Subgroups — C₆₇×#60040 #30739291

Order 17152.

2096 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2790	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2669	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2603	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2600	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2579	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2554	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2534	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2526	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2468	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2457	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2411	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2374	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	2	yes	—
25	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#120×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	complemented
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	#397×C₆₇	C₂²	1	2	yes	complemented
42	#396×C₆₇	C₂²	1	2	yes	—
43	#396×C₆₇	C₂²	1	2	yes	—
44	#396×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	—
49	#394×C₆₇	C₂²	1	2	yes	complemented
50	#394×C₆₇	C₂²	1	2	yes	complemented
51	#392×C₆₇	C₂²	1	2	yes	—
52	#392×C₆₇	C₂²	1	2	yes	—
53	#390×C₆₇	C₂²	1	2	yes	—
54	#390×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#390×C₆₇	C₂²	1	2	yes	complemented
59	#389×C₆₇	C₂²	1	2	yes	complemented
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	complemented
68	#388×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	2	yes	complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	2	yes	complemented
75	#387×C₆₇	C₂²	1	2	yes	complemented
76	#387×C₆₇	C₂²	1	2	yes	complemented
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	1	yes	characteristic
81	#386×C₆₇	C₂²	1	1	yes	characteristic
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	complemented
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#385×C₆₇	C₂²	1	2	yes	complemented
93	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#381×C₆₇	C₂²	1	1	yes	characteristic
95	#381×C₆₇	C₂²	1	2	yes	complemented
96	#380×C₆₇	C₂²	1	1	yes	characteristic
97	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#379×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	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	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	#376×C₆₇	C₂²	1	2	yes	complemented
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	#127×C₆₇	—	2	4	no	—
124	#126×C₆₇	—	4	4	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	4	4	no	—
127	#121×C₆₇	—	2	8	no	—
128	#120×C₆₇	—	2	4	no	—
129	#120×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	C₄×D₄×C₆₇	—	4	4	no	—
133	C₄×D₄×C₆₇	—	4	2	no	—
134	C₄×D₄×C₆₇	—	4	2	no	—
135	C₄×D₄×C₆₇	—	4	4	no	—
136	#117×C₆₇	—	2	8	no	—
137	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	—	4	4	no	—
154	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
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	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×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	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	C₂⁴×C₆₇	—	2	2	no	—
212	C₂⁴×C₆₇	—	2	4	no	—
213	C₂⁴×C₆₇	—	4	2	no	—
214	C₂⁴×C₆₇	—	4	1	no	—
215	C₂⁴×C₆₇	—	4	1	no	—
216	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
217	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
219	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	2	no	—
230	C₂×D₄×C₆₇	—	4	1	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	1	no	—
234	C₂×D₄×C₆₇	—	4	2	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	1	no	—
237	C₂×D₄×C₆₇	—	4	1	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	4	2	no	—
240	C₂×D₄×C₆₇	#41	1	4	yes	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	4	1	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	1	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	2	no	—
260	C₂²×C₄×C₆₇	—	4	1	no	—
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	1	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	1	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	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	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	4	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	1	no	—
