Subgroups — C₆₇×#36693 #30715944

Order 17152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2839	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2838	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2838	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2837	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2832	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2831	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2830	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2829	C₂	1	2	yes	maximal
9	C₆₇×#2401	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2398	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2398	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2392	C₂	1	1	yes	maximal, characteristic
17	C₆₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
24	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₇	C₂²	1	2	yes	—
26	#401×C₆₇	C₂²	1	2	yes	—
27	#400×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	1	yes	characteristic
34	#400×C₆₇	C₂²	1	2	yes	—
35	#400×C₆₇	C₂²	1	2	yes	—
36	#399×C₆₇	C₂²	1	2	yes	—
37	#399×C₆₇	C₂²	1	1	yes	characteristic
38	#399×C₆₇	C₂²	1	2	yes	—
39	#398×C₆₇	C₂²	1	2	yes	—
40	#398×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	#398×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	1	yes	characteristic
46	#397×C₆₇	C₂²	1	2	yes	—
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#397×C₆₇	C₂²	1	2	yes	—
51	#397×C₆₇	C₂²	1	2	yes	—
52	#397×C₆₇	C₂²	1	2	yes	—
53	#397×C₆₇	C₂²	1	2	yes	—
54	#397×C₆₇	C₂²	1	2	yes	—
55	#397×C₆₇	C₂²	1	1	yes	characteristic
56	#396×C₆₇	C₂²	1	2	yes	—
57	#396×C₆₇	C₂²	1	2	yes	—
58	#396×C₆₇	C₂²	1	2	yes	—
59	#396×C₆₇	C₂²	1	2	yes	—
60	#396×C₆₇	C₂²	1	2	yes	—
61	#395×C₆₇	C₂²	1	2	yes	—
62	#395×C₆₇	C₂²	1	1	yes	characteristic
63	#395×C₆₇	C₂²	1	2	yes	—
64	#395×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#394×C₆₇	C₂²	1	2	yes	—
68	#394×C₆₇	C₂²	1	2	yes	—
69	#394×C₆₇	C₂²	1	2	yes	—
70	#394×C₆₇	C₂²	1	1	yes	characteristic
71	#394×C₆₇	C₂²	1	2	yes	—
72	#393×C₆₇	C₂²	1	2	yes	—
73	#393×C₆₇	C₂²	1	2	yes	—
74	#393×C₆₇	C₂²	1	2	yes	—
75	#393×C₆₇	C₂²	1	1	yes	characteristic
76	#393×C₆₇	C₂²	1	2	yes	—
77	#392×C₆₇	C₂²	1	1	yes	characteristic
78	#391×C₆₇	C₂²	1	2	yes	—
79	#390×C₆₇	C₂²	1	2	yes	—
80	#389×C₆₇	C₂²	1	2	yes	—
81	#389×C₆₇	C₂²	1	2	yes	—
82	#388×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	#387×C₆₇	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₄×Q₈×C₆₇	—	2	4	no	—
114	C₄×Q₈×C₆₇	—	4	4	no	—
115	C₄×D₄×C₆₇	—	2	4	no	—
116	C₄×D₄×C₆₇	—	4	4	no	—
117	#117×C₆₇	—	2	4	no	—
118	#117×C₆₇	—	4	4	no	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊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×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
170	#95×C₆₇	C₂³	1	2	yes	—
171	#95×C₆₇	C₂³	1	2	yes	—
172	#95×C₆₇	C₂³	1	2	yes	—
173	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
189	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
201	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₆₇	—	2	2	no	—
203	C₂×Q₈×C₆₇	—	4	2	no	—
204	C₂×Q₈×C₆₇	—	4	2	no	—
205	C₂×Q₈×C₆₇	—	4	2	no	—
206	C₂×Q₈×C₆₇	—	4	2	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	4	2	no	—
209	C₂×D₄×C₆₇	—	4	2	no	—
210	C₂×D₄×C₆₇	—	4	2	no	—
211	C₂×D₄×C₆₇	—	4	2	no	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	2	yes	—
