Subgroups — C₆₇×#59915 #30739166

Order 17152.

2156 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2804	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2790	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2748	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2579	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2502	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2473	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2437	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic
17	D₄×C₄⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic
19	C₂×#385×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	complemented
35	#400×C₆₇	C₂²	1	2	yes	complemented
36	#400×C₆₇	C₂²	1	2	yes	complemented
37	#399×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	complemented
39	#398×C₆₇	C₂²	1	2	yes	complemented
40	#398×C₆₇	C₂²	1	2	yes	complemented
41	#398×C₆₇	C₂²	1	2	yes	complemented
42	#398×C₆₇	C₂²	1	2	yes	complemented
43	#398×C₆₇	C₂²	1	2	yes	complemented
44	#396×C₆₇	C₂²	1	2	yes	—
45	#396×C₆₇	C₂²	1	2	yes	—
46	#396×C₆₇	C₂²	1	2	yes	complemented
47	#396×C₆₇	C₂²	1	2	yes	complemented
48	#393×C₆₇	C₂²	1	2	yes	—
49	#393×C₆₇	C₂²	1	2	yes	complemented
50	#391×C₆₇	C₂²	1	2	yes	complemented
51	#391×C₆₇	C₂²	1	2	yes	complemented
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	2	yes	complemented
56	#389×C₆₇	C₂²	1	2	yes	complemented
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#387×C₆₇	C₂²	1	2	yes	complemented
60	#387×C₆₇	C₂²	1	2	yes	complemented
61	#387×C₆₇	C₂²	1	2	yes	complemented
62	#387×C₆₇	C₂²	1	2	yes	complemented
63	#387×C₆₇	C₂²	1	2	yes	complemented
64	#387×C₆₇	C₂²	1	2	yes	complemented
65	#386×C₆₇	C₂²	1	1	yes	characteristic
66	#386×C₆₇	C₂²	1	1	yes	characteristic
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	1	yes	characteristic
70	#386×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	2	yes	—
73	#385×C₆₇	C₂²	1	2	yes	—
74	#385×C₆₇	C₂²	1	2	yes	—
75	#385×C₆₇	C₂²	1	2	yes	—
76	#385×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	1	yes	characteristic
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×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	complemented
88	#385×C₆₇	C₂²	1	2	yes	complemented
89	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#384×C₆₇	C₂²	1	2	yes	complemented
93	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#380×C₆₇	C₂²	1	2	yes	—
95	#380×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
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	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₇	—	4	2	no	—
112	C₂³×C₄×C₆₇	—	4	4	no	—
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	#125×C₆₇	—	4	2	no	—
125	C₂²⋊Q₈×C₆₇	—	2	8	no	—
126	C₂²⋊Q₈×C₆₇	—	4	4	no	—
127	#120×C₆₇	Q₈	1	8	yes	complemented
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	4	2	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
133	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
134	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
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	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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
159	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
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	#95×C₆₇	C₂³	1	2	yes	—
209	C₂⁴×C₆₇	—	2	4	no	—
210	C₂⁴×C₆₇	—	2	4	no	—
211	C₂⁴×C₆₇	—	4	1	no	—
212	C₂⁴×C₆₇	—	4	1	no	—
213	C₂⁴×C₆₇	C₂×Q₈	1	4	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₆₇	—	2	4	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	4	1	no	—
223	C₂×D₄×C₆₇	—	4	1	no	—
224	C₂×D₄×C₆₇	C₂×Q₈	1	8	yes	—
225	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	4	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	2	4	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	2	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	4	1	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	2	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	1	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	1	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	16	no	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₆₇	—	2	4	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	2	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	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	1	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	1	no	—
293	C₄⋊C₄×C₆₇	—	4	2	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	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	1	no	—
305	C₂²⋊C₄×C₆₇	—	4	1	no	—
306	C₂²⋊C₄×C₆₇	—	4	1	no	—
307	C₂²⋊C₄×C₆₇	—	4	1	no	—
308	C₂²⋊C₄×C₆₇	—	4	1	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
