Subgroups — C₆₇×#59504 #30738755

Order 17152.

1728 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2741	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2738	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2601	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2577	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2573	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2509	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2481	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2479	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
18	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2344	C₂	1	2	yes	maximal, complemented
21	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#126×C₆₇	C₂²	1	2	yes	—
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	2	yes	—
37	#400×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	2	yes	—
39	#399×C₆₇	C₂²	1	2	yes	—
40	#399×C₆₇	C₂²	1	2	yes	—
41	#398×C₆₇	C₂²	1	2	yes	—
42	#398×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#397×C₆₇	C₂²	1	2	yes	—
45	#397×C₆₇	C₂²	1	2	yes	—
46	#397×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	2	yes	—
49	#394×C₆₇	C₂²	1	2	yes	—
50	#394×C₆₇	C₂²	1	2	yes	—
51	#390×C₆₇	C₂²	1	1	yes	characteristic
52	#390×C₆₇	C₂²	1	1	yes	characteristic
53	#390×C₆₇	C₂²	1	2	yes	—
54	#390×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	2	yes	—
59	#389×C₆₇	C₂²	1	1	yes	characteristic
60	#389×C₆₇	C₂²	1	1	yes	characteristic
61	#389×C₆₇	C₂²	1	2	yes	—
62	#389×C₆₇	C₂²	1	1	yes	characteristic
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	1	yes	characteristic
70	#388×C₆₇	C₂²	1	1	yes	characteristic
71	#388×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#388×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	1	yes	characteristic
80	#387×C₆₇	C₂²	1	1	yes	characteristic
81	#387×C₆₇	C₂²	1	1	yes	characteristic
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#384×C₆₇	C₂²	1	1	yes	characteristic
95	#384×C₆₇	C₂²	1	1	yes	characteristic
96	#383×C₆₇	C₂²	1	1	yes	characteristic
97	#383×C₆₇	C₂²	1	2	yes	—
98	#382×C₆₇	C₂²	1	1	yes	characteristic
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#381×C₆₇	C₂²	1	2	yes	—
101	#381×C₆₇	C₂²	1	2	yes	—
102	#380×C₆₇	C₂²	1	2	yes	—
103	#380×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	2	yes	—
106	#380×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄³×C₆₇	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	#126×C₆₇	—	2	4	no	—
130	#126×C₆₇	—	4	4	no	—
131	#125×C₆₇	—	2	4	no	—
132	#121×C₆₇	—	2	4	no	—
133	C₄×D₄×C₆₇	—	2	4	no	—
134	C₄×D₄×C₆₇	—	2	4	no	—
135	C₄×D₄×C₆₇	—	2	4	no	—
136	#117×C₆₇	—	2	4	no	—
137	#117×C₆₇	—	4	4	no	—
138	#117×C₆₇	—	4	4	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
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	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×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	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	1	yes	characteristic
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	2	no	—
237	C₂×D₄×C₆₇	—	2	2	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	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	1	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	2	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	—	4	2	no	—
300	C₄⋊C₄×C₆₇	#41	1	4	yes	—
301	C₄⋊C₄×C₆₇	#41	1	4	yes	—
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	—	2	4	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	1	no	—
315	C₂²⋊C₄×C₆₇	—	4	1	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	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	—	2	2	no	—
323	C₄²×C₆₇	—	2	2	no	—
324	C₄²×C₆₇	—	2	2	no	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	4	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	4	2	no	—
332	C₄²×C₆₇	—	4	1	no	—
333	C₄²×C₆₇	—	4	1	no	—
334	C₄²×C₆₇	—	4	2	no	—
