Subgroups — C₆₇×#35062 #30714313

Order 17152.

3010 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2853	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2630	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2602	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2413	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2411	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2405	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2403	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#123×C₆₇	—	2	8	no	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#123×C₆₇	C₂²	1	2	yes	—
26	C₂×#123×C₆₇	C₂²	1	2	yes	—
27	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#120×C₆₇	C₂²	1	2	yes	—
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	—	2	8	no	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#398×C₆₇	C₂²	1	4	yes	complemented
47	#397×C₆₇	C₂²	1	4	yes	complemented
48	#396×C₆₇	C₂²	1	4	yes	complemented
49	#396×C₆₇	C₂²	1	4	yes	complemented
50	#394×C₆₇	C₂²	1	4	yes	complemented
51	#394×C₆₇	C₂²	1	4	yes	complemented
52	#394×C₆₇	C₂²	1	4	yes	complemented
53	#392×C₆₇	C₂²	1	4	yes	—
54	#390×C₆₇	C₂²	1	4	yes	complemented
55	#389×C₆₇	C₂²	1	4	yes	complemented
56	#388×C₆₇	C₂²	1	4	yes	complemented
57	#388×C₆₇	C₂²	1	4	yes	complemented
58	#388×C₆₇	C₂²	1	4	yes	complemented
59	#388×C₆₇	C₂²	1	4	yes	complemented
60	#387×C₆₇	C₂²	1	4	yes	complemented
61	#387×C₆₇	C₂²	1	4	yes	complemented
62	#386×C₆₇	C₂²	1	2	yes	—
63	#386×C₆₇	C₂²	1	2	yes	—
64	#386×C₆₇	C₂²	1	2	yes	—
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	4	yes	complemented
67	#386×C₆₇	C₂²	1	4	yes	complemented
68	#385×C₆₇	C₂²	1	2	yes	complemented
69	#385×C₆₇	C₂²	1	2	yes	complemented
70	#385×C₆₇	C₂²	1	4	yes	complemented
71	#385×C₆₇	C₂²	1	4	yes	complemented
72	#385×C₆₇	C₂²	1	2	yes	complemented
73	#385×C₆₇	C₂²	1	2	yes	complemented
74	#381×C₆₇	C₂²	1	2	yes	complemented
75	#381×C₆₇	C₂²	1	2	yes	complemented
76	#381×C₆₇	C₂²	1	2	yes	complemented
77	#380×C₆₇	C₂²	1	2	yes	complemented
78	#380×C₆₇	C₂²	1	2	yes	complemented
79	#379×C₆₇	C₂²	1	1	yes	characteristic
80	#379×C₆₇	C₂²	1	1	yes	characteristic
81	#379×C₆₇	C₂²	1	2	yes	complemented
82	#379×C₆₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
87	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	—	2	4	no	—
89	C₂²×D₄×C₆₇	—	2	8	no	—
90	C₂²×D₄×C₆₇	—	2	4	no	—
91	C₂²×D₄×C₆₇	—	4	4	no	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	—	2	4	no	—
98	C₂³×C₄×C₆₇	—	4	4	no	—
99	C₂³×C₄×C₆₇	—	4	4	no	—
100	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	#123×C₆₇	—	2	8	no	—
116	#123×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	2	8	no	—
118	#123×C₆₇	—	2	8	no	—
119	#123×C₆₇	—	2	8	no	—
120	#123×C₆₇	—	4	4	no	—
121	#120×C₆₇	—	2	8	no	—
122	#120×C₆₇	—	4	4	no	—
123	C₄×D₄×C₆₇	—	2	8	no	—
124	C₄×D₄×C₆₇	—	2	8	no	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	#117×C₆₇	—	4	4	no	—
128	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
129	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
130	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	4	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
142	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
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	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	4	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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	4	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
