Subgroups — C₆₇×#59367 #30738618

Order 17152.

2062 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2771	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2752	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2751	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2600	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2575	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2539	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2516	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2459	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2447	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2357	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×#381×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₆₇	C₂²	1	2	yes	—
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#120×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	2	yes	complemented
33	#400×C₆₇	C₂²	1	2	yes	complemented
34	#400×C₆₇	C₂²	1	2	yes	complemented
35	#399×C₆₇	C₂²	1	1	yes	characteristic
36	#399×C₆₇	C₂²	1	1	yes	characteristic
37	#399×C₆₇	C₂²	1	1	yes	characteristic
38	#399×C₆₇	C₂²	1	1	yes	characteristic
39	#397×C₆₇	C₂²	1	1	yes	characteristic
40	#397×C₆₇	C₂²	1	2	yes	—
41	#397×C₆₇	C₂²	1	1	yes	characteristic
42	#397×C₆₇	C₂²	1	2	yes	complemented
43	#397×C₆₇	C₂²	1	2	yes	complemented
44	#397×C₆₇	C₂²	1	2	yes	complemented
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	complemented
48	#393×C₆₇	C₂²	1	2	yes	—
49	#393×C₆₇	C₂²	1	2	yes	complemented
50	#392×C₆₇	C₂²	1	1	yes	characteristic
51	#392×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#391×C₆₇	C₂²	1	2	yes	complemented
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#390×C₆₇	C₂²	1	2	yes	—
56	#390×C₆₇	C₂²	1	2	yes	—
57	#390×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	complemented
59	#388×C₆₇	C₂²	1	2	yes	—
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	complemented
64	#388×C₆₇	C₂²	1	2	yes	complemented
65	#388×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	complemented
67	#388×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#387×C₆₇	C₂²	1	2	yes	complemented
70	#387×C₆₇	C₂²	1	2	yes	complemented
71	#387×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	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
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	2	yes	complemented
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#382×C₆₇	C₂²	1	2	yes	complemented
87	#381×C₆₇	C₂²	1	1	yes	characteristic
88	#381×C₆₇	C₂²	1	2	yes	—
89	#381×C₆₇	C₂²	1	2	yes	—
90	#381×C₆₇	C₂²	1	1	yes	characteristic
91	#381×C₆₇	C₂²	1	1	yes	characteristic
92	#381×C₆₇	C₂²	1	1	yes	characteristic
93	#381×C₆₇	C₂²	1	1	yes	characteristic
94	#381×C₆₇	C₂²	1	2	yes	complemented
95	#379×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	—	2	4	no	—
114	C₂³×C₄×C₆₇	—	4	2	no	—
115	C₂³×C₄×C₆₇	—	4	2	no	—
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	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	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	#124×C₆₇	—	4	4	no	—
125	#123×C₆₇	—	2	8	no	—
126	C₂²⋊Q₈×C₆₇	—	2	8	no	—
127	#121×C₆₇	—	4	2	no	—
128	#120×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	#117×C₆₇	—	4	2	no	—
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	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
147	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	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×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×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	1	yes	characteristic