312	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
313	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
314	C₄²×C₆₇	—	2	4	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	—	4	1	no	—
317	C₄²×C₆₇	—	4	1	no	—
318	C₄²×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	4	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	16	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	4	4	no	—
334	C₂³×C₆₇	—	4	4	no	—
335	C₂³×C₆₇	—	4	4	no	—
336	C₂³×C₆₇	—	4	8	no	—
337	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
338	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
339	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
340	C₂³×C₆₇	C₂×#41	1	4	yes	—
341	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
342	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
343	Q₈×C₆₇	—	8	4	no	—
344	D₄×C₆₇	—	2	16	no	—
345	D₄×C₆₇	—	4	4	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	1	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	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	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	1	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	1	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	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	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	4	4	no	—
386	C₂×C₄×C₆₇	—	4	8	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	4	8	no	—
391	C₂×C₄×C₆₇	—	4	4	no	—
392	C₂×C₄×C₆₇	—	8	2	no	—
393	C₂×C₄×C₆₇	—	8	4	no	—
394	C₂×C₄×C₆₇	—	8	4	no	—
395	C₂×C₄×C₆₇	—	8	2	no	—
396	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
397	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
398	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
399	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
400	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	2	4	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	2	4	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	4	16	no	—
412	C₂²×C₆₇	—	4	1	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	#554	1	8	yes	—
419	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
420	C₂²×C₆₇	C₂²×#41	1	2	yes	—
421	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
422	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²×C₆₇	#585	1	1	yes	characteristic
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	2	4	no	—
426	C₄×C₆₇	—	2	2	no	—
427	C₄×C₆₇	—	2	4	no	—
428	C₄×C₆₇	—	2	2	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	2	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	1	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	2	no	—
440	#59915	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₆₇	—	2	8	no	—
442	C₂×C₆₇	—	4	2	no	—
443	C₂×C₆₇	—	4	2	no	—
444	C₂×C₆₇	C₂×#554	1	2	yes	—
445	C₂×C₆₇	#3481	1	1	yes	characteristic
446	C₂×C₆₇	#3501	1	1	yes	characteristic
447	C₂×C₆₇	#3513	1	2	yes	—
448	C₂×C₆₇	#3532	1	1	yes	characteristic
449	#2804	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2790	C₂×C₆₇	1	2	yes	complemented
451	#2748	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2589	C₂×C₆₇	1	2	yes	complemented
453	#2579	C₂×C₆₇	1	2	yes	complemented
454	#2579	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2566	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2505	C₂×C₆₇	1	2	yes	complemented
457	#2502	C₂×C₆₇	1	2	yes	complemented
458	#2473	C₂×C₆₇	1	2	yes	complemented
459	#2450	C₂×C₆₇	1	2	yes	complemented
460	#2450	C₂×C₆₇	1	2	yes	complemented
461	#2437	C₂×C₆₇	1	2	yes	complemented
462	#2368	C₂×C₆₇	1	2	yes	complemented
463	#2358	C₂×C₆₇	1	1	yes	characteristic
464	#2358	C₂×C₆₇	1	1	yes	characteristic
465	D₄×C₄⋊C₄	C₂×C₆₇	1	2	yes	complemented
466	C₄×#120	C₂×C₆₇	1	1	yes	characteristic
467	C₂×#385	C₂×C₆₇	1	2	yes	complemented
468	C₆₇	#59915	1	1	yes	characteristic, direct product factor, Sylow
469	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
473	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
478	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
479	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
480	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
481	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
483	#400	C₂²×C₆₇	1	2	yes	complemented
484	#400	C₂²×C₆₇	1	2	yes	complemented
485	#400	C₂²×C₆₇	1	2	yes	complemented
486	#399	C₂²×C₆₇	1	2	yes	—
487	#398	C₂²×C₆₇	1	2	yes	complemented
488	#398	C₂²×C₆₇	1	2	yes	complemented
489	#398	C₂²×C₆₇	1	2	yes	complemented
490	#398	C₂²×C₆₇	1	2	yes	complemented
491	#398	C₂²×C₆₇	1	2	yes	complemented
492	#398	C₂²×C₆₇	1	2	yes	complemented
493	#396	C₂²×C₆₇	1	2	yes	—
494	#396	C₂²×C₆₇	1	2	yes	—
495	#396	C₂²×C₆₇	1	2	yes	complemented
496	#396	C₂²×C₆₇	1	2	yes	complemented