310	C₂²⋊C₄×C₆₇	—	4	1	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	1	no	—
313	C₂²⋊C₄×C₆₇	—	4	1	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
320	C₄²×C₆₇	—	2	4	no	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	—	2	2	no	—
323	C₄²×C₆₇	—	2	4	no	—
324	C₄²×C₆₇	—	2	2	no	—
325	C₄²×C₆₇	—	2	4	no	—
326	C₄²×C₆₇	—	4	1	no	—
327	C₄²×C₆₇	—	4	2	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	4	4	no	—
351	C₂³×C₆₇	—	4	8	no	—
352	C₂³×C₆₇	—	8	4	no	—
353	C₂³×C₆₇	—	8	2	no	—
354	C₂³×C₆₇	—	8	2	no	—
355	C₂³×C₆₇	C₂×#41	1	2	yes	—
356	C₂³×C₆₇	C₂×#41	1	2	yes	—
357	C₂³×C₆₇	C₂×#41	1	4	yes	—
358	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
359	D₄×C₆₇	—	4	4	no	—
360	D₄×C₆₇	—	4	8	no	—
361	D₄×C₆₇	—	4	8	no	—
362	D₄×C₆₇	—	4	8	no	—
363	D₄×C₆₇	—	4	4	no	—
364	D₄×C₆₇	—	4	8	no	—
365	D₄×C₆₇	—	8	4	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	1	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	1	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	1	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	4	4	no	—
403	C₂×C₄×C₆₇	—	4	8	no	—
404	C₂×C₄×C₆₇	—	8	2	no	—
405	C₂×C₄×C₆₇	—	8	2	no	—
406	C₂×C₄×C₆₇	—	8	4	no	—
407	C₂×C₄×C₆₇	—	8	2	no	—
408	C₂×C₄×C₆₇	—	8	2	no	—
409	C₂×C₄×C₆₇	—	8	4	no	—
410	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
412	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
413	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
414	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	4	no	—
418	C₂²×C₆₇	—	2	4	no	—
419	C₂²×C₆₇	—	2	4	no	—
420	C₂²×C₆₇	—	2	2	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	1	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	2	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	2	no	—
439	C₂²×C₆₇	—	8	8	no	—
440	C₂²×C₆₇	C₂²×#41	1	2	yes	—
441	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
442	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₆₇	#585	1	1	yes	characteristic
445	C₄×C₆₇	—	2	4	no	—
446	C₄×C₆₇	—	2	4	no	—
447	C₄×C₆₇	—	2	4	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	—	4	2	no	—
452	C₄×C₆₇	—	4	2	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	1	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	—	4	2	no	—
460	#60040	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₆₇	—	4	2	no	—
462	C₂×C₆₇	—	4	4	no	—
463	C₂×C₆₇	—	4	2	no	—
464	C₂×C₆₇	—	8	2	no	—
465	C₂×C₆₇	#3481	1	1	yes	characteristic
466	C₂×C₆₇	#3481	1	2	yes	—
467	C₂×C₆₇	#3494	1	2	yes	—
468	C₂×C₆₇	#3505	1	1	yes	characteristic
469	C₂×C₆₇	#3543	1	1	yes	characteristic
470	#2790	C₂×C₆₇	1	2	yes	complemented
471	#2709	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#2669	C₂×C₆₇	1	1	yes	characteristic
473	#2603	C₂×C₆₇	1	2	yes	complemented
474	#2600	C₂×C₆₇	1	2	yes	complemented
475	#2579	C₂×C₆₇	1	1	yes	characteristic, complemented
476	#2554	C₂×C₆₇	1	2	yes	complemented
477	#2534	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#2526	C₂×C₆₇	1	2	yes	complemented
479	#2476	C₂×C₆₇	1	2	yes	complemented
480	#2468	C₂×C₆₇	1	2	yes	complemented
481	#2457	C₂×C₆₇	1	2	yes	complemented
482	#2411	C₂×C₆₇	1	2	yes	complemented
483	#2374	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#2361	C₂×C₆₇	1	2	yes	complemented
485	#2358	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#2358	C₂×C₆₇	1	2	yes	complemented
487	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2298	C₂×C₆₇	1	2	yes	complemented
489	C₆₇	#60040	1	1	yes	characteristic, direct product factor, Sylow
490	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
492	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#123	C₂²×C₆₇	1	2	yes	—
494	C₂×#121	C₂²×C₆₇	1	2	yes	—
495	C₂×#120	C₂²×C₆₇	1	2	yes	—
496	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
500	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
502	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
503	C₂×#117	C₂²×C₆₇	1	2	yes	—
504	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
506	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
507	#400	C₂²×C₆₇	1	2	yes	complemented
508	#398	C₂²×C₆₇	1	2	yes	complemented
509	#398	C₂²×C₆₇	1	2	yes	complemented
510	#398	C₂²×C₆₇	1	2	yes	complemented
511	#397	C₂²×C₆₇	1	2	yes	complemented
512	#396	C₂²×C₆₇	1	2	yes	—
513	#396	C₂²×C₆₇	1	2	yes	—
514	#396	C₂²×C₆₇	1	2	yes	—
515	#394	C₂²×C₆₇	1	2	yes	—
516	#394	C₂²×C₆₇	1	2	yes	—
517	#394	C₂²×C₆₇	1	2	yes	—
