Subgroups — C₆₇×#34970 #30714221

Order 17152.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2531	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2526	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2428	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2395	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#125×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
21	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#123×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	2	yes	—
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
43	#400×C₆₇	C₂²	1	2	yes	—
44	#399×C₆₇	C₂²	1	2	yes	—
45	#398×C₆₇	C₂²	1	2	yes	—
46	#398×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	#396×C₆₇	C₂²	1	2	yes	—
52	#396×C₆₇	C₂²	1	2	yes	—
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	—
56	#394×C₆₇	C₂²	1	2	yes	—
57	#394×C₆₇	C₂²	1	2	yes	—
58	#392×C₆₇	C₂²	1	2	yes	—
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	2	yes	—
63	#390×C₆₇	C₂²	1	2	yes	—
64	#390×C₆₇	C₂²	1	1	yes	characteristic
65	#390×C₆₇	C₂²	1	1	yes	characteristic
66	#390×C₆₇	C₂²	1	2	yes	—
67	#390×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×C₆₇	C₂²	1	2	yes	—
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#388×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×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	#386×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	#386×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#384×C₆₇	C₂²	1	1	yes	characteristic
94	#382×C₆₇	C₂²	1	1	yes	characteristic
95	#381×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	1	yes	characteristic
97	#380×C₆₇	C₂²	1	1	yes	characteristic
98	#380×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	#376×C₆₇	C₂²	1	1	yes	characteristic
120	#376×C₆₇	C₂²	1	1	yes	characteristic
121	C₄³×C₆₇	C₂²	1	1	yes	characteristic
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	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	#127×C₆₇	—	2	4	no	—
137	#125×C₆₇	—	2	4	no	—
138	#123×C₆₇	—	2	8	no	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	2	8	no	—
142	C₄×D₄×C₆₇	—	2	4	no	—
143	C₄×D₄×C₆₇	—	2	4	no	—
144	C₄×D₄×C₆₇	—	2	4	no	—
145	C₄×D₄×C₆₇	—	2	4	no	—
146	C₄×D₄×C₆₇	—	4	4	no	—
147	C₄×D₄×C₆₇	—	4	4	no	—
148	C₄×D₄×C₆₇	—	4	4	no	—
149	C₄×D₄×C₆₇	—	4	4	no	—
150	#117×C₆₇	—	2	4	no	—
151	#117×C₆₇	—	2	4	no	—
152	#117×C₆₇	—	4	4	no	—
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	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	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₆₇	—	2	4	no	—
198	C₂×C₄²×C₆₇	—	4	4	no	—
199	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	1	yes	characteristic
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
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	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
242	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	4	2	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	#41	1	4	yes	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	4	no	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	4	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	4	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	4	no	—
312	C₄⋊C₄×C₆₇	—	2	4	no	—
313	C₄⋊C₄×C₆₇	—	2	4	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	4	2	no	—
316	C₄⋊C₄×C₆₇	—	4	2	no	—
317	C₄⋊C₄×C₆₇	—	4	2	no	—
318	C₄⋊C₄×C₆₇	—	4	2	no	—
319	C₄⋊C₄×C₆₇	—	4	2	no	—
320	C₄⋊C₄×C₆₇	—	4	2	no	—
321	C₄⋊C₄×C₆₇	#41	1	4	yes	—
322	C₄⋊C₄×C₆₇	#41	1	4	yes	—