335	C₄²×C₆₇	—	4	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	2	1	no	—
345	C₂³×C₆₇	—	2	1	no	—
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	C₂×#41	1	4	yes	—
350	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
351	D₄×C₆₇	—	2	8	no	—
352	D₄×C₆₇	—	8	4	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	1	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	1	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	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	1	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	1	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	4	8	no	—
409	C₂×C₄×C₆₇	—	4	8	no	—
410	C₂×C₄×C₆₇	—	4	8	no	—
411	C₂×C₄×C₆₇	—	4	4	no	—
412	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
413	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
414	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
415	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
416	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
417	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
418	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
420	C₂²×C₆₇	—	2	4	no	—
421	C₂²×C₆₇	—	2	4	no	—
422	C₂²×C₆₇	—	2	4	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	2	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	1	no	—
428	C₂²×C₆₇	—	4	1	no	—
429	C₂²×C₆₇	—	4	1	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	1	no	—
432	C₂²×C₆₇	—	4	1	no	—
433	C₂²×C₆₇	—	4	1	no	—
434	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
435	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
439	C₂²×C₆₇	#585	1	1	yes	characteristic
440	C₂²×C₆₇	#585	1	1	yes	characteristic
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	4	no	—
443	C₄×C₆₇	—	2	2	no	—
444	C₄×C₆₇	—	2	2	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	4	1	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	—	4	2	no	—
452	C₄×C₆₇	—	4	1	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	1	no	—
455	C₄×C₆₇	—	4	1	no	—
456	C₄×C₆₇	—	4	1	no	—
457	C₄×C₆₇	—	4	1	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	—	4	1	no	—
460	C₄×C₆₇	—	4	2	no	—
461	C₄×C₆₇	#552	1	4	yes	—
462	#59504	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂×C₆₇	—	4	4	no	—
464	C₂×C₆₇	—	8	1	no	—
465	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
466	C₂×C₆₇	#3475	1	1	yes	characteristic
467	C₂×C₆₇	#3481	1	1	yes	characteristic
468	C₂×C₆₇	#3517	1	1	yes	characteristic
469	C₂×C₆₇	#3518	1	1	yes	characteristic
470	C₂×C₆₇	#3521	1	1	yes	characteristic
471	C₂×C₆₇	#3559	1	1	yes	characteristic
472	#2741	C₂×C₆₇	1	2	yes	complemented
473	#2738	C₂×C₆₇	1	2	yes	complemented
474	#2601	C₂×C₆₇	1	2	yes	complemented
475	#2577	C₂×C₆₇	1	2	yes	complemented
476	#2573	C₂×C₆₇	1	2	yes	complemented
477	#2570	C₂×C₆₇	1	1	yes	characteristic, complemented
478	#2509	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#2507	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#2496	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#2481	C₂×C₆₇	1	2	yes	complemented
482	#2479	C₂×C₆₇	1	2	yes	complemented
483	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#2441	C₂×C₆₇	1	1	yes	characteristic, complemented
485	#2420	C₂×C₆₇	1	1	yes	characteristic
486	#2420	C₂×C₆₇	1	1	yes	characteristic
487	#2363	C₂×C₆₇	1	1	yes	characteristic
488	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
489	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#2344	C₂×C₆₇	1	2	yes	complemented
492	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
493	C₄×#126	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
495	C₆₇	#59504	1	1	yes	characteristic, direct product factor, Sylow
496	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
497	C₂×#126	C₂²×C₆₇	1	2	yes	—
498	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
499	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#117	C₂²×C₆₇	1	2	yes	—
505	C₂×#117	C₂²×C₆₇	1	2	yes	—