518	#394	C₂²×C₆₇	1	2	yes	—
519	#394	C₂²×C₆₇	1	2	yes	complemented
520	#394	C₂²×C₆₇	1	2	yes	complemented
521	#392	C₂²×C₆₇	1	2	yes	—
522	#392	C₂²×C₆₇	1	2	yes	—
523	#390	C₂²×C₆₇	1	1	yes	characteristic
524	#390	C₂²×C₆₇	1	2	yes	—
525	#390	C₂²×C₆₇	1	2	yes	—
526	#390	C₂²×C₆₇	1	2	yes	—
527	#390	C₂²×C₆₇	1	2	yes	complemented
528	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
529	#389	C₂²×C₆₇	1	2	yes	complemented
530	#388	C₂²×C₆₇	1	2	yes	—
531	#388	C₂²×C₆₇	1	2	yes	—
532	#388	C₂²×C₆₇	1	2	yes	—
533	#388	C₂²×C₆₇	1	2	yes	—
534	#388	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#388	C₂²×C₆₇	1	2	yes	—
537	#388	C₂²×C₆₇	1	2	yes	complemented
538	#388	C₂²×C₆₇	1	2	yes	complemented
539	#388	C₂²×C₆₇	1	2	yes	complemented
540	#388	C₂²×C₆₇	1	2	yes	complemented
541	#388	C₂²×C₆₇	1	2	yes	complemented
542	#387	C₂²×C₆₇	1	2	yes	complemented
543	#387	C₂²×C₆₇	1	2	yes	complemented
544	#387	C₂²×C₆₇	1	2	yes	complemented
545	#387	C₂²×C₆₇	1	2	yes	complemented
546	#387	C₂²×C₆₇	1	2	yes	complemented
547	#386	C₂²×C₆₇	1	1	yes	characteristic
548	#386	C₂²×C₆₇	1	1	yes	characteristic
549	#386	C₂²×C₆₇	1	2	yes	—
550	#386	C₂²×C₆₇	1	2	yes	—
551	#386	C₂²×C₆₇	1	2	yes	—
552	#386	C₂²×C₆₇	1	2	yes	—
553	#386	C₂²×C₆₇	1	2	yes	—
554	#386	C₂²×C₆₇	1	2	yes	—
555	#386	C₂²×C₆₇	1	2	yes	complemented
556	#385	C₂²×C₆₇	1	2	yes	—
557	#385	C₂²×C₆₇	1	2	yes	—
558	#385	C₂²×C₆₇	1	2	yes	—
559	#385	C₂²×C₆₇	1	2	yes	—
560	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
561	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#385	C₂²×C₆₇	1	2	yes	complemented
563	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	#381	C₂²×C₆₇	1	1	yes	characteristic
565	#381	C₂²×C₆₇	1	2	yes	complemented
566	#380	C₂²×C₆₇	1	1	yes	characteristic
567	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#379	C₂²×C₆₇	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
570	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
571	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
575	#376	C₂²×C₆₇	1	2	yes	complemented
576	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
579	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
580	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
581	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
582	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
584	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
586	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
591	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
592	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
593	#127	—	2	4	no	—
594	#126	—	4	4	no	—
595	#123	—	2	4	no	—
596	#123	—	4	4	no	—
597	#121	—	2	8	no	—
598	#120	—	2	4	no	—
599	#120	—	2	8	no	—
600	C₄×D₄	—	4	4	no	—
601	C₄×D₄	—	4	4	no	—
602	C₄×D₄	—	4	4	no	—
603	C₄×D₄	—	4	2	no	—
604	C₄×D₄	—	4	2	no	—
605	C₄×D₄	—	4	4	no	—
606	#117	—	2	8	no	—
607	C₂×C₄⋊C₄	—	4	2	no	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	—	4	4	no	—
624	C₂×C₂²⋊C₄	—	4	2	no	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	#95	C₂³×C₆₇	1	2	yes	—
676	#95	C₂³×C₆₇	1	2	yes	—
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	2	yes	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	4	no	—
683	C₂⁴	—	4	2	no	—
684	C₂⁴	—	4	1	no	—
685	C₂⁴	—	4	1	no	—
686	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
687	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
689	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	#41×C₆₇	1	4	yes	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
790	C₄²	—	2	4	no	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	4	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	1	no	—
798	C₄²	—	4	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	8	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	2	no	—
824	C₂³	—	8	2	no	—
825	C₂³	C₂×#41×C₆₇	1	2	yes	—
826	C₂³	C₂×#41×C₆₇	1	2	yes	—
827	C₂³	C₂×#41×C₆₇	1	4	yes	—
828	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
829	D₄	—	4	4	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	8	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	8	no	—
835	D₄	—	8	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	8	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	2	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	4	no	—
880	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
881	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