323	C₂²⋊C₄×C₆₇	—	2	2	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	2	no	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	—	2	4	no	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	—	4	2	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	4	2	no	—
344	C₂²⋊C₄×C₆₇	—	4	2	no	—
345	C₂²⋊C₄×C₆₇	—	4	2	no	—
346	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	2	2	no	—
349	C₄²×C₆₇	—	2	2	no	—
350	C₄²×C₆₇	—	2	2	no	—
351	C₄²×C₆₇	—	2	2	no	—
352	C₄²×C₆₇	—	2	2	no	—
353	C₄²×C₆₇	—	2	2	no	—
354	C₄²×C₆₇	—	2	2	no	—
355	C₄²×C₆₇	—	2	2	no	—
356	C₄²×C₆₇	—	2	2	no	—
357	C₄²×C₆₇	—	2	2	no	—
358	C₄²×C₆₇	—	2	2	no	—
359	C₄²×C₆₇	—	2	4	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	2	4	no	—
362	C₄²×C₆₇	—	2	2	no	—
363	C₄²×C₆₇	—	2	2	no	—
364	C₄²×C₆₇	—	4	2	no	—
365	C₄²×C₆₇	—	4	2	no	—
366	C₄²×C₆₇	#41	1	4	yes	—
367	C₂³×C₆₇	—	2	1	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	2	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	C₂×#41	1	4	yes	—
387	C₂³×C₆₇	C₂×#41	1	2	yes	—
388	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
389	D₄×C₆₇	—	2	8	no	—
390	D₄×C₆₇	—	4	8	no	—
391	D₄×C₆₇	—	4	8	no	—
392	D₄×C₆₇	—	4	8	no	—
393	D₄×C₆₇	—	4	8	no	—
394	D₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	2	8	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	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	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	4	8	no	—
444	C₂×C₄×C₆₇	—	4	8	no	—
445	C₂×C₄×C₆₇	—	4	4	no	—
446	C₂×C₄×C₆₇	—	4	4	no	—
447	C₂×C₄×C₆₇	—	4	8	no	—
448	C₂×C₄×C₆₇	—	4	8	no	—
449	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
450	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
451	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
452	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
453	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
454	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
455	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
456	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
457	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
458	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
459	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
460	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
461	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
462	C₂²×C₆₇	—	2	4	no	—
463	C₂²×C₆₇	—	2	2	no	—
464	C₂²×C₆₇	—	2	4	no	—
465	C₂²×C₆₇	—	2	2	no	—
466	C₂²×C₆₇	—	2	4	no	—
467	C₂²×C₆₇	—	2	2	no	—
468	C₂²×C₆₇	—	4	1	no	—
469	C₂²×C₆₇	—	4	2	no	—
470	C₂²×C₆₇	—	4	2	no	—
471	C₂²×C₆₇	—	4	1	no	—
472	C₂²×C₆₇	—	4	2	no	—
473	C₂²×C₆₇	—	4	1	no	—
474	C₂²×C₆₇	—	4	1	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	—	4	2	no	—
477	C₂²×C₆₇	—	4	2	no	—
478	C₂²×C₆₇	—	4	2	no	—
479	C₂²×C₆₇	—	4	2	no	—
480	C₂²×C₆₇	—	4	2	no	—
481	C₂²×C₆₇	—	4	2	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
485	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
486	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
487	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
488	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₄×C₆₇	—	2	2	no	—
491	C₄×C₆₇	—	2	2	no	—
492	C₄×C₆₇	—	2	2	no	—
493	C₄×C₆₇	—	2	2	no	—
494	C₄×C₆₇	—	2	4	no	—
495	C₄×C₆₇	—	2	2	no	—
496	C₄×C₆₇	—	2	2	no	—
497	C₄×C₆₇	—	4	1	no	—
498	C₄×C₆₇	—	4	1	no	—
499	C₄×C₆₇	—	4	2	no	—
500	C₄×C₆₇	—	4	2	no	—
501	C₄×C₆₇	—	4	1	no	—
502	C₄×C₆₇	—	4	1	no	—
503	C₄×C₆₇	—	4	2	no	—
504	C₄×C₆₇	—	4	2	no	—
505	C₄×C₆₇	—	4	1	no	—
506	C₄×C₆₇	—	4	1	no	—
507	C₄×C₆₇	—	4	2	no	—
508	C₄×C₆₇	#529	1	4	yes	—
509	C₄×C₆₇	#540	1	4	yes	—
510	#34970	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂×C₆₇	—	4	4	no	—
