Subgroups — C₆₇×#36697 #30715948

Order 17152.

1484 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2843	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2839	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2838	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2837	C₂	1	2	yes	maximal
5	C₆₇×#2836	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2832	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2831	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2823	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2821	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2402	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2401	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2398	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2395	C₂	1	2	yes	maximal
18	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#126×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#126×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₆₇	C₂²	1	2	yes	—
27	#401×C₆₇	C₂²	1	2	yes	—
28	#400×C₆₇	C₂²	1	2	yes	—
29	#400×C₆₇	C₂²	1	2	yes	—
30	#400×C₆₇	C₂²	1	2	yes	—
31	#400×C₆₇	C₂²	1	2	yes	—
32	#400×C₆₇	C₂²	1	2	yes	—
33	#400×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#400×C₆₇	C₂²	1	1	yes	characteristic
37	#400×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	2	yes	—
39	#400×C₆₇	C₂²	1	1	yes	characteristic
40	#399×C₆₇	C₂²	1	2	yes	—
41	#399×C₆₇	C₂²	1	2	yes	—
42	#399×C₆₇	C₂²	1	2	yes	—
43	#398×C₆₇	C₂²	1	2	yes	—
44	#398×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	1	yes	characteristic
46	#398×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#398×C₆₇	C₂²	1	2	yes	—
49	#398×C₆₇	C₂²	1	2	yes	—
50	#398×C₆₇	C₂²	1	1	yes	characteristic
51	#398×C₆₇	C₂²	1	2	yes	—
52	#398×C₆₇	C₂²	1	2	yes	—
53	#398×C₆₇	C₂²	1	2	yes	—
54	#398×C₆₇	C₂²	1	2	yes	—
55	#397×C₆₇	C₂²	1	2	yes	—
56	#397×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	—
58	#397×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#397×C₆₇	C₂²	1	2	yes	—
62	#396×C₆₇	C₂²	1	2	yes	—
63	#396×C₆₇	C₂²	1	2	yes	—
64	#396×C₆₇	C₂²	1	2	yes	—
65	#396×C₆₇	C₂²	1	2	yes	—
66	#396×C₆₇	C₂²	1	2	yes	—
67	#395×C₆₇	C₂²	1	2	yes	—
68	#395×C₆₇	C₂²	1	2	yes	—
69	#395×C₆₇	C₂²	1	1	yes	characteristic
70	#395×C₆₇	C₂²	1	1	yes	characteristic
71	#395×C₆₇	C₂²	1	2	yes	—
72	#394×C₆₇	C₂²	1	1	yes	characteristic
73	#394×C₆₇	C₂²	1	2	yes	—
74	#394×C₆₇	C₂²	1	2	yes	—
75	#394×C₆₇	C₂²	1	1	yes	characteristic
76	#393×C₆₇	C₂²	1	2	yes	—
77	#393×C₆₇	C₂²	1	2	yes	—
78	#393×C₆₇	C₂²	1	2	yes	—
79	#391×C₆₇	C₂²	1	1	yes	characteristic
80	#391×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	2	yes	—
82	#389×C₆₇	C₂²	1	2	yes	—
83	#388×C₆₇	C₂²	1	2	yes	—
84	#388×C₆₇	C₂²	1	2	yes	—
85	#388×C₆₇	C₂²	1	2	yes	—
86	#387×C₆₇	C₂²	1	2	yes	—