506	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
507	#400	C₂²×C₆₇	1	2	yes	—
508	#400	C₂²×C₆₇	1	2	yes	—
509	#400	C₂²×C₆₇	1	2	yes	—
510	#400	C₂²×C₆₇	1	2	yes	—
511	#399	C₂²×C₆₇	1	2	yes	—
512	#399	C₂²×C₆₇	1	2	yes	—
513	#398	C₂²×C₆₇	1	2	yes	—
514	#398	C₂²×C₆₇	1	2	yes	—
515	#398	C₂²×C₆₇	1	2	yes	—
516	#397	C₂²×C₆₇	1	2	yes	—
517	#397	C₂²×C₆₇	1	2	yes	—
518	#397	C₂²×C₆₇	1	2	yes	—
519	#396	C₂²×C₆₇	1	2	yes	—
520	#396	C₂²×C₆₇	1	2	yes	—
521	#394	C₂²×C₆₇	1	2	yes	—
522	#394	C₂²×C₆₇	1	2	yes	—
523	#390	C₂²×C₆₇	1	2	yes	—
524	#390	C₂²×C₆₇	1	1	yes	characteristic
525	#390	C₂²×C₆₇	1	1	yes	characteristic
526	#390	C₂²×C₆₇	1	1	yes	characteristic
527	#389	C₂²×C₆₇	1	1	yes	characteristic
528	#389	C₂²×C₆₇	1	1	yes	characteristic
529	#389	C₂²×C₆₇	1	1	yes	characteristic
530	#389	C₂²×C₆₇	1	1	yes	characteristic
531	#389	C₂²×C₆₇	1	2	yes	—
532	#389	C₂²×C₆₇	1	2	yes	—
533	#389	C₂²×C₆₇	1	2	yes	—
534	#389	C₂²×C₆₇	1	1	yes	characteristic
535	#389	C₂²×C₆₇	1	1	yes	characteristic
536	#389	C₂²×C₆₇	1	1	yes	characteristic
537	#389	C₂²×C₆₇	1	1	yes	characteristic
538	#389	C₂²×C₆₇	1	1	yes	characteristic
539	#388	C₂²×C₆₇	1	1	yes	characteristic
540	#388	C₂²×C₆₇	1	1	yes	characteristic
541	#388	C₂²×C₆₇	1	1	yes	characteristic
542	#388	C₂²×C₆₇	1	2	yes	—
543	#388	C₂²×C₆₇	1	2	yes	—
544	#388	C₂²×C₆₇	1	2	yes	—
545	#388	C₂²×C₆₇	1	2	yes	—
546	#388	C₂²×C₆₇	1	2	yes	—
547	#388	C₂²×C₆₇	1	2	yes	—
548	#388	C₂²×C₆₇	1	2	yes	—
549	#387	C₂²×C₆₇	1	1	yes	characteristic
550	#387	C₂²×C₆₇	1	1	yes	characteristic
551	#387	C₂²×C₆₇	1	1	yes	characteristic
552	#387	C₂²×C₆₇	1	2	yes	—
553	#387	C₂²×C₆₇	1	2	yes	—
554	#387	C₂²×C₆₇	1	2	yes	—
555	#387	C₂²×C₆₇	1	2	yes	—
556	#387	C₂²×C₆₇	1	2	yes	—
557	#387	C₂²×C₆₇	1	2	yes	—
558	#387	C₂²×C₆₇	1	2	yes	—
559	#387	C₂²×C₆₇	1	2	yes	—
560	#386	C₂²×C₆₇	1	2	yes	—
561	#386	C₂²×C₆₇	1	2	yes	—
562	#386	C₂²×C₆₇	1	2	yes	—
563	#385	C₂²×C₆₇	1	2	yes	—
564	#385	C₂²×C₆₇	1	2	yes	—
565	#385	C₂²×C₆₇	1	2	yes	—
566	#384	C₂²×C₆₇	1	1	yes	characteristic
567	#384	C₂²×C₆₇	1	1	yes	characteristic
568	#383	C₂²×C₆₇	1	1	yes	characteristic
569	#383	C₂²×C₆₇	1	2	yes	—
570	#382	C₂²×C₆₇	1	1	yes	characteristic
571	#382	C₂²×C₆₇	1	1	yes	characteristic
572	#381	C₂²×C₆₇	1	2	yes	—
573	#381	C₂²×C₆₇	1	2	yes	—
574	#380	C₂²×C₆₇	1	2	yes	—
575	#380	C₂²×C₆₇	1	2	yes	—
576	#380	C₂²×C₆₇	1	1	yes	characteristic
577	#380	C₂²×C₆₇	1	2	yes	—
578	#380	C₂²×C₆₇	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
588	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
592	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
594	C₄³	C₂²×C₆₇	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
597	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
599	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
600	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
601	#126	—	2	4	no	—
602	#126	—	4	4	no	—
603	#125	—	2	4	no	—
604	#121	—	2	4	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	4	no	—
608	#117	—	2	4	no	—
609	#117	—	4	4	no	—
610	#117	—	4	4	no	—
611	C₂×C₄⋊C₄	—	2	8	no	—
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	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	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	2	yes	—
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	1	yes	characteristic
675	#95	C₂³×C₆₇	1	1	yes	characteristic
676	#95	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	1	yes	characteristic
678	#95	C₂³×C₆₇	1	1	yes	characteristic
679	#95	C₂³×C₆₇	1	1	yes	characteristic
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	2	yes	—
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	1	yes	characteristic
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	2	yes	—
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	2	yes	—
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	1	yes	characteristic
692	#95	C₂³×C₆₇	1	1	yes	characteristic
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	1	yes	characteristic