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	—	2	2	no	—
209	C₂⁴×C₆₇	—	2	2	no	—
210	C₂⁴×C₆₇	—	2	2	no	—
211	C₂⁴×C₆₇	—	2	4	no	—
212	C₂⁴×C₆₇	—	4	2	no	—
213	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₆₇	—	2	4	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	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	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	2	no	—
229	C₂×D₄×C₆₇	—	4	1	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	4	1	no	—
242	C₂²×C₄×C₆₇	—	4	1	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	1	no	—
246	C₂²×C₄×C₆₇	—	4	1	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	16	no	—
253	C₂²×C₄×C₆₇	#41	1	4	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	4	2	no	—
276	C₄⋊C₄×C₆₇	—	4	2	no	—
277	C₄⋊C₄×C₆₇	—	4	1	no	—
278	C₄⋊C₄×C₆₇	—	4	1	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	4	1	no	—
293	C₂²⋊C₄×C₆₇	—	4	1	no	—
294	C₂²⋊C₄×C₆₇	—	4	1	no	—
295	C₂²⋊C₄×C₆₇	—	4	1	no	—
296	C₂²⋊C₄×C₆₇	—	4	1	no	—
297	C₂²⋊C₄×C₆₇	—	4	1	no	—
298	C₂²⋊C₄×C₆₇	—	4	2	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	2	no	—
301	C₂²⋊C₄×C₆₇	—	4	2	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	4	2	no	—
310	C₄²×C₆₇	—	4	2	no	—
311	C₄²×C₆₇	—	4	2	no	—
312	C₄²×C₆₇	—	4	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	2	no	—
315	C₂³×C₆₇	—	2	1	no	—
316	C₂³×C₆₇	—	2	1	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	8	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	1	no	—
322	C₂³×C₆₇	—	2	1	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	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	—	4	8	no	—
335	C₂³×C₆₇	—	4	8	no	—
336	C₂³×C₆₇	—	4	4	no	—
337	C₂³×C₆₇	—	4	4	no	—
338	C₂³×C₆₇	C₂×#41	1	2	yes	—
339	C₂³×C₆₇	C₂×#41	1	4	yes	—
340	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
341	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
342	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
343	Q₈×C₆₇	—	8	4	no	—
344	D₄×C₆₇	—	4	8	no	—
345	D₄×C₆₇	—	4	8	no	—
346	D₄×C₆₇	—	4	8	no	—
347	D₄×C₆₇	—	8	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	4	4	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	4	4	no	—
391	C₂×C₄×C₆₇	—	8	4	no	—
392	C₂×C₄×C₆₇	—	8	4	no	—
393	C₂×C₄×C₆₇	—	8	2	no	—
394	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
395	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
396	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	4	no	—
400	C₂²×C₆₇	—	2	2	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	2	4	no	—
405	C₂²×C₆₇	—	4	16	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	#559	1	4	yes	—
420	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
421	C₂²×C₆₇	C₂²×#41	1	2	yes	—
422	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₆₇	#585	1	2	yes	—
425	C₄×C₆₇	—	2	4	no	—
426	C₄×C₆₇	—	2	4	no	—
427	C₄×C₆₇	—	2	4	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	1	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	2	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	1	no	—
440	#59367	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₆₇	—	2	4	no	—
442	C₂×C₆₇	—	4	2	no	—
443	C₂×C₆₇	—	4	2	no	—
444	C₂×C₆₇	—	8	2	no	—
445	C₂×C₆₇	#3475	1	2	yes	—
446	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
447	C₂×C₆₇	#3490	1	1	yes	characteristic
448	C₂×C₆₇	#3513	1	2	yes	—
449	C₂×C₆₇	#3533	1	1	yes	characteristic
450	#2771	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#2752	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2751	C₂×C₆₇	1	2	yes	complemented