87	#387×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#384×C₆₇	C₂²	1	1	yes	characteristic
90	#383×C₆₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	#376×C₆₇	C₂²	1	1	yes	characteristic
105	#376×C₆₇	C₂²	1	1	yes	characteristic
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₇	—	2	4	no	—
113	#126×C₆₇	—	2	8	no	—
114	C₄×Q₈×C₆₇	—	4	2	no	—
115	C₄×Q₈×C₆₇	—	4	2	no	—
116	C₄×Q₈×C₆₇	—	4	2	no	—
117	C₄×D₄×C₆₇	—	4	2	no	—
118	#117×C₆₇	—	4	4	no	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
169	#95×C₆₇	C₂³	1	2	yes	—
170	#95×C₆₇	C₂³	1	1	yes	characteristic
171	#95×C₆₇	C₂³	1	1	yes	characteristic
172	#95×C₆₇	C₂³	1	1	yes	characteristic
173	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	1	yes	characteristic
175	#95×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
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	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	2	2	no	—
204	C₂×Q₈×C₆₇	—	4	1	no	—
205	C₂×Q₈×C₆₇	—	4	1	no	—
206	C₂×Q₈×C₆₇	—	4	1	no	—
207	C₂×Q₈×C₆₇	—	4	1	no	—
208	C₂×Q₈×C₆₇	—	4	1	no	—
209	C₂×Q₈×C₆₇	—	4	2	no	—
210	C₂×D₄×C₆₇	—	4	1	no	—
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₆₇	—	2	4	no	—
234	C₄⋊C₄×C₆₇	—	2	4	no	—
235	C₄⋊C₄×C₆₇	—	2	4	no	—
236	C₄⋊C₄×C₆₇	—	2	4	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	4	2	no	—
239	C₄⋊C₄×C₆₇	—	4	2	no	—
240	C₄⋊C₄×C₆₇	—	4	2	no	—
241	C₄⋊C₄×C₆₇	—	4	2	no	—
242	C₄⋊C₄×C₆₇	—	4	2	no	—
243	C₄⋊C₄×C₆₇	—	4	2	no	—
244	C₄⋊C₄×C₆₇	—	4	2	no	—
245	C₄⋊C₄×C₆₇	—	4	2	no	—
246	C₄⋊C₄×C₆₇	—	4	2	no	—
247	C₄⋊C₄×C₆₇	—	4	2	no	—
248	C₄⋊C₄×C₆₇	—	4	2	no	—
249	C₄⋊C₄×C₆₇	—	4	2	no	—
250	C₄⋊C₄×C₆₇	—	4	2	no	—
251	C₄⋊C₄×C₆₇	—	4	1	no	—
252	C₄⋊C₄×C₆₇	—	4	1	no	—
253	C₄⋊C₄×C₆₇	—	4	1	no	—
254	C₄⋊C₄×C₆₇	—	4	1	no	—
255	C₄⋊C₄×C₆₇	—	4	1	no	—
256	C₄⋊C₄×C₆₇	—	4	2	no	—
257	C₄⋊C₄×C₆₇	—	4	2	no	—
258	C₄⋊C₄×C₆₇	—	4	1	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	4	2	no	—
263	C₂²⋊C₄×C₆₇	—	4	2	no	—
264	C₂²⋊C₄×C₆₇	—	4	2	no	—
265	C₂²⋊C₄×C₆₇	—	4	2	no	—
266	C₂²⋊C₄×C₆₇	—	4	2	no	—
267	C₂²⋊C₄×C₆₇	—	4	2	no	—
268	C₂²⋊C₄×C₆₇	—	4	2	no	—
269	C₂²⋊C₄×C₆₇	—	4	2	no	—
270	C₂²⋊C₄×C₆₇	—	4	2	no	—
271	C₂²⋊C₄×C₆₇	—	4	2	no	—
272	C₄²×C₆₇	—	2	4	no	—
273	C₄²×C₆₇	—	2	4	no	—
274	C₄²×C₆₇	—	2	2	no	—
275	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	—	2	2	no	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	—	2	4	no	—
280	C₄²×C₆₇	—	4	2	no	—
281	C₄²×C₆₇	—	4	1	no	—
282	C₄²×C₆₇	#41	1	4	yes	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
291	Q₈×C₆₇	—	4	4	no	—
292	Q₈×C₆₇	—	4	4	no	—
293	Q₈×C₆₇	—	4	4	no	—
294	D₄×C₆₇	—	4	4	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	1	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	1	no	—
311	C₂×C₄×C₆₇	—	2	1	no	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	1	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	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	1	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	4	8	no	—