882	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
883	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
884	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	8	no	—
910	C₂²	C₂²×#41×C₆₇	1	2	yes	—
911	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
912	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
913	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
914	C₂²	#585×C₆₇	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	4	no	—
918	C₄	—	2	4	no	—
919	C₄	—	2	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₂	—	4	4	no	—
931	C₂	—	4	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₆₇×#3481	1	1	yes	characteristic
935	C₂	C₆₇×#3481	1	2	yes	—
936	C₂	C₆₇×#3494	1	2	yes	—
937	C₂	C₆₇×#3505	1	1	yes	characteristic
938	C₂	C₆₇×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2669	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. C₆₇×#2790	C₂	semidirect
2. C₆₇×#2709	C₂	semidirect
4. C₆₇×#2603	C₂	semidirect
5. C₆₇×#2600	C₂	semidirect
6. C₆₇×#2579	C₂	semidirect
7. C₆₇×#2554	C₂	semidirect
8. C₆₇×#2534	C₂	semidirect
9. C₆₇×#2526	C₂	semidirect
10. C₆₇×#2476	C₂	semidirect
11. C₆₇×#2468	C₂	semidirect
12. C₆₇×#2457	C₂	semidirect
13. C₆₇×#2411	C₂	semidirect
14. C₆₇×#2374	C₂	semidirect
15. C₆₇×#2361	C₂	semidirect
16. C₆₇×#2358	C₂	semidirect
17. C₆₇×#2358	C₂	semidirect
18. C₄×#127×C₆₇	C₂	semidirect
19. C₆₇×#2298	C₂	semidirect
21. C₂×#126×C₆₇	C₂²	semidirect
31. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. C₂×C₄×D₄×C₆₇	C₂²	semidirect
34. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
38. #398×C₆₇	C₂²	semidirect
39. #398×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
41. #397×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
57. #390×C₆₇	C₂²	semidirect
58. #390×C₆₇	C₂²	semidirect
59. #389×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
85. #386×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
92. #385×C₆₇	C₂²	semidirect
93. #384×C₆₇	C₂²	semidirect
95. #381×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
100. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. #376×C₆₇	C₂²	semidirect
106. C₄³×C₆₇	C₂²	semidirect
460. #60040	C₆₇	direct (N × H)
470. #2790	C₂×C₆₇	semidirect
471. #2709	C₂×C₆₇	semidirect
473. #2603	C₂×C₆₇	semidirect
474. #2600	C₂×C₆₇	semidirect
475. #2579	C₂×C₆₇	semidirect
476. #2554	C₂×C₆₇	semidirect
477. #2534	C₂×C₆₇	semidirect
478. #2526	C₂×C₆₇	semidirect
479. #2476	C₂×C₆₇	semidirect
480. #2468	C₂×C₆₇	semidirect
481. #2457	C₂×C₆₇	semidirect
482. #2411	C₂×C₆₇	semidirect
483. #2374	C₂×C₆₇	semidirect
484. #2361	C₂×C₆₇	semidirect
485. #2358	C₂×C₆₇	semidirect
486. #2358	C₂×C₆₇	semidirect
487. C₄×#127	C₂×C₆₇	semidirect
488. #2298	C₂×C₆₇	semidirect
489. C₆₇	#60040	direct (N × H)
491. C₂×#126	C₂²×C₆₇	semidirect
501. C₂×C₄×D₄	C₂²×C₆₇	semidirect
502. C₂×C₄×D₄	C₂²×C₆₇	semidirect
504. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
507. #400	C₂²×C₆₇	semidirect
508. #398	C₂²×C₆₇	semidirect
509. #398	C₂²×C₆₇	semidirect
510. #398	C₂²×C₆₇	semidirect
511. #397	C₂²×C₆₇	semidirect
519. #394	C₂²×C₆₇	semidirect
520. #394	C₂²×C₆₇	semidirect
527. #390	C₂²×C₆₇	semidirect
528. #390	C₂²×C₆₇	semidirect
529. #389	C₂²×C₆₇	semidirect
537. #388	C₂²×C₆₇	semidirect
538. #388	C₂²×C₆₇	semidirect
539. #388	C₂²×C₆₇	semidirect
540. #388	C₂²×C₆₇	semidirect
541. #388	C₂²×C₆₇	semidirect
542. #387	C₂²×C₆₇	semidirect
543. #387	C₂²×C₆₇	semidirect
544. #387	C₂²×C₆₇	semidirect
545. #387	C₂²×C₆₇	semidirect
546. #387	C₂²×C₆₇	semidirect
555. #386	C₂²×C₆₇	semidirect
560. #385	C₂²×C₆₇	semidirect
561. #385	C₂²×C₆₇	semidirect
562. #385	C₂²×C₆₇	semidirect
563. #384	C₂²×C₆₇	semidirect
565. #381	C₂²×C₆₇	semidirect
567. #380	C₂²×C₆₇	semidirect
569. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
570. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
574. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
575. #376	C₂²×C₆₇	semidirect
576. C₄³	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2790	2
C₆₇×#2709	2
C₆₇×#2669	2
C₆₇×#2603	2
C₆₇×#2600	2
C₆₇×#2579	2
C₆₇×#2554	2
C₆₇×#2534	2
C₆₇×#2526	2
C₆₇×#2476	2
C₆₇×#2468	2
C₆₇×#2457	2
C₆₇×#2411	2
C₆₇×#2374	2
C₆₇×#2361	2
C₆₇×#2358	2
C₄×#127×C₆₇	2
C₆₇×#2298	2
#60040	67

Subgroups — C67×#60040 #30739291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60040 #30739291