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	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	2	no	—
238	C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₄⋊C₄×C₆₇	—	2	4	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	2	no	—
252	C₄⋊C₄×C₆₇	—	4	2	no	—
253	C₄⋊C₄×C₆₇	—	4	2	no	—
254	C₄⋊C₄×C₆₇	—	4	2	no	—
255	C₄⋊C₄×C₆₇	—	4	2	no	—
256	C₂²⋊C₄×C₆₇	—	2	2	no	—
257	C₂²⋊C₄×C₆₇	—	2	2	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	4	2	no	—
260	C₂²⋊C₄×C₆₇	—	4	2	no	—
261	C₂²⋊C₄×C₆₇	—	4	2	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	C₂²⋊C₄×C₆₇	—	4	2	no	—
273	C₂²⋊C₄×C₆₇	—	4	2	no	—
274	C₂²⋊C₄×C₆₇	—	4	2	no	—
275	C₄²×C₆₇	—	2	2	no	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	2	2	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	—	2	4	no	—
280	C₄²×C₆₇	—	2	2	no	—
281	C₄²×C₆₇	—	2	2	no	—
282	C₄²×C₆₇	—	2	2	no	—
283	C₄²×C₆₇	—	4	2	no	—
284	C₄²×C₆₇	—	4	2	no	—
285	C₄²×C₆₇	#41	1	4	yes	—
286	C₂³×C₆₇	—	2	1	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	1	no	—
290	C₂³×C₆₇	—	2	1	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	2	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
299	Q₈×C₆₇	—	4	4	no	—
300	Q₈×C₆₇	—	4	8	no	—
301	D₄×C₆₇	—	4	4	no	—
302	D₄×C₆₇	—	4	8	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	1	no	—
306	C₂×C₄×C₆₇	—	2	1	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	2	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	2	2	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	1	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	1	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	2	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	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	4	4	no	—
346	C₂×C₄×C₆₇	—	4	8	no	—
347	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
348	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
349	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
351	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
352	C₂²×C₆₇	—	4	1	no	—
353	C₂²×C₆₇	—	4	2	no	—
354	C₂²×C₆₇	—	4	2	no	—
355	C₂²×C₆₇	—	4	1	no	—
356	C₂²×C₆₇	—	4	1	no	—
357	C₂²×C₆₇	—	4	2	no	—
358	C₂²×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	4	2	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂²×C₆₇	#585	1	2	yes	—
368	C₂²×C₆₇	#585	1	2	yes	—
369	C₄×C₆₇	—	2	2	no	—
370	C₄×C₆₇	—	2	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	1	no	—
373	C₄×C₆₇	—	4	1	no	—
374	C₄×C₆₇	—	4	1	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	—	4	2	no	—
385	C₄×C₆₇	#542	1	4	yes	—
386	#36693	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂×C₆₇	—	8	2	no	—
388	C₂×C₆₇	—	8	1	no	—
389	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
390	C₂×C₆₇	#3455	1	1	yes	characteristic
391	C₂×C₆₇	#3455	1	1	yes	characteristic
392	C₂×C₆₇	#3529	1	2	yes	—
393	C₂×C₆₇	#3531	1	2	yes	—
394	#2839	C₂×C₆₇	1	2	yes	complemented
395	#2838	C₂×C₆₇	1	2	yes	complemented
396	#2838	C₂×C₆₇	1	2	yes	complemented
397	#2837	C₂×C₆₇	1	2	yes	complemented
398	#2832	C₂×C₆₇	1	2	yes	complemented
399	#2831	C₂×C₆₇	1	2	yes	complemented
400	#2830	C₂×C₆₇	1	2	yes	complemented
401	#2829	C₂×C₆₇	1	2	yes	—
402	#2401	C₂×C₆₇	1	2	yes	complemented
403	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#2398	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#2398	C₂×C₆₇	1	2	yes	complemented
406	#2396	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#2396	C₂×C₆₇	1	2	yes	complemented