342	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
343	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
344	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
345	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
346	C₂²×C₆₇	—	4	2	no	—
347	C₂²×C₆₇	—	4	2	no	—
348	C₂²×C₆₇	—	4	2	no	—
349	C₂²×C₆₇	—	4	2	no	—
350	C₂²×C₆₇	—	4	2	no	—
351	C₂²×C₆₇	—	4	2	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
356	C₂²×C₆₇	#585	1	1	yes	characteristic
357	C₂²×C₆₇	#585	1	2	yes	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	2	4	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	1	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	—	4	1	no	—
364	C₄×C₆₇	—	4	2	no	—
365	C₄×C₆₇	—	4	2	no	—
366	C₄×C₆₇	—	4	2	no	—
367	C₄×C₆₇	—	4	2	no	—
368	C₄×C₆₇	—	4	1	no	—
369	C₄×C₆₇	—	4	1	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	1	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	#563	1	4	yes	—
376	#36697	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂×C₆₇	—	8	2	no	—
378	C₂×C₆₇	#3460	1	1	yes	characteristic
379	C₂×C₆₇	#3461	1	2	yes	—
380	C₂×C₆₇	C₂×#563	1	1	yes	characteristic
381	C₂×C₆₇	#3529	1	1	yes	characteristic
382	C₂×C₆₇	#3531	1	2	yes	—
383	#2843	C₂×C₆₇	1	1	yes	characteristic, complemented
384	#2839	C₂×C₆₇	1	2	yes	complemented
385	#2838	C₂×C₆₇	1	2	yes	complemented
386	#2837	C₂×C₆₇	1	2	yes	—
387	#2836	C₂×C₆₇	1	2	yes	complemented
388	#2833	C₂×C₆₇	1	1	yes	characteristic, complemented
389	#2832	C₂×C₆₇	1	1	yes	characteristic
390	#2831	C₂×C₆₇	1	2	yes	complemented
391	#2823	C₂×C₆₇	1	1	yes	characteristic
392	#2821	C₂×C₆₇	1	2	yes	complemented
393	#2402	C₂×C₆₇	1	2	yes	complemented
394	#2401	C₂×C₆₇	1	2	yes	complemented
395	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#2398	C₂×C₆₇	1	1	yes	characteristic
397	#2396	C₂×C₆₇	1	2	yes	complemented
398	#2396	C₂×C₆₇	1	2	yes	complemented
399	#2395	C₂×C₆₇	1	2	yes	—
400	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₄×#126	C₂×C₆₇	1	2	yes	complemented
402	C₆₇	#36697	1	1	yes	characteristic, direct product factor, Sylow
403	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×#126	C₂²×C₆₇	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
409	C₂×#117	C₂²×C₆₇	1	2	yes	—
410	#401	C₂²×C₆₇	1	2	yes	—
411	#400	C₂²×C₆₇	1	2	yes	—
412	#400	C₂²×C₆₇	1	2	yes	—
413	#400	C₂²×C₆₇	1	2	yes	—
414	#400	C₂²×C₆₇	1	2	yes	—
415	#400	C₂²×C₆₇	1	2	yes	—
416	#400	C₂²×C₆₇	1	2	yes	—
417	#400	C₂²×C₆₇	1	2	yes	—
418	#400	C₂²×C₆₇	1	2	yes	—
419	#400	C₂²×C₆₇	1	1	yes	characteristic
420	#400	C₂²×C₆₇	1	2	yes	—
421	#400	C₂²×C₆₇	1	2	yes	—
422	#400	C₂²×C₆₇	1	1	yes	characteristic
423	#399	C₂²×C₆₇	1	2	yes	—
424	#399	C₂²×C₆₇	1	2	yes	—
425	#399	C₂²×C₆₇	1	2	yes	—
426	#398	C₂²×C₆₇	1	2	yes	—