453	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#2600	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2575	C₂×C₆₇	1	2	yes	complemented
456	#2539	C₂×C₆₇	1	1	yes	characteristic
457	#2516	C₂×C₆₇	1	2	yes	complemented
458	#2488	C₂×C₆₇	1	2	yes	complemented
459	#2482	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#2472	C₂×C₆₇	1	2	yes	complemented
461	#2459	C₂×C₆₇	1	2	yes	complemented
462	#2447	C₂×C₆₇	1	2	yes	complemented
463	#2444	C₂×C₆₇	1	2	yes	complemented
464	#2368	C₂×C₆₇	1	2	yes	complemented
465	#2359	C₂×C₆₇	1	2	yes	complemented
466	#2357	C₂×C₆₇	1	2	yes	complemented
467	C₄×#120	C₂×C₆₇	1	2	yes	complemented
468	C₂×#381	C₂×C₆₇	1	1	yes	characteristic, complemented
469	C₆₇	#59367	1	1	yes	characteristic, direct product factor, Sylow
470	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#124	C₂²×C₆₇	1	2	yes	—
472	C₂×#123	C₂²×C₆₇	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
474	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#120	C₂²×C₆₇	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
478	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
479	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
482	#400	C₂²×C₆₇	1	2	yes	complemented
483	#400	C₂²×C₆₇	1	2	yes	complemented
484	#400	C₂²×C₆₇	1	2	yes	complemented
485	#399	C₂²×C₆₇	1	1	yes	characteristic
486	#399	C₂²×C₆₇	1	1	yes	characteristic
487	#399	C₂²×C₆₇	1	1	yes	characteristic
488	#399	C₂²×C₆₇	1	1	yes	characteristic
489	#397	C₂²×C₆₇	1	2	yes	—
490	#397	C₂²×C₆₇	1	1	yes	characteristic
491	#397	C₂²×C₆₇	1	1	yes	characteristic
492	#397	C₂²×C₆₇	1	2	yes	complemented
493	#397	C₂²×C₆₇	1	2	yes	complemented
494	#397	C₂²×C₆₇	1	2	yes	complemented
495	#394	C₂²×C₆₇	1	2	yes	—
496	#394	C₂²×C₆₇	1	2	yes	—
497	#394	C₂²×C₆₇	1	2	yes	complemented
498	#393	C₂²×C₆₇	1	2	yes	—
499	#393	C₂²×C₆₇	1	2	yes	complemented
500	#392	C₂²×C₆₇	1	1	yes	characteristic
501	#392	C₂²×C₆₇	1	1	yes	characteristic
502	#391	C₂²×C₆₇	1	2	yes	complemented
503	#391	C₂²×C₆₇	1	2	yes	complemented
504	#391	C₂²×C₆₇	1	2	yes	complemented
505	#390	C₂²×C₆₇	1	2	yes	—
506	#390	C₂²×C₆₇	1	2	yes	—
507	#390	C₂²×C₆₇	1	2	yes	—
508	#389	C₂²×C₆₇	1	2	yes	complemented
509	#388	C₂²×C₆₇	1	2	yes	—
510	#388	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#388	C₂²×C₆₇	1	2	yes	—
513	#388	C₂²×C₆₇	1	2	yes	complemented
514	#388	C₂²×C₆₇	1	2	yes	complemented
515	#388	C₂²×C₆₇	1	2	yes	complemented
516	#388	C₂²×C₆₇	1	2	yes	complemented
517	#388	C₂²×C₆₇	1	2	yes	complemented
518	#387	C₂²×C₆₇	1	2	yes	complemented
519	#387	C₂²×C₆₇	1	2	yes	complemented
520	#387	C₂²×C₆₇	1	2	yes	complemented
521	#387	C₂²×C₆₇	1	2	yes	complemented
522	#387	C₂²×C₆₇	1	2	yes	complemented
523	#387	C₂²×C₆₇	1	2	yes	complemented
524	#387	C₂²×C₆₇	1	2	yes	complemented
525	#386	C₂²×C₆₇	1	2	yes	—
526	#386	C₂²×C₆₇	1	2	yes	—
527	#386	C₂²×C₆₇	1	2	yes	—
528	#386	C₂²×C₆₇	1	2	yes	—
529	#386	C₂²×C₆₇	1	2	yes	—
530	#386	C₂²×C₆₇	1	2	yes	complemented
531	#385	C₂²×C₆₇	1	2	yes	—
532	#385	C₂²×C₆₇	1	2	yes	—
533	#385	C₂²×C₆₇	1	2	yes	—
534	#385	C₂²×C₆₇	1	2	yes	—
535	#385	C₂²×C₆₇	1	2	yes	complemented
536	#382	C₂²×C₆₇	1	2	yes	complemented
537	#381	C₂²×C₆₇	1	2	yes	—
538	#381	C₂²×C₆₇	1	1	yes	characteristic
539	#381	C₂²×C₆₇	1	1	yes	characteristic
540	#381	C₂²×C₆₇	1	2	yes	—
541	#381	C₂²×C₆₇	1	1	yes	characteristic
542	#381	C₂²×C₆₇	1	1	yes	characteristic
543	#381	C₂²×C₆₇	1	1	yes	characteristic
544	#381	C₂²×C₆₇	1	2	yes	complemented
545	#379	C₂²×C₆₇	1	2	yes	—
546	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
547	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