497	#393	C₂²×C₆₇	1	2	yes	—
498	#393	C₂²×C₆₇	1	2	yes	complemented
499	#391	C₂²×C₆₇	1	2	yes	complemented
500	#391	C₂²×C₆₇	1	2	yes	complemented
501	#391	C₂²×C₆₇	1	2	yes	complemented
502	#390	C₂²×C₆₇	1	1	yes	characteristic
503	#390	C₂²×C₆₇	1	1	yes	characteristic
504	#389	C₂²×C₆₇	1	2	yes	complemented
505	#389	C₂²×C₆₇	1	2	yes	complemented
506	#388	C₂²×C₆₇	1	2	yes	—
507	#388	C₂²×C₆₇	1	2	yes	—
508	#387	C₂²×C₆₇	1	2	yes	complemented
509	#387	C₂²×C₆₇	1	2	yes	complemented
510	#387	C₂²×C₆₇	1	2	yes	complemented
511	#387	C₂²×C₆₇	1	2	yes	complemented
512	#387	C₂²×C₆₇	1	2	yes	complemented
513	#387	C₂²×C₆₇	1	2	yes	complemented
514	#386	C₂²×C₆₇	1	2	yes	—
515	#386	C₂²×C₆₇	1	1	yes	characteristic
516	#386	C₂²×C₆₇	1	1	yes	characteristic
517	#386	C₂²×C₆₇	1	2	yes	—
518	#386	C₂²×C₆₇	1	2	yes	—
519	#386	C₂²×C₆₇	1	1	yes	characteristic
520	#385	C₂²×C₆₇	1	2	yes	—
521	#385	C₂²×C₆₇	1	2	yes	—
522	#385	C₂²×C₆₇	1	2	yes	—
523	#385	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	#385	C₂²×C₆₇	1	2	yes	—
534	#385	C₂²×C₆₇	1	1	yes	characteristic
535	#385	C₂²×C₆₇	1	2	yes	—
536	#385	C₂²×C₆₇	1	2	yes	complemented
537	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	#385	C₂²×C₆₇	1	2	yes	complemented
539	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	#384	C₂²×C₆₇	1	2	yes	complemented
542	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	#380	C₂²×C₆₇	1	2	yes	—
544	#380	C₂²×C₆₇	1	2	yes	—
545	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
546	#380	C₂²×C₆₇	1	2	yes	complemented
547	#379	C₂²×C₆₇	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
550	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
551	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
553	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
554	C₂×#95	C₂²×C₆₇	1	2	yes	—
555	C₂×#95	C₂²×C₆₇	1	2	yes	—
556	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
557	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
559	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	—	4	4	no	—
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	2	yes	—
567	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
568	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
569	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
573	#125	—	4	2	no	—
574	C₂²⋊Q₈	—	2	8	no	—
575	C₂²⋊Q₈	—	4	4	no	—
576	#120	Q₈×C₆₇	1	8	yes	complemented
577	C₄×D₄	—	2	8	no	—
578	C₄×D₄	—	4	2	no	—
579	C₄×D₄	—	4	4	no	—
580	C₄×D₄	—	4	4	no	—
581	C₂×C₄⋊C₄	—	4	4	no	—
582	C₂×C₄⋊C₄	—	4	2	no	—
583	C₂×C₄⋊C₄	—	4	4	no	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
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	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	—	2	8	no	—
608	C₂×C₂²⋊C₄	—	4	4	no	—
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×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
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	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	C₂⁴	—	2	4	no	—
659	C₂⁴	—	2	4	no	—
660	C₂⁴	—	4	1	no	—
661	C₂⁴	—	4	1	no	—
662	C₂⁴	C₂×Q₈×C₆₇	1	4	yes	—
663	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
664	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	—	4	1	no	—
673	C₂×D₄	C₂×Q₈×C₆₇	1	8	yes	—
674	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
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	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	4	1	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	—	4	1	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	16	no	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	—	4	1	no	—
759	C₂²⋊C₄	—	4	1	no	—
760	C₂²⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
761	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
762	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	4	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	16	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	8	no	—
786	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
787	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
788	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
789	C₂³	C₂×#41×C₆₇	1	4	yes	—
790	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
791	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
792	Q₈	—	8	4	no	—
793	D₄	—	2	16	no	—
794	D₄	—	4	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	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	1	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	1	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	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	8	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	4	no	—
843	C₂×C₄	—	8	4	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