168	C₂×C₄²×C₆₇	—	2	4	no	—
169	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
172	#95×C₆₇	C₂³	1	4	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	4	yes	—
176	#95×C₆₇	C₂³	1	4	yes	—
177	#95×C₆₇	C₂³	1	4	yes	—
178	#95×C₆₇	C₂³	1	4	yes	—
179	#95×C₆₇	C₂³	1	4	yes	—
180	C₂⁴×C₆₇	—	2	2	no	—
181	C₂⁴×C₆₇	—	2	4	no	—
182	C₂⁴×C₆₇	—	2	4	no	—
183	C₂⁴×C₆₇	—	2	4	no	—
184	C₂⁴×C₆₇	—	2	2	no	—
185	C₂⁴×C₆₇	—	2	4	no	—
186	C₂⁴×C₆₇	—	2	4	no	—
187	C₂⁴×C₆₇	—	4	2	no	—
188	C₂⁴×C₆₇	—	4	2	no	—
189	C₂⁴×C₆₇	—	4	2	no	—
190	C₂⁴×C₆₇	—	4	2	no	—
191	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
192	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
193	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
195	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₆₇	—	2	32	no	—
198	C₂×D₄×C₆₇	—	2	4	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	8	no	—
207	C₂×D₄×C₆₇	—	2	4	no	—
208	C₂×D₄×C₆₇	—	4	2	no	—
209	C₂×D₄×C₆₇	—	4	2	no	—
210	C₂×D₄×C₆₇	—	4	4	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	4	16	no	—
213	C₂×D₄×C₆₇	#41	1	8	yes	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	4	16	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	4	2	no	—
232	C₂²×C₄×C₆₇	—	4	4	no	—
233	C₂²×C₄×C₆₇	—	4	4	no	—
234	C₂²×C₄×C₆₇	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	2	no	—
236	C₂²×C₄×C₆₇	—	4	2	no	—
237	C₂²×C₄×C₆₇	—	4	16	no	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	4	no	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	8	no	—
263	C₄⋊C₄×C₆₇	—	4	4	no	—
264	C₄⋊C₄×C₆₇	—	4	4	no	—
265	C₄⋊C₄×C₆₇	—	4	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	—	2	8	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	4	no	—
278	C₂²⋊C₄×C₆₇	—	2	4	no	—
279	C₂²⋊C₄×C₆₇	—	2	4	no	—
280	C₂²⋊C₄×C₆₇	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	8	no	—
282	C₂²⋊C₄×C₆₇	—	4	2	no	—
283	C₂²⋊C₄×C₆₇	—	4	4	no	—
284	C₂²⋊C₄×C₆₇	—	4	4	no	—
285	C₂²⋊C₄×C₆₇	—	4	2	no	—
286	C₂²⋊C₄×C₆₇	—	4	4	no	—
287	C₂²⋊C₄×C₆₇	—	4	4	no	—
288	C₄²×C₆₇	—	2	4	no	—
289	C₄²×C₆₇	—	2	4	no	—
290	C₄²×C₆₇	—	4	4	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	2	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	8	no	—
296	C₂³×C₆₇	—	2	8	no	—
297	C₂³×C₆₇	—	2	8	no	—
298	C₂³×C₆₇	—	2	2	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	4	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	4	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	4	no	—
310	C₂³×C₆₇	—	4	4	no	—
311	C₂³×C₆₇	—	4	16	no	—
312	C₂³×C₆₇	—	4	16	no	—
313	C₂³×C₆₇	—	4	4	no	—
314	C₂³×C₆₇	—	4	4	no	—
315	C₂³×C₆₇	—	4	4	no	—
316	C₂³×C₆₇	—	4	4	no	—
317	C₂³×C₆₇	—	4	4	no	—
318	C₂³×C₆₇	—	8	8	no	—
319	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
321	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
322	C₂³×C₆₇	C₂×#41	1	4	yes	—
323	C₂³×C₆₇	C₂×#41	1	4	yes	—
324	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
325	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
326	D₄×C₆₇	—	2	16	no	—
327	D₄×C₆₇	—	2	16	no	—
328	D₄×C₆₇	—	4	8	no	—
329	D₄×C₆₇	—	4	8	no	—
330	D₄×C₆₇	—	8	8	no	—
331	C₂×C₄×C₆₇	—	2	8	no	—
332	C₂×C₄×C₆₇	—	2	8	no	—
333	C₂×C₄×C₆₇	—	2	8	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	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	4	no	—
346	C₂×C₄×C₆₇	—	2	4	no	—
347	C₂×C₄×C₆₇	—	2	4	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	4	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	4	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	4	no	—