408	#2395	C₂×C₆₇	1	2	yes	complemented
409	#2392	C₂×C₆₇	1	1	yes	characteristic
410	#2298	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
413	C₆₇	#36693	1	1	yes	characteristic, direct product factor, Sylow
414	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
418	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#117	C₂²×C₆₇	1	2	yes	—
420	#401	C₂²×C₆₇	1	2	yes	—
421	#400	C₂²×C₆₇	1	2	yes	—
422	#400	C₂²×C₆₇	1	2	yes	—
423	#400	C₂²×C₆₇	1	2	yes	—
424	#400	C₂²×C₆₇	1	2	yes	—
425	#400	C₂²×C₆₇	1	2	yes	—
426	#400	C₂²×C₆₇	1	2	yes	—
427	#400	C₂²×C₆₇	1	1	yes	characteristic
428	#400	C₂²×C₆₇	1	2	yes	—
429	#400	C₂²×C₆₇	1	2	yes	—
430	#399	C₂²×C₆₇	1	2	yes	—
431	#399	C₂²×C₆₇	1	1	yes	characteristic
432	#399	C₂²×C₆₇	1	2	yes	—
433	#398	C₂²×C₆₇	1	2	yes	—
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	#398	C₂²×C₆₇	1	2	yes	—
439	#398	C₂²×C₆₇	1	1	yes	characteristic
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	#397	C₂²×C₆₇	1	2	yes	—
446	#397	C₂²×C₆₇	1	2	yes	—
447	#397	C₂²×C₆₇	1	2	yes	—
448	#397	C₂²×C₆₇	1	2	yes	—
449	#397	C₂²×C₆₇	1	1	yes	characteristic
450	#396	C₂²×C₆₇	1	2	yes	—
451	#396	C₂²×C₆₇	1	2	yes	—
452	#396	C₂²×C₆₇	1	2	yes	—
453	#396	C₂²×C₆₇	1	2	yes	—
454	#396	C₂²×C₆₇	1	2	yes	—
455	#395	C₂²×C₆₇	1	2	yes	—
456	#395	C₂²×C₆₇	1	1	yes	characteristic
457	#395	C₂²×C₆₇	1	2	yes	—
458	#395	C₂²×C₆₇	1	2	yes	—
459	#394	C₂²×C₆₇	1	2	yes	—
460	#394	C₂²×C₆₇	1	2	yes	—
461	#394	C₂²×C₆₇	1	2	yes	—
462	#394	C₂²×C₆₇	1	2	yes	—
463	#394	C₂²×C₆₇	1	2	yes	—
464	#394	C₂²×C₆₇	1	1	yes	characteristic
465	#394	C₂²×C₆₇	1	2	yes	—
466	#393	C₂²×C₆₇	1	2	yes	—
467	#393	C₂²×C₆₇	1	2	yes	—
468	#393	C₂²×C₆₇	1	2	yes	—
469	#393	C₂²×C₆₇	1	1	yes	characteristic
470	#393	C₂²×C₆₇	1	2	yes	—
471	#392	C₂²×C₆₇	1	1	yes	characteristic
472	#391	C₂²×C₆₇	1	2	yes	—
473	#390	C₂²×C₆₇	1	2	yes	—
474	#389	C₂²×C₆₇	1	2	yes	—
475	#389	C₂²×C₆₇	1	2	yes	—
476	#388	C₂²×C₆₇	1	2	yes	—
477	#388	C₂²×C₆₇	1	2	yes	—
478	#388	C₂²×C₆₇	1	2	yes	—
479	#388	C₂²×C₆₇	1	2	yes	—
480	#387	C₂²×C₆₇	1	2	yes	—
481	#387	C₂²×C₆₇	1	2	yes	—
482	#387	C₂²×C₆₇	1	2	yes	—
483	#387	C₂²×C₆₇	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
491	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
493	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
494	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
495	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
497	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
498	#376	C₂²×C₆₇	1	1	yes	characteristic
499	#376	C₂²×C₆₇	1	2	yes	—
500	C₄³	C₂²×C₆₇	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
503	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
505	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
507	C₄×Q₈	—	2	4	no	—
508	C₄×Q₈	—	4	4	no	—
509	C₄×D₄	—	2	4	no	—
510	C₄×D₄	—	4	4	no	—
511	#117	—	2	4	no	—
512	#117	—	4	4	no	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
553	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
555	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
557	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
559	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
562	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
563	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
583	#95	C₂³×C₆₇	1	1	yes	characteristic
584	#95	C₂³×C₆₇	1	2	yes	—
585	#95	C₂³×C₆₇	1	2	yes	—