548	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
551	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
553	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
555	C₂×#95	C₂²×C₆₇	1	2	yes	—
556	C₂×#95	C₂²×C₆₇	1	2	yes	—
557	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
558	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
559	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
560	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
561	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
562	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂³×C₄	—	2	4	no	—
564	C₂³×C₄	—	4	2	no	—
565	C₂³×C₄	—	4	2	no	—
566	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
568	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
569	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
571	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
572	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
574	#124	—	4	4	no	—
575	#123	—	2	8	no	—
576	C₂²⋊Q₈	—	2	8	no	—
577	#121	—	4	2	no	—
578	#120	—	2	8	no	—
579	C₄×D₄	—	2	8	no	—
580	C₄×D₄	—	4	4	no	—
581	C₄×D₄	—	4	4	no	—
582	#117	—	4	2	no	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	—	4	2	no	—
597	C₂×C₂²⋊C₄	—	4	2	no	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	1	yes	characteristic
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	1	yes	characteristic
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	1	yes	characteristic
653	#95	C₂³×C₆₇	1	1	yes	characteristic
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	C₂⁴	—	2	2	no	—
659	C₂⁴	—	2	2	no	—
660	C₂⁴	—	2	2	no	—
661	C₂⁴	—	2	4	no	—
662	C₂⁴	—	4	2	no	—
663	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
664	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
665	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
666	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	4	1	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	4	1	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	1	no	—
696	C₂²×C₄	—	4	1	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	16	no	—
703	C₂²×C₄	#41×C₆₇	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₂²⋊C₄	—	4	1	no	—
744	C₂²⋊C₄	—	4	1	no	—
745	C₂²⋊C₄	—	4	1	no	—
746	C₂²⋊C₄	—	4	1	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
758	C₄²	—	2	4	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	2	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	4	8	no	—
785	C₂³	—	4	8	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	4	4	no	—
788	C₂³	C₂×#41×C₆₇	1	2	yes	—
789	C₂³	C₂×#41×C₆₇	1	4	yes	—
790	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
791	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
792	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
793	Q₈	—	8	4	no	—
794	D₄	—	4	8	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	8	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	4	no	—
844	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
845	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
846	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	4	16	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	#559×C₆₇	1	4	yes	—
870	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
871	C₂²	C₂²×#41×C₆₇	1	2	yes	—
872	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
873	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
874	C₂²	#585×C₆₇	1	2	yes	—
875	C₄	—	2	4	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	4	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₂	—	2	4	no	—