356	C₂×C₄×C₆₇	—	2	4	no	—
357	C₂×C₄×C₆₇	—	4	4	no	—
358	C₂×C₄×C₆₇	—	4	4	no	—
359	C₂×C₄×C₆₇	—	4	4	no	—
360	C₂×C₄×C₆₇	—	4	4	no	—
361	C₂×C₄×C₆₇	—	4	8	no	—
362	C₂×C₄×C₆₇	—	4	8	no	—
363	C₂×C₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	4	no	—
367	C₂×C₄×C₆₇	—	4	4	no	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
373	C₂²×C₆₇	—	2	2	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	2	no	—
377	C₂²×C₆₇	—	2	8	no	—
378	C₂²×C₆₇	—	2	8	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	2	no	—
383	C₂²×C₆₇	—	2	8	no	—
384	C₂²×C₆₇	—	4	16	no	—
385	C₂²×C₆₇	—	4	16	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	4	no	—
389	C₂²×C₆₇	—	4	4	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	4	no	—
394	C₂²×C₆₇	—	4	4	no	—
395	C₂²×C₆₇	—	8	8	no	—
396	C₂²×C₆₇	#525	1	4	yes	—
397	C₂²×C₆₇	#534	1	4	yes	—
398	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
399	C₂²×C₆₇	C₂²×#41	1	2	yes	—
400	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
401	C₂²×C₆₇	#585	1	2	yes	—
402	C₄×C₆₇	—	2	4	no	—
403	C₄×C₆₇	—	2	2	no	—
404	C₄×C₆₇	—	2	2	no	—
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	2	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	2	no	—
410	C₄×C₆₇	—	4	2	no	—
411	C₄×C₆₇	—	4	2	no	—
412	C₄×C₆₇	—	4	4	no	—
413	C₄×C₆₇	—	4	4	no	—
414	#35062	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₆₇	—	2	4	no	—
416	C₂×C₆₇	—	2	4	no	—
417	C₂×C₆₇	—	4	2	no	—
418	C₂×C₆₇	—	4	4	no	—
419	C₂×C₆₇	—	8	2	no	—
420	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
421	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
422	C₂×C₆₇	#3449	1	1	yes	characteristic
423	C₂×C₆₇	#3513	1	4	yes	—
424	C₂²×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#2853	C₂×C₆₇	1	2	yes	complemented
427	#2849	C₂×C₆₇	1	2	yes	complemented
428	#2630	C₂×C₆₇	1	4	yes	complemented
429	#2602	C₂×C₆₇	1	4	yes	complemented
430	#2579	C₂×C₆₇	1	2	yes	complemented
431	#2534	C₂×C₆₇	1	2	yes	complemented
432	#2483	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#2413	C₂×C₆₇	1	2	yes	complemented
434	#2411	C₂×C₆₇	1	2	yes	complemented
435	#2405	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#2405	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#2403	C₂×C₆₇	1	1	yes	characteristic
438	#2322	C₂×C₆₇	1	2	yes	complemented
439	#2321	C₂×C₆₇	1	2	yes	complemented
440	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
441	C₆₇	#35062	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
445	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₂×#123	—	2	8	no	—
447	C₂×#123	C₂²×C₆₇	1	2	yes	—
448	C₂×#123	C₂²×C₆₇	1	2	yes	—
449	C₂×#123	C₂²×C₆₇	1	2	yes	—
450	C₂×#123	C₂²×C₆₇	1	2	yes	—
451	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
452	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
453	C₂×#120	C₂²×C₆₇	1	2	yes	—
454	C₂×#120	C₂²×C₆₇	1	2	yes	—
455	C₂×C₄×D₄	—	2	8	no	—
456	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
458	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
459	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
460	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
461	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
463	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
464	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
467	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
468	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
469	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	#398	C₂²×C₆₇	1	4	yes	complemented
