆₇	—	2	1	no	—
179	C₂²×C₄×C₆₇	—	2	1	no	—
180	C₂²×C₄×C₆₇	—	2	1	no	—
181	C₂²×C₄×C₆₇	—	2	1	no	—
182	C₂²×C₄×C₆₇	—	2	1	no	—
183	C₂²×C₄×C₆₇	—	2	1	no	—
184	C₂²×C₄×C₆₇	—	4	1	no	—
185	C₂²×C₄×C₆₇	—	4	1	no	—
186	C₂²×C₄×C₆₇	—	4	1	no	—
187	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
203	M₁₆×C₆₇	—	4	4	no	—
204	M₁₆×C₆₇	—	4	4	no	—
205	M₁₆×C₆₇	—	4	4	no	—
206	C₂×C₈×C₆₇	—	2	1	no	—
207	C₂×C₈×C₆₇	—	2	1	no	—
208	C₂×C₈×C₆₇	—	2	1	no	—
209	C₂×C₈×C₆₇	—	2	1	no	—
210	C₂×C₈×C₆₇	—	2	1	no	—
211	C₂×C₈×C₆₇	—	2	1	no	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	2	1	no	—
214	C₂×C₈×C₆₇	—	2	1	no	—
215	C₂×C₈×C₆₇	—	2	1	no	—
216	C₂×C₈×C₆₇	—	2	1	no	—
217	C₂×C₈×C₆₇	—	2	1	no	—
218	C₂×C₈×C₆₇	—	2	1	no	—
219	C₂×C₈×C₆₇	—	2	1	no	—
220	C₂×C₈×C₆₇	—	2	1	no	—
221	C₂×C₈×C₆₇	—	2	1	no	—
222	C₂×C₈×C₆₇	—	2	1	no	—
223	C₂×C₈×C₆₇	—	2	1	no	—
224	C₂×C₈×C₆₇	—	2	1	no	—
225	C₂×C₈×C₆₇	—	2	1	no	—
226	C₂×C₈×C₆₇	—	2	1	no	—
227	C₂×C₈×C₆₇	—	2	1	no	—
228	C₂×C₈×C₆₇	—	4	4	no	—
229	C₂×C₈×C₆₇	#41	1	2	yes	—
230	C₂×C₈×C₆₇	#41	1	2	yes	—
231	C₄⋊C₄×C₆₇	—	2	2	no	—
232	C₄⋊C₄×C₆₇	—	2	2	no	—
233	C₄⋊C₄×C₆₇	—	2	2	no	—
234	C₄⋊C₄×C₆₇	—	2	2	no	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	2	no	—
238	C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₄⋊C₄×C₆₇	—	2	2	no	—
240	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
241	C₂²⋊C₄×C₆₇	—	2	2	no	—
242	C₂²⋊C₄×C₆₇	—	2	2	no	—
243	C₂²⋊C₄×C₆₇	—	2	2	no	—
244	C₂²⋊C₄×C₆₇	—	2	2	no	—
245	C₂²⋊C₄×C₆₇	—	2	2	no	—
246	C₂²⋊C₄×C₆₇	—	2	2	no	—
247	C₂²⋊C₄×C₆₇	—	2	2	no	—
248	C₂²⋊C₄×C₆₇	—	2	2	no	—
249	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
250	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
251	C₄²×C₆₇	—	2	2	no	—
252	C₄²×C₆₇	—	2	2	no	—
253	C₄²×C₆₇	—	2	1	no	—
254	C₄²×C₆₇	—	2	1	no	—
255	C₄²×C₆₇	—	2	1	no	—
256	C₄²×C₆₇	—	2	1	no	—
257	C₄²×C₆₇	—	2	1	no	—
258	C₄²×C₆₇	—	2	1	no	—
259	C₄²×C₆₇	C₂×D₄	1	2	yes	—
260	C₄²×C₆₇	C₂×D₄	1	2	yes	—
261	C₂³×C₆₇	—	2	1	no	—
262	C₂³×C₆₇	—	2	1	no	—
263	C₂³×C₆₇	—	2	1	no	—
264	C₂³×C₆₇	—	2	1	no	—
265	C₂³×C₆₇	—	2	1	no	—
266	C₂³×C₆₇	—	2	1	no	—
267	C₂³×C₆₇	—	2	1	no	—
268	C₂³×C₆₇	—	2	1	no	—
269	C₂³×C₆₇	—	2	1	no	—
270	C₂³×C₆₇	—	2	1	no	—
271	C₂³×C₆₇	—	2	1	no	—
272	C₂³×C₆₇	—	2	1	no	—
273	C₂³×C₆₇	—	2	1	no	—
274	C₂³×C₆₇	—	2	1	no	—
275	C₂³×C₆₇	—	2	1	no	—
276	C₂³×C₆₇	—	2	1	no	—
277	C₂³×C₆₇	—	2	1	no	—
278	C₂³×C₆₇	—	2	1	no	—
279	C₂³×C₆₇	—	2	1	no	—
280	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
283	Q₈×C₆₇	—	4	4	no	—
284	D₄×C₆₇	—	4	4	no	—
285	D₄×C₆₇	—	4	4	no	—
286	D₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	—	2	1	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	1	no	—
292	C₂×C₄×C₆₇	—	2	1	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	1	no	—
306	C₂×C₄×C₆₇	—	2	1	no	—
307	C₂×C₄×C₆₇	—	2	1	no	—
308	C₂×C₄×C₆₇	—	2	1	no	—
309	C₂×C₄×C₆₇	—	2	1	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	1	no	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	1	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	1	no	—
319	C₂×C₄×C₆₇	—	2	1	no	—
320	C₂×C₄×C₆₇	—	2	1	no	—
321	C₂×C₄×C₆₇	—	2	1	no	—
322	C₂×C₄×C₆₇	—	2	1	no	—
323	C₂×C₄×C₆₇	—	4	4	no	—
324	C₂×C₄×C₆₇	—	4	4	no	—
325	C₂×C₄×C₆₇	—	4	1	no	—