586	#95	C₂³×C₆₇	1	2	yes	—
587	#95	C₂³×C₆₇	1	2	yes	—
588	#95	C₂³×C₆₇	1	1	yes	characteristic
589	#95	C₂³×C₆₇	1	1	yes	characteristic
590	#95	C₂³×C₆₇	1	2	yes	—
591	#95	C₂³×C₆₇	1	2	yes	—
592	#95	C₂³×C₆₇	1	2	yes	—
593	#95	C₂³×C₆₇	1	2	yes	—
594	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
595	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
596	C₂×Q₈	—	2	2	no	—
597	C₂×Q₈	—	4	2	no	—
598	C₂×Q₈	—	4	2	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×Q₈	—	4	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	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	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	#41×C₆₇	1	4	yes	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
693	Q₈	—	4	4	no	—
694	Q₈	—	4	8	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	8	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	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	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	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	1	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	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
742	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
743	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
744	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
745	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
759	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
760	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
761	C₂²	#585×C₆₇	1	2	yes	—
762	C₂²	#585×C₆₇	1	2	yes	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	2	no	—
779	C₄	#542×C₆₇	1	4	yes	—
780	C₂	—	8	1	no	—
781	C₂	—	8	2	no	—
782	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
783	C₂	C₆₇×#3455	1	1	yes	characteristic
784	C₂	C₆₇×#3455	1	1	yes	characteristic
785	C₂	C₆₇×#3529	1	2	yes	—
786	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	#392×C₆₇	C₂²
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×#2839	C₂	semidirect
2. C₆₇×#2838	C₂	semidirect
3. C₆₇×#2838	C₂	semidirect
4. C₆₇×#2837	C₂	semidirect
5. C₆₇×#2832	C₂	semidirect
6. C₆₇×#2831	C₂	semidirect
7. C₆₇×#2830	C₂	semidirect
9. C₆₇×#2401	C₂	semidirect
10. C₆₇×#2399	C₂	semidirect
11. C₆₇×#2398	C₂	semidirect
12. C₆₇×#2398	C₂	semidirect
13. C₆₇×#2396	C₂	semidirect
14. C₆₇×#2396	C₂	semidirect
15. C₆₇×#2395	C₂	semidirect
17. C₆₇×#2298	C₂	semidirect
18. C₆₇×#2295	C₂	semidirect
19. C₆₇×#2293	C₂	semidirect
386. #36693	C₆₇	direct (N × H)
394. #2839	C₂×C₆₇	semidirect
395. #2838	C₂×C₆₇	semidirect
396. #2838	C₂×C₆₇	semidirect
397. #2837	C₂×C₆₇	semidirect
398. #2832	C₂×C₆₇	semidirect
399. #2831	C₂×C₆₇	semidirect
400. #2830	C₂×C₆₇	semidirect
402. #2401	C₂×C₆₇	semidirect
403. #2399	C₂×C₆₇	semidirect
404. #2398	C₂×C₆₇	semidirect
405. #2398	C₂×C₆₇	semidirect
406. #2396	C₂×C₆₇	semidirect
407. #2396	C₂×C₆₇	semidirect
408. #2395	C₂×C₆₇	semidirect
410. #2298	C₂×C₆₇	semidirect
411. #2295	C₂×C₆₇	semidirect
412. #2293	C₂×C₆₇	semidirect
413. C₆₇	#36693	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×#2839	2
C₆₇×#2838	2
C₆₇×#2837	2
C₆₇×#2832	2
C₆₇×#2831	2
C₆₇×#2830	2
C₆₇×#2829	2
C₆₇×#2401	2
C₆₇×#2399	2
C₆₇×#2398	2
C₆₇×#2396	2
C₆₇×#2395	2
C₆₇×#2392	2
C₆₇×#2298	2
C₆₇×#2295	2
C₆₇×#2293	2
#36693	67

Subgroups — C67×#36693 #30715944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36693 #30715944