471	#397	C₂²×C₆₇	1	4	yes	complemented
472	#396	C₂²×C₆₇	1	4	yes	complemented
473	#396	C₂²×C₆₇	1	4	yes	complemented
474	#394	C₂²×C₆₇	1	4	yes	complemented
475	#394	C₂²×C₆₇	1	4	yes	complemented
476	#394	C₂²×C₆₇	1	4	yes	complemented
477	#392	C₂²×C₆₇	1	4	yes	—
478	#390	C₂²×C₆₇	1	4	yes	complemented
479	#389	C₂²×C₆₇	1	4	yes	complemented
480	#388	C₂²×C₆₇	1	4	yes	complemented
481	#388	C₂²×C₆₇	1	4	yes	complemented
482	#388	C₂²×C₆₇	1	4	yes	complemented
483	#388	C₂²×C₆₇	1	4	yes	complemented
484	#387	C₂²×C₆₇	1	4	yes	complemented
485	#387	C₂²×C₆₇	1	4	yes	complemented
486	#386	C₂²×C₆₇	1	2	yes	—
487	#386	C₂²×C₆₇	1	2	yes	—
488	#386	C₂²×C₆₇	1	2	yes	—
489	#386	C₂²×C₆₇	1	2	yes	—
490	#386	C₂²×C₆₇	1	4	yes	complemented
491	#386	C₂²×C₆₇	1	4	yes	complemented
492	#385	C₂²×C₆₇	1	2	yes	complemented
493	#385	C₂²×C₆₇	1	2	yes	complemented
494	#385	C₂²×C₆₇	1	4	yes	complemented
495	#385	C₂²×C₆₇	1	4	yes	complemented
496	#385	C₂²×C₆₇	1	2	yes	complemented
497	#385	C₂²×C₆₇	1	2	yes	complemented
498	#381	C₂²×C₆₇	1	2	yes	complemented
499	#381	C₂²×C₆₇	1	2	yes	complemented
500	#381	C₂²×C₆₇	1	2	yes	complemented
501	#380	C₂²×C₆₇	1	2	yes	complemented
502	#380	C₂²×C₆₇	1	2	yes	complemented
503	#379	C₂²×C₆₇	1	1	yes	characteristic
504	#379	C₂²×C₆₇	1	1	yes	characteristic
505	#379	C₂²×C₆₇	1	2	yes	complemented
506	#379	C₂²×C₆₇	1	2	yes	complemented
507	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
508	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
509	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
510	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
511	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
512	C₂²×D₄	—	2	4	no	—
513	C₂²×D₄	—	2	8	no	—
514	C₂²×D₄	—	2	4	no	—
515	C₂²×D₄	—	4	4	no	—
516	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
517	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
518	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
519	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
520	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
521	C₂³×C₄	—	2	4	no	—
522	C₂³×C₄	—	4	4	no	—
523	C₂³×C₄	—	4	4	no	—
524	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
525	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
534	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
535	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
539	#123	—	2	8	no	—
540	#123	—	2	8	no	—
541	#123	—	2	8	no	—
542	#123	—	2	8	no	—
543	#123	—	2	8	no	—
544	#123	—	4	4	no	—
545	#120	—	2	8	no	—
546	#120	—	4	4	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	8	no	—
549	C₄×D₄	—	2	8	no	—
550	C₄×D₄	—	2	8	no	—
551	#117	—	4	4	no	—
552	C₂×C₄⋊C₄	—	2	4	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	4	no	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
563	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	—	2	4	no	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
592	C₂×C₄²	—	2	4	no	—
593	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
596	#95	C₂³×C₆₇	1	4	yes	—
597	#95	C₂³×C₆₇	1	4	yes	—
598	#95	C₂³×C₆₇	1	4	yes	—
599	#95	C₂³×C₆₇	1	4	yes	—
600	#95	C₂³×C₆₇	1	4	yes	—
601	#95	C₂³×C₆₇	1	4	yes	—
602	#95	C₂³×C₆₇	1	4	yes	—
603	#95	C₂³×C₆₇	1	4	yes	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	4	no	—
610	C₂⁴	—	2	4	no	—
611	C₂⁴	—	4	2	no	—
612	C₂⁴	—	4	2	no	—
613	C₂⁴	—	4	2	no	—
614	C₂⁴	—	4	2	no	—
615	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
616	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