326	C₂×C₄×C₆₇	—	4	1	no	—
327	C₂×C₄×C₆₇	—	4	1	no	—
328	C₂×C₄×C₆₇	—	4	1	no	—
329	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
332	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
333	C₂×C₄×C₆₇	#131	1	2	yes	—
334	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
340	C₈×C₆₇	—	2	2	no	—
341	C₈×C₆₇	—	2	2	no	—
342	C₈×C₆₇	—	4	1	no	—
343	C₈×C₆₇	—	4	1	no	—
344	C₈×C₆₇	—	4	1	no	—
345	C₈×C₆₇	—	4	1	no	—
346	C₈×C₆₇	—	4	1	no	—
347	C₈×C₆₇	—	4	1	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	—	2	2	no	—
353	C₂²×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	4	1	no	—
355	C₂²×C₆₇	—	4	1	no	—
356	C₂²×C₆₇	—	4	1	no	—
357	C₂²×C₆₇	—	4	1	no	—
358	C₂²×C₆₇	—	4	1	no	—
359	C₂²×C₆₇	—	4	1	no	—
360	C₂²×C₆₇	—	4	1	no	—
361	C₂²×C₆₇	—	4	1	no	—
362	C₂²×C₆₇	—	4	1	no	—
363	C₂²×C₆₇	—	4	1	no	—
364	C₂²×C₆₇	—	4	1	no	—
365	C₂²×C₆₇	—	4	1	no	—
366	C₂²×C₆₇	—	4	1	no	—
367	C₂²×C₆₇	—	4	1	no	—
368	C₂²×C₆₇	—	4	1	no	—
369	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
371	C₂²×C₆₇	#520	1	1	yes	characteristic
372	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
373	C₂²×C₆₇	#568	1	1	yes	characteristic
374	C₂²×C₆₇	#568	1	1	yes	characteristic
375	C₂²×C₆₇	#568	1	1	yes	characteristic
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	2	no	—
379	C₄×C₆₇	—	2	2	no	—
380	C₄×C₆₇	—	2	2	no	—
381	C₄×C₆₇	—	4	1	no	—
382	C₄×C₆₇	—	4	1	no	—
383	C₄×C₆₇	—	4	1	no	—
384	C₄×C₆₇	—	4	1	no	—
385	C₄×C₆₇	—	4	1	no	—
386	C₄×C₆₇	—	4	1	no	—
387	C₄×C₆₇	#546	1	1	yes	characteristic
388	C₄×C₆₇	#546	1	1	yes	characteristic
389	C₄×C₆₇	#547	1	1	yes	characteristic
390	C₄×C₆₇	#547	1	1	yes	characteristic
391	#22472	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂×C₆₇	—	4	2	no	—
393	C₂×C₆₇	—	4	2	no	—
394	C₂×C₆₇	—	8	1	no	—
395	C₂×C₆₇	#2339	1	1	yes	characteristic
396	C₂×C₆₇	#2879	1	1	yes	characteristic
397	C₂×C₆₇	#2880	1	1	yes	characteristic
398	C₂×C₆₇	#2967	1	1	yes	characteristic
399	C₂×C₆₇	#2969	1	1	yes	characteristic
400	C₂×C₆₇	#2993	1	1	yes	characteristic
401	C₂×C₆₇	#2995	1	1	yes	characteristic
402	C₂×#529	C₂×C₆₇	1	1	yes	characteristic
403	C₂×#436	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#1985	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#1984	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
408	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#1870	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#1869	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#1818	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#1817	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#1798	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#1750	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#1729	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#1728	C₂×C₆₇	1	1	yes	characteristic, complemented
417	C₆₇	#22472	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
419	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
420	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
421	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
422	#529	—	2	4	no	—
423	#529	—	2	4	no	—
424	C₂×#126	C₄×C₆₇	1	1	yes	characteristic