427	#398	C₂²×C₆₇	1	2	yes	—
428	#398	C₂²×C₆₇	1	1	yes	characteristic
429	#398	C₂²×C₆₇	1	2	yes	—
430	#398	C₂²×C₆₇	1	2	yes	—
431	#398	C₂²×C₆₇	1	2	yes	—
432	#398	C₂²×C₆₇	1	2	yes	—
433	#398	C₂²×C₆₇	1	1	yes	characteristic
434	#398	C₂²×C₆₇	1	2	yes	—
435	#398	C₂²×C₆₇	1	2	yes	—
436	#398	C₂²×C₆₇	1	2	yes	—
437	#398	C₂²×C₆₇	1	2	yes	—
438	#397	C₂²×C₆₇	1	2	yes	—
439	#397	C₂²×C₆₇	1	2	yes	—
440	#397	C₂²×C₆₇	1	2	yes	—
441	#397	C₂²×C₆₇	1	2	yes	—
442	#397	C₂²×C₆₇	1	2	yes	—
443	#397	C₂²×C₆₇	1	2	yes	—
444	#397	C₂²×C₆₇	1	2	yes	—
445	#396	C₂²×C₆₇	1	2	yes	—
446	#396	C₂²×C₆₇	1	2	yes	—
447	#396	C₂²×C₆₇	1	2	yes	—
448	#396	C₂²×C₆₇	1	2	yes	—
449	#396	C₂²×C₆₇	1	2	yes	—
450	#395	C₂²×C₆₇	1	2	yes	—
451	#395	C₂²×C₆₇	1	2	yes	—
452	#395	C₂²×C₆₇	1	1	yes	characteristic
453	#395	C₂²×C₆₇	1	1	yes	characteristic
454	#395	C₂²×C₆₇	1	2	yes	—
455	#394	C₂²×C₆₇	1	1	yes	characteristic
456	#394	C₂²×C₆₇	1	2	yes	—
457	#394	C₂²×C₆₇	1	2	yes	—
458	#394	C₂²×C₆₇	1	1	yes	characteristic
459	#393	C₂²×C₆₇	1	2	yes	—
460	#393	C₂²×C₆₇	1	2	yes	—
461	#393	C₂²×C₆₇	1	2	yes	—
462	#391	C₂²×C₆₇	1	1	yes	characteristic
463	#391	C₂²×C₆₇	1	1	yes	characteristic
464	#389	C₂²×C₆₇	1	2	yes	—
465	#389	C₂²×C₆₇	1	2	yes	—
466	#388	C₂²×C₆₇	1	2	yes	—
467	#388	C₂²×C₆₇	1	2	yes	—
468	#388	C₂²×C₆₇	1	2	yes	—
469	#387	C₂²×C₆₇	1	2	yes	—
470	#387	C₂²×C₆₇	1	2	yes	—
471	#387	C₂²×C₆₇	1	2	yes	—
472	#384	C₂²×C₆₇	1	1	yes	characteristic
473	#383	C₂²×C₆₇	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
477	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
487	#376	C₂²×C₆₇	1	1	yes	characteristic
488	#376	C₂²×C₆₇	1	1	yes	characteristic
489	C₄³	C₂²×C₆₇	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
495	C₄⋊Q₈	—	2	4	no	—
496	#126	—	2	8	no	—
497	C₄×Q₈	—	4	2	no	—
498	C₄×Q₈	—	4	2	no	—
499	C₄×Q₈	—	4	2	no	—
500	C₄×D₄	—	4	2	no	—
501	#117	—	4	4	no	—
502	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
541	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
548	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
552	#95	C₂³×C₆₇	1	2	yes	—
553	#95	C₂³×C₆₇	1	1	yes	characteristic
554	#95	C₂³×C₆₇	1	1	yes	characteristic
555	#95	C₂³×C₆₇	1	1	yes	characteristic
556	#95	C₂³×C₆₇	1	2	yes	—
557	#95	C₂³×C₆₇	1	1	yes	characteristic
558	#95	C₂³×C₆₇	1	2	yes	—
559	#95	C₂³×C₆₇	1	2	yes	—
560	#95	C₂³×C₆₇	1	2	yes	—
561	#95	C₂³×C₆₇	1	2	yes	—
562	#95	C₂³×C₆₇	1	2	yes	—
563	#95	C₂³×C₆₇	1	2	yes	—
564	#95	C₂³×C₆₇	1	2	yes	—
565	#95	C₂³×C₆₇	1	2	yes	—
566	#95	C₂³×C₆₇	1	2	yes	—
567	#95	C₂³×C₆₇	1	2	yes	—
568	#95	C₂³×C₆₇	1	2	yes	—
569	#95	C₂³×C₆₇	1	2	yes	—
570	#95	C₂³×C₆₇	1	2	yes	—
571	#95	C₂³×C₆₇	1	2	yes	—
572	#95	C₂³×C₆₇	1	2	yes	—
573	#95	C₂³×C₆₇	1	2	yes	—
574	#95	C₂³×C₆₇	1	2	yes	—
575	#95	C₂³×C₆₇	1	2	yes	—
576	#95	C₂³×C₆₇	1	2	yes	—
577	#95	C₂³×C₆₇	1	2	yes	—
578	#95	C₂³×C₆₇	1	2	yes	—