617	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
619	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂×D₄	—	2	32	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	16	no	—
637	C₂×D₄	#41×C₆₇	1	8	yes	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	2	no	—
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	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	16	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	4	no	—
657	C₂²×C₄	—	4	4	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	16	no	—
662	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
663	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
664	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
665	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
666	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
667	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
668	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
671	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	8	no	—
687	C₄⋊C₄	—	4	4	no	—
688	C₄⋊C₄	—	4	4	no	—
689	C₄⋊C₄	—	4	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₄²	—	2	4	no	—
713	C₄²	—	2	4	no	—
714	C₄²	—	4	4	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	8	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	16	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	8	8	no	—
743	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
744	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
745	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
746	C₂³	C₂×#41×C₆₇	1	4	yes	—
747	C₂³	C₂×#41×C₆₇	1	4	yes	—
748	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
749	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
750	D₄	—	2	16	no	—
751	D₄	—	2	16	no	—
752	D₄	—	4	8	no	—
753	D₄	—	4	8	no	—
754	D₄	—	8	8	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
796	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	8	no	—
802	C₂²	—	2	8	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	8	no	—
808	C₂²	—	4	16	no	—
809	C₂²	—	4	16	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	8	8	no	—
820	C₂²	#525×C₆₇	1	4	yes	—
821	C₂²	#534×C₆₇	1	4	yes	—
822	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
823	C₂²	C₂²×#41×C₆₇	1	2	yes	—
824	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
825	C₂²	#585×C₆₇	1	2	yes	—
826	C₄	—	2	4	no	—
827	C₄	—	2	2	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	4	no	—
838	C₂	—	2	4	no	—
839	C₂	—	2	4	no	—
840	C₂	—	4	2	no	—
841	C₂	—	4	4	no	—
842	C₂	—	8	2	no	—
843	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
844	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
845	C₂	C₆₇×#3449	1	1	yes	characteristic
846	C₂	C₆₇×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2403	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2853	C₂	semidirect
4. C₆₇×#2849	C₂	semidirect
5. C₆₇×#2630	C₂	semidirect
6. C₆₇×#2602	C₂	semidirect
7. C₆₇×#2579	C₂	semidirect
8. C₆₇×#2534	C₂	semidirect
9. C₆₇×#2483	C₂	semidirect
10. C₆₇×#2413	C₂	semidirect
11. C₆₇×#2411	C₂	semidirect
12. C₆₇×#2405	C₂	semidirect
13. C₆₇×#2405	C₂	semidirect
15. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2321	C₂	semidirect
17. C₆₇×#2280	C₂	semidirect
21. C₂⁴×C₄×C₆₇	C₂²	semidirect
27. C₂×#123×C₆₇	C₂²	semidirect
28. C₂×#123×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×#117×C₆₇	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
45. C₂²×C₄²×C₆₇	C₂²	semidirect
46. #398×C₆₇	C₂²	semidirect