425	C₂×#126	C₄×C₆₇	1	1	yes	characteristic
426	C₂×#125	C₄×C₆₇	1	1	yes	characteristic
427	C₂×#124	C₄×C₆₇	1	1	yes	characteristic
428	C₂×#123	C₄×C₆₇	1	1	yes	characteristic
429	C₂×#123	C₄×C₆₇	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic
431	C₂×#121	C₄×C₆₇	1	1	yes	characteristic
432	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
439	#436	—	2	4	no	—
440	#435	—	2	4	no	—
441	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
451	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
452	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
453	#336	C₂²×C₆₇	1	1	yes	characteristic
454	#336	C₂²×C₆₇	1	1	yes	characteristic
455	#336	C₂²×C₆₇	1	1	yes	characteristic
456	#336	C₂²×C₆₇	1	1	yes	characteristic
457	#336	C₂²×C₆₇	1	1	yes	characteristic
458	#336	C₂²×C₆₇	1	1	yes	characteristic
459	#336	C₂²×C₆₇	1	1	yes	characteristic
460	#336	C₂²×C₆₇	1	1	yes	characteristic
461	#336	C₂²×C₆₇	1	1	yes	characteristic
462	#336	C₂²×C₆₇	1	1	yes	characteristic
463	#336	C₂²×C₆₇	1	1	yes	characteristic
464	#336	C₂²×C₆₇	1	1	yes	characteristic
465	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
466	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
467	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
468	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
469	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
470	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
474	C₂×M₁₆	—	2	2	no	—
475	C₂×M₁₆	—	2	2	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	2	2	no	—
478	C₂×M₁₆	—	2	2	no	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	4	1	no	—
481	C₂×M₁₆	—	4	1	no	—
482	C₂×M₁₆	—	4	1	no	—
483	C₂²×C₈	—	2	2	no	—
484	C₂²×C₈	—	2	2	no	—
485	C₂²×C₈	—	4	1	no	—
486	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
494	#126	—	2	4	no	—
495	#126	—	2	4	no	—
496	#125	—	2	4	no	—
497	#124	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	#121	—	2	4	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	D₄×C₆₇	1	4	yes	—
509	C₄×D₄	D₄×C₆₇	1	4	yes	—
510	#117	—	2	2	no	—
511	#117	—	2	2	no	—
512	#117	—	2	2	no	—
513	#117	—	2	2	no	—
514	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
537	C₂×C₄²	C₂×C₄×C₆₇	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
542	C₄⋊C₈	—	2	2	no	—
543	C₄⋊C₈	—	2	2	no	—
544	C₂²⋊C₈	—	2	2	no	—
545	C₂²⋊C₈	—	2	2	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	C₂²⋊C₈	—	2	2	no	—
548	C₂²⋊C₈	—	2	2	no	—
549	C₂²⋊C₈	—	2	2	no	—
550	C₂²⋊C₈	—	4	1	no	—
551	C₂²⋊C₈	—	4	1	no	—
552	#97	—	2	2	no	—
553	C₄×C₈	—	2	2	no	—
554	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
555	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
556	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	1	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
591	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
592	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
593	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
594	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
595	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
603	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
605	M₁₆	—	4	4	no	—