695	#95	C₂³×C₆₇	1	1	yes	characteristic
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	1	yes	characteristic
698	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	#41×C₆₇	1	4	yes	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	#41×C₆₇	1	4	yes	—
773	C₄⋊C₄	#41×C₆₇	1	4	yes	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	1	no	—
791	C₂²⋊C₄	—	4	1	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	4	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	1	no	—
807	C₄²	—	4	1	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	C₂×#41×C₆₇	1	4	yes	—
822	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
823	D₄	—	2	8	no	—
824	D₄	—	8	4	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	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	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	8	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
885	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
886	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
887	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
888	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
889	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
890	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
891	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
907	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
908	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
909	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
910	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
911	C₂²	#585×C₆₇	1	1	yes	characteristic
912	C₂²	#585×C₆₇	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	1	no	—
933	C₄	#552×C₆₇	1	4	yes	—
934	C₂	—	4	4	no	—
935	C₂	—	8	1	no	—
936	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
937	C₂	C₆₇×#3475	1	1	yes	characteristic
938	C₂	C₆₇×#3481	1	1	yes	characteristic
939	C₂	C₆₇×#3517	1	1	yes	characteristic
940	C₂	C₆₇×#3518	1	1	yes	characteristic
941	C₂	C₆₇×#3521	1	1	yes	characteristic
942	C₂	C₆₇×#3559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×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×#2741	C₂	semidirect
2. C₆₇×#2738	C₂	semidirect
3. C₆₇×#2601	C₂	semidirect
4. C₆₇×#2577	C₂	semidirect
5. C₆₇×#2573	C₂	semidirect
6. C₆₇×#2570	C₂	semidirect
7. C₆₇×#2509	C₂	semidirect
8. C₆₇×#2507	C₂	semidirect
9. C₆₇×#2496	C₂	semidirect
10. C₆₇×#2481	C₂	semidirect
11. C₆₇×#2479	C₂	semidirect
12. C₆₇×#2454	C₂	semidirect
13. C₆₇×#2441	C₂	semidirect
17. C₆₇×#2354	C₂	semidirect
18. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
19. C₆₇×#2347	C₂	semidirect
20. C₆₇×#2344	C₂	semidirect
21. C₄×#125×C₆₇	C₂	semidirect
22. C₄×#126×C₆₇	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
462. #59504	C₆₇	direct (N × H)
472. #2741	C₂×C₆₇	semidirect
473. #2738	C₂×C₆₇	semidirect
474. #2601	C₂×C₆₇	semidirect
475. #2577	C₂×C₆₇	semidirect
476. #2573	C₂×C₆₇	semidirect
477. #2570	C₂×C₆₇	semidirect
478. #2509	C₂×C₆₇	semidirect
479. #2507	C₂×C₆₇	semidirect
480. #2496	C₂×C₆₇	semidirect
481. #2481	C₂×C₆₇	semidirect
482. #2479	C₂×C₆₇	semidirect
483. #2454	C₂×C₆₇	semidirect
484. #2441	C₂×C₆₇	semidirect
488. #2354	C₂×C₆₇	semidirect
489. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
490. #2347	C₂×C₆₇	semidirect
491. #2344	C₂×C₆₇	semidirect
492. C₄×#125	C₂×C₆₇	semidirect
493. C₄×#126	C₂×C₆₇	semidirect
494. #2293	C₂×C₆₇	semidirect
495. C₆₇	#59504	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2741	2
C₆₇×#2738	2
C₆₇×#2601	2
C₆₇×#2577	2
C₆₇×#2573	2
C₆₇×#2570	2
C₆₇×#2509	2
C₆₇×#2507	2
C₆₇×#2496	2
C₆₇×#2481	2
C₆₇×#2479	2
C₆₇×#2454	2
C₆₇×#2441	2
C₆₇×#2420	2
C₆₇×#2363	2
C₆₇×#2354	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2347	2
C₆₇×#2344	2
C₄×#125×C₆₇	2
C₄×#126×C₆₇	2
C₆₇×#2293	2
#59504	67

Subgroups — C67×#59504 #30738755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59504 #30738755