846	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
847	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
848	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
849	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	4	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	4	16	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	#554×C₆₇	1	8	yes	—
868	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
869	C₂²	C₂²×#41×C₆₇	1	2	yes	—
870	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
871	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
872	C₂²	#585×C₆₇	1	1	yes	characteristic
873	C₄	—	2	2	no	—
874	C₄	—	2	4	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	2	no	—
877	C₄	—	2	4	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₂	—	2	8	no	—
890	C₂	—	4	2	no	—
891	C₂	—	4	2	no	—
892	C₂	C₂×#554×C₆₇	1	2	yes	—
893	C₂	C₆₇×#3481	1	1	yes	characteristic
894	C₂	C₆₇×#3501	1	1	yes	characteristic
895	C₂	C₆₇×#3513	1	2	yes	—
896	C₂	C₆₇×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#120×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×#2804	C₂	semidirect
2. C₆₇×#2790	C₂	semidirect
3. C₆₇×#2748	C₂	semidirect
4. C₆₇×#2589	C₂	semidirect
5. C₆₇×#2579	C₂	semidirect
6. C₆₇×#2579	C₂	semidirect
7. C₆₇×#2566	C₂	semidirect
8. C₆₇×#2505	C₂	semidirect
9. C₆₇×#2502	C₂	semidirect
10. C₆₇×#2473	C₂	semidirect
11. C₆₇×#2450	C₂	semidirect
12. C₆₇×#2450	C₂	semidirect
13. C₆₇×#2437	C₂	semidirect
14. C₆₇×#2368	C₂	semidirect
17. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
19. C₂×#385×C₆₇	C₂	semidirect
21. C₂×#125×C₆₇	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
35. #400×C₆₇	C₂²	semidirect
36. #400×C₆₇	C₂²	semidirect
38. #398×C₆₇	C₂²	semidirect
39. #398×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
41. #398×C₆₇	C₂²	semidirect
42. #398×C₆₇	C₂²	semidirect
43. #398×C₆₇	C₂²	semidirect
46. #396×C₆₇	C₂²	semidirect
47. #396×C₆₇	C₂²	semidirect
49. #393×C₆₇	C₂²	semidirect
50. #391×C₆₇	C₂²	semidirect
51. #391×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
55. #389×C₆₇	C₂²	semidirect
56. #389×C₆₇	C₂²	semidirect
59. #387×C₆₇	C₂²	semidirect
60. #387×C₆₇	C₂²	semidirect
61. #387×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
87. #385×C₆₇	C₂²	semidirect
88. #385×C₆₇	C₂²	semidirect
89. #385×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #384×C₆₇	C₂²	semidirect
92. #384×C₆₇	C₂²	semidirect
93. #382×C₆₇	C₂²	semidirect
96. #380×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
100. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
127. #120×C₆₇	Q₈	semidirect
440. #59915	C₆₇	direct (N × H)
449. #2804	C₂×C₆₇	semidirect
450. #2790	C₂×C₆₇	semidirect
451. #2748	C₂×C₆₇	semidirect
452. #2589	C₂×C₆₇	semidirect
453. #2579	C₂×C₆₇	semidirect
454. #2579	C₂×C₆₇	semidirect
455. #2566	C₂×C₆₇	semidirect
456. #2505	C₂×C₆₇	semidirect
457. #2502	C₂×C₆₇	semidirect
458. #2473	C₂×C₆₇	semidirect
459. #2450	C₂×C₆₇	semidirect
460. #2450	C₂×C₆₇	semidirect
461. #2437	C₂×C₆₇	semidirect
462. #2368	C₂×C₆₇	semidirect
465. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
467. C₂×#385	C₂×C₆₇	semidirect
468. C₆₇	#59915	direct (N × H)
470. C₂×#125	C₂²×C₆₇	semidirect
480. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
483. #400	C₂²×C₆₇	semidirect
484. #400	C₂²×C₆₇	semidirect
485. #400	C₂²×C₆₇	semidirect
487. #398	C₂²×C₆₇	semidirect
488. #398	C₂²×C₆₇	semidirect
489. #398	C₂²×C₆₇	semidirect
490. #398	C₂²×C₆₇	semidirect
491. #398	C₂²×C₆₇	semidirect
492. #398	C₂²×C₆₇	semidirect
495. #396	C₂²×C₆₇	semidirect
496. #396	C₂²×C₆₇	semidirect
498. #393	C₂²×C₆₇	semidirect
499. #391	C₂²×C₆₇	semidirect
500. #391	C₂²×C₆₇	semidirect
501. #391	C₂²×C₆₇	semidirect
504. #389	C₂²×C₆₇	semidirect
505. #389	C₂²×C₆₇	semidirect
508. #387	C₂²×C₆₇	semidirect
509. #387	C₂²×C₆₇	semidirect
510. #387	C₂²×C₆₇	semidirect
511. #387	C₂²×C₆₇	semidirect
512. #387	C₂²×C₆₇	semidirect
513. #387	C₂²×C₆₇	semidirect
536. #385	C₂²×C₆₇	semidirect
537. #385	C₂²×C₆₇	semidirect
538. #385	C₂²×C₆₇	semidirect
539. #385	C₂²×C₆₇	semidirect
540. #384	C₂²×C₆₇	semidirect
541. #384	C₂²×C₆₇	semidirect
542. #382	C₂²×C₆₇	semidirect
545. #380	C₂²×C₆₇	semidirect
546. #380	C₂²×C₆₇	semidirect
548. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
549. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
576. #120	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×#2804	2
C₆₇×#2790	2
C₆₇×#2748	2
C₆₇×#2589	2
C₆₇×#2579	2
C₆₇×#2566	2
C₆₇×#2505	2
C₆₇×#2502	2
C₆₇×#2473	2
C₆₇×#2450	2
C₆₇×#2437	2
C₆₇×#2368	2
C₆₇×#2358	2
D₄×C₄⋊C₄×C₆₇	2
C₄×#120×C₆₇	2
C₂×#385×C₆₇	2
#59915	67

Subgroups — C67×#59915 #30739166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59915 #30739166