606	M₁₆	—	4	4	no	—
607	M₁₆	—	4	4	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	4	4	no	—
631	C₂×C₈	#41×C₆₇	1	2	yes	—
632	C₂×C₈	#41×C₆₇	1	2	yes	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
652	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	C₂×D₄×C₆₇	1	2	yes	—
662	C₄²	C₂×D₄×C₆₇	1	2	yes	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
683	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
684	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
685	Q₈	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
732	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
733	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
734	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
735	C₂×C₄	#131×C₆₇	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
738	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
740	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
741	C₂×C₄	2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₈	—	4	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
772	C₂²	C₄×#41×C₆₇	1	1	yes	characteristic
773	C₂²	#520×C₆₇	1	1	yes	characteristic
774	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
775	C₂²	#568×C₆₇	1	1	yes	characteristic
776	C₂²	#568×C₆₇	1	1	yes	characteristic
777	C₂²	#568×C₆₇	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	#546×C₆₇	1	1	yes	characteristic
790	C₄	#546×C₆₇	1	1	yes	characteristic
791	C₄	#547×C₆₇	1	1	yes	characteristic
792	C₄	#547×C₆₇	1	1	yes	characteristic
793	C₂	—	4	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	1	no	—
796	C₂	C₆₇×#2339	1	1	yes	characteristic
797	C₂	C₆₇×#2879	1	1	yes	characteristic
798	C₂	C₆₇×#2880	1	1	yes	characteristic
799	C₂	C₆₇×#2967	1	1	yes	characteristic
800	C₂	C₆₇×#2969	1	1	yes	characteristic
801	C₂	C₆₇×#2993	1	1	yes	characteristic
802	C₂	C₆₇×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂×#121×C₆₇	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#436×C₆₇	C₂	semidirect
3. C₂×#435×C₆₇	C₂	semidirect
4. C₆₇×#1985	C₂	semidirect
5. C₆₇×#1984	C₂	semidirect
6. C₆₇×#1870	C₂	semidirect
7. C₆₇×#1870	C₂	semidirect
8. C₆₇×#1870	C₂	semidirect
9. C₆₇×#1869	C₂	semidirect
10. C₆₇×#1818	C₂	semidirect
11. C₆₇×#1817	C₂	semidirect
12. C₆₇×#1798	C₂	semidirect
13. C₆₇×#1750	C₂	semidirect
14. C₆₇×#1729	C₂	semidirect
15. C₆₇×#1728	C₂	semidirect
391. #22472	C₆₇	direct (N × H)
403. C₂×#436	C₂×C₆₇	semidirect
404. C₂×#435	C₂×C₆₇	semidirect
405. #1985	C₂×C₆₇	semidirect
406. #1984	C₂×C₆₇	semidirect
407. #1870	C₂×C₆₇	semidirect
408. #1870	C₂×C₆₇	semidirect
409. #1870	C₂×C₆₇	semidirect
410. #1869	C₂×C₆₇	semidirect
411. #1818	C₂×C₆₇	semidirect
412. #1817	C₂×C₆₇	semidirect
413. #1798	C₂×C₆₇	semidirect
414. #1750	C₂×C₆₇	semidirect
415. #1729	C₂×C₆₇	semidirect
416. #1728	C₂×C₆₇	semidirect
417. C₆₇	#22472	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₆₇	2
C₂×#436×C₆₇	2
C₂×#435×C₆₇	2
C₆₇×#1985	2
C₆₇×#1984	2
C₆₇×#1870	2
C₆₇×#1869	2
C₆₇×#1818	2
C₆₇×#1817	2
C₆₇×#1798	2
C₆₇×#1750	2
C₆₇×#1729	2
C₆₇×#1728	2
#22472	67

Subgroups — C67×#22472 #30701723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22472 #30701723