579	#95	C₂³×C₆₇	1	2	yes	—
580	#95	C₂³×C₆₇	1	2	yes	—
581	#95	C₂³×C₆₇	1	2	yes	—
582	#95	C₂³×C₆₇	1	2	yes	—
583	#95	C₂³×C₆₇	1	2	yes	—
584	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	1	no	—
588	C₂×Q₈	—	4	1	no	—
589	C₂×Q₈	—	4	1	no	—
590	C₂×Q₈	—	4	1	no	—
591	C₂×Q₈	—	4	1	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	1	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	1	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	2	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	1	no	—
665	C₄²	#41×C₆₇	1	4	yes	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
674	Q₈	—	4	4	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	4	4	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	4	8	no	—
725	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
726	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
727	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
728	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
737	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
738	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
739	C₂²	#585×C₆₇	1	2	yes	—
740	C₂²	#585×C₆₇	1	1	yes	characteristic
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	#563×C₆₇	1	4	yes	—
759	C₂	—	8	2	no	—
760	C₂	C₆₇×#3460	1	1	yes	characteristic
761	C₂	C₆₇×#3461	1	2	yes	—
762	C₂	C₂×#563×C₆₇	1	1	yes	characteristic
763	C₂	C₆₇×#3529	1	1	yes	characteristic
764	C₂	C₆₇×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2843	C₂	semidirect
2. C₆₇×#2839	C₂	semidirect
3. C₆₇×#2838	C₂	semidirect
5. C₆₇×#2836	C₂	semidirect
6. C₆₇×#2833	C₂	semidirect
8. C₆₇×#2831	C₂	semidirect
10. C₆₇×#2821	C₂	semidirect
11. C₆₇×#2402	C₂	semidirect
12. C₆₇×#2401	C₂	semidirect
13. C₆₇×#2399	C₂	semidirect
15. C₆₇×#2396	C₂	semidirect
16. C₆₇×#2396	C₂	semidirect
18. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
19. C₄×#126×C₆₇	C₂	semidirect
376. #36697	C₆₇	direct (N × H)
383. #2843	C₂×C₆₇	semidirect
384. #2839	C₂×C₆₇	semidirect
385. #2838	C₂×C₆₇	semidirect
387. #2836	C₂×C₆₇	semidirect
388. #2833	C₂×C₆₇	semidirect
390. #2831	C₂×C₆₇	semidirect
392. #2821	C₂×C₆₇	semidirect
393. #2402	C₂×C₆₇	semidirect
394. #2401	C₂×C₆₇	semidirect
395. #2399	C₂×C₆₇	semidirect
397. #2396	C₂×C₆₇	semidirect
398. #2396	C₂×C₆₇	semidirect
400. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
401. C₄×#126	C₂×C₆₇	semidirect
402. C₆₇	#36697	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×#2843	2
C₆₇×#2839	2
C₆₇×#2838	2
C₆₇×#2837	2
C₆₇×#2836	2
C₆₇×#2833	2
C₆₇×#2832	2
C₆₇×#2831	2
C₆₇×#2823	2
C₆₇×#2821	2
C₆₇×#2402	2
C₆₇×#2401	2
C₆₇×#2399	2
C₆₇×#2398	2
C₆₇×#2396	2
C₆₇×#2395	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#126×C₆₇	2
#36697	67

Subgroups — C67×#36697 #30715948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36697 #30715948