891	C₂	—	4	2	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	2	no	—
894	C₂	C₆₇×#3475	1	2	yes	—
895	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
896	C₂	C₆₇×#3490	1	1	yes	characteristic
897	C₂	C₆₇×#3513	1	2	yes	—
898	C₂	C₆₇×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2539	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×#2771	C₂	semidirect
2. C₆₇×#2752	C₂	semidirect
3. C₆₇×#2751	C₂	semidirect
4. C₆₇×#2607	C₂	semidirect
5. C₆₇×#2600	C₂	semidirect
6. C₆₇×#2575	C₂	semidirect
8. C₆₇×#2516	C₂	semidirect
9. C₆₇×#2488	C₂	semidirect
10. C₆₇×#2482	C₂	semidirect
11. C₆₇×#2472	C₂	semidirect
12. C₆₇×#2459	C₂	semidirect
13. C₆₇×#2447	C₂	semidirect
14. C₆₇×#2444	C₂	semidirect
15. C₆₇×#2368	C₂	semidirect
16. C₆₇×#2359	C₂	semidirect
17. C₆₇×#2357	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#381×C₆₇	C₂	semidirect
32. #400×C₆₇	C₂²	semidirect
33. #400×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
42. #397×C₆₇	C₂²	semidirect
43. #397×C₆₇	C₂²	semidirect
44. #397×C₆₇	C₂²	semidirect
47. #394×C₆₇	C₂²	semidirect
49. #393×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
53. #391×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
58. #389×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #388×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #388×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
70. #387×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #382×C₆₇	C₂²	semidirect
94. #381×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
440. #59367	C₆₇	direct (N × H)
450. #2771	C₂×C₆₇	semidirect
451. #2752	C₂×C₆₇	semidirect
452. #2751	C₂×C₆₇	semidirect
453. #2607	C₂×C₆₇	semidirect
454. #2600	C₂×C₆₇	semidirect
455. #2575	C₂×C₆₇	semidirect
457. #2516	C₂×C₆₇	semidirect
458. #2488	C₂×C₆₇	semidirect
459. #2482	C₂×C₆₇	semidirect
460. #2472	C₂×C₆₇	semidirect
461. #2459	C₂×C₆₇	semidirect
462. #2447	C₂×C₆₇	semidirect
463. #2444	C₂×C₆₇	semidirect
464. #2368	C₂×C₆₇	semidirect
465. #2359	C₂×C₆₇	semidirect
466. #2357	C₂×C₆₇	semidirect
467. C₄×#120	C₂×C₆₇	semidirect
468. C₂×#381	C₂×C₆₇	semidirect
469. C₆₇	#59367	direct (N × H)
482. #400	C₂²×C₆₇	semidirect
483. #400	C₂²×C₆₇	semidirect
484. #400	C₂²×C₆₇	semidirect
492. #397	C₂²×C₆₇	semidirect
493. #397	C₂²×C₆₇	semidirect
494. #397	C₂²×C₆₇	semidirect
497. #394	C₂²×C₆₇	semidirect
499. #393	C₂²×C₆₇	semidirect
502. #391	C₂²×C₆₇	semidirect
503. #391	C₂²×C₆₇	semidirect
504. #391	C₂²×C₆₇	semidirect
508. #389	C₂²×C₆₇	semidirect
513. #388	C₂²×C₆₇	semidirect
514. #388	C₂²×C₆₇	semidirect
515. #388	C₂²×C₆₇	semidirect
516. #388	C₂²×C₆₇	semidirect
517. #388	C₂²×C₆₇	semidirect
518. #387	C₂²×C₆₇	semidirect
519. #387	C₂²×C₆₇	semidirect
520. #387	C₂²×C₆₇	semidirect
521. #387	C₂²×C₆₇	semidirect
522. #387	C₂²×C₆₇	semidirect
523. #387	C₂²×C₆₇	semidirect
524. #387	C₂²×C₆₇	semidirect
530. #386	C₂²×C₆₇	semidirect
535. #385	C₂²×C₆₇	semidirect
536. #382	C₂²×C₆₇	semidirect
544. #381	C₂²×C₆₇	semidirect
546. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
547. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
548. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
554. C₄×C₂²⋊C₄	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×#2771	2
C₆₇×#2752	2
C₆₇×#2751	2
C₆₇×#2607	2
C₆₇×#2600	2
C₆₇×#2575	2
C₆₇×#2539	2
C₆₇×#2516	2
C₆₇×#2488	2
C₆₇×#2482	2
C₆₇×#2472	2
C₆₇×#2459	2
C₆₇×#2447	2
C₆₇×#2444	2
C₆₇×#2368	2
C₆₇×#2359	2
C₆₇×#2357	2
C₄×#120×C₆₇	2
C₂×#381×C₆₇	2
#59367	67

Subgroups — C67×#59367 #30738618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59367 #30738618