47. #397×C₆₇	C₂²	semidirect
48. #396×C₆₇	C₂²	semidirect
49. #396×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
51. #394×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
54. #390×C₆₇	C₂²	semidirect
55. #389×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
57. #388×C₆₇	C₂²	semidirect
58. #388×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #387×C₆₇	C₂²	semidirect
61. #387×C₆₇	C₂²	semidirect
66. #386×C₆₇	C₂²	semidirect
67. #386×C₆₇	C₂²	semidirect
68. #385×C₆₇	C₂²	semidirect
69. #385×C₆₇	C₂²	semidirect
70. #385×C₆₇	C₂²	semidirect
71. #385×C₆₇	C₂²	semidirect
72. #385×C₆₇	C₂²	semidirect
73. #385×C₆₇	C₂²	semidirect
74. #381×C₆₇	C₂²	semidirect
75. #381×C₆₇	C₂²	semidirect
76. #381×C₆₇	C₂²	semidirect
77. #380×C₆₇	C₂²	semidirect
78. #380×C₆₇	C₂²	semidirect
81. #379×C₆₇	C₂²	semidirect
82. #379×C₆₇	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₂³×C₄×C₆₇	D₄	semidirect
414. #35062	C₆₇	direct (N × H)
424. C₂²×#123	C₂×C₆₇	semidirect
425. C₂²×C₄×D₄	C₂×C₆₇	semidirect
426. #2853	C₂×C₆₇	semidirect
427. #2849	C₂×C₆₇	semidirect
428. #2630	C₂×C₆₇	semidirect
429. #2602	C₂×C₆₇	semidirect
430. #2579	C₂×C₆₇	semidirect
431. #2534	C₂×C₆₇	semidirect
432. #2483	C₂×C₆₇	semidirect
433. #2413	C₂×C₆₇	semidirect
434. #2411	C₂×C₆₇	semidirect
435. #2405	C₂×C₆₇	semidirect
436. #2405	C₂×C₆₇	semidirect
438. #2322	C₂×C₆₇	semidirect
439. #2321	C₂×C₆₇	semidirect
440. #2280	C₂×C₆₇	semidirect
441. C₆₇	#35062	direct (N × H)
445. C₂⁴×C₄	C₂²×C₆₇	semidirect
451. C₂×#123	C₂²×C₆₇	semidirect
452. C₂×#123	C₂²×C₆₇	semidirect
458. C₂×C₄×D₄	C₂²×C₆₇	semidirect
459. C₂×C₄×D₄	C₂²×C₆₇	semidirect
460. C₂×#117	C₂²×C₆₇	semidirect
461. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
462. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
463. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
466. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
467. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
468. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
469. C₂²×C₄²	C₂²×C₆₇	semidirect
470. #398	C₂²×C₆₇	semidirect
471. #397	C₂²×C₆₇	semidirect
472. #396	C₂²×C₆₇	semidirect
473. #396	C₂²×C₆₇	semidirect
474. #394	C₂²×C₆₇	semidirect
475. #394	C₂²×C₆₇	semidirect
476. #394	C₂²×C₆₇	semidirect
478. #390	C₂²×C₆₇	semidirect
479. #389	C₂²×C₆₇	semidirect
480. #388	C₂²×C₆₇	semidirect
481. #388	C₂²×C₆₇	semidirect
482. #388	C₂²×C₆₇	semidirect
483. #388	C₂²×C₆₇	semidirect
484. #387	C₂²×C₆₇	semidirect
485. #387	C₂²×C₆₇	semidirect
490. #386	C₂²×C₆₇	semidirect
491. #386	C₂²×C₆₇	semidirect
492. #385	C₂²×C₆₇	semidirect
493. #385	C₂²×C₆₇	semidirect
494. #385	C₂²×C₆₇	semidirect
495. #385	C₂²×C₆₇	semidirect
496. #385	C₂²×C₆₇	semidirect
497. #385	C₂²×C₆₇	semidirect
498. #381	C₂²×C₆₇	semidirect
499. #381	C₂²×C₆₇	semidirect
500. #381	C₂²×C₆₇	semidirect
501. #380	C₂²×C₆₇	semidirect
502. #380	C₂²×C₆₇	semidirect
505. #379	C₂²×C₆₇	semidirect
506. #379	C₂²×C₆₇	semidirect
507. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
508. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
524. C₂³×C₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#123×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2853	2
C₆₇×#2849	2
C₆₇×#2630	2
C₆₇×#2602	2
C₆₇×#2579	2
C₆₇×#2534	2
C₆₇×#2483	2
C₆₇×#2413	2
C₆₇×#2411	2
C₆₇×#2405	2
C₆₇×#2403	2
C₆₇×#2322	2
C₆₇×#2321	2
C₆₇×#2280	2
#35062	67

Subgroups — C67×#35062 #30714313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35062 #30714313