512	C₂×C₆₇	—	4	2	no	—
513	C₂×C₆₇	—	8	2	no	—
514	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
515	C₂×C₆₇	#3444	1	1	yes	characteristic
516	C₂×C₆₇	C₂×#540	1	1	yes	characteristic
517	C₂×C₆₇	#3481	1	1	yes	characteristic
518	C₂×C₆₇	#3481	1	1	yes	characteristic
519	C₂×C₆₇	#3481	1	1	yes	characteristic
520	C₂×C₆₇	#3483	1	1	yes	characteristic
521	#2531	C₂×C₆₇	1	2	yes	complemented
522	#2526	C₂×C₆₇	1	2	yes	complemented
523	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2507	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#2497	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#2490	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#2476	C₂×C₆₇	1	2	yes	complemented
528	#2471	C₂×C₆₇	1	2	yes	complemented
529	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#2428	C₂×C₆₇	1	1	yes	characteristic
532	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2395	C₂×C₆₇	1	2	yes	complemented
534	#2392	C₂×C₆₇	1	2	yes	complemented
535	C₄×#127	C₂×C₆₇	1	1	yes	characteristic, complemented
536	C₄×#125	C₂×C₆₇	1	1	yes	characteristic, complemented
537	C₄×#123	C₂×C₆₇	1	2	yes	complemented
538	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
539	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
540	C₄×#121	C₂×C₆₇	1	2	yes	complemented
541	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
542	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
543	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₆₇	#34970	1	1	yes	characteristic, direct product factor, Sylow
545	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
546	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
547	C₂×#123	C₂²×C₆₇	1	2	yes	—
548	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
549	C₂×#121	C₂²×C₆₇	1	2	yes	—
550	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
554	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
556	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
557	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
558	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
559	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
560	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×#117	C₂²×C₆₇	1	2	yes	—
562	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
563	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
564	#400	C₂²×C₆₇	1	2	yes	—
565	#399	C₂²×C₆₇	1	2	yes	—
566	#398	C₂²×C₆₇	1	2	yes	—
567	#398	C₂²×C₆₇	1	2	yes	—
568	#397	C₂²×C₆₇	1	2	yes	—
569	#397	C₂²×C₆₇	1	2	yes	—
570	#397	C₂²×C₆₇	1	2	yes	—
571	#397	C₂²×C₆₇	1	2	yes	—
572	#396	C₂²×C₆₇	1	2	yes	—
573	#396	C₂²×C₆₇	1	2	yes	—
574	#394	C₂²×C₆₇	1	2	yes	—
575	#394	C₂²×C₆₇	1	2	yes	—
576	#394	C₂²×C₆₇	1	2	yes	—
577	#394	C₂²×C₆₇	1	2	yes	—
578	#394	C₂²×C₆₇	1	2	yes	—
579	#392	C₂²×C₆₇	1	2	yes	—
580	#390	C₂²×C₆₇	1	1	yes	characteristic
581	#390	C₂²×C₆₇	1	2	yes	—
582	#390	C₂²×C₆₇	1	2	yes	—
583	#390	C₂²×C₆₇	1	1	yes	characteristic
584	#390	C₂²×C₆₇	1	1	yes	characteristic
585	#390	C₂²×C₆₇	1	1	yes	characteristic
586	#390	C₂²×C₆₇	1	1	yes	characteristic
587	#390	C₂²×C₆₇	1	1	yes	characteristic
588	#390	C₂²×C₆₇	1	2	yes	—
589	#389	C₂²×C₆₇	1	1	yes	characteristic
590	#389	C₂²×C₆₇	1	1	yes	characteristic
591	#389	C₂²×C₆₇	1	1	yes	characteristic
592	#389	C₂²×C₆₇	1	1	yes	characteristic
593	#389	C₂²×C₆₇	1	1	yes	characteristic
594	#389	C₂²×C₆₇	1	1	yes	characteristic
595	#389	C₂²×C₆₇	1	2	yes	—
596	#388	C₂²×C₆₇	1	2	yes	—
597	#388	C₂²×C₆₇	1	2	yes	—
598	#388	C₂²×C₆₇	1	2	yes	—
599	#388	C₂²×C₆₇	1	2	yes	—
600	#388	C₂²×C₆₇	1	2	yes	—
601	#388	C₂²×C₆₇	1	2	yes	—
602	#388	C₂²×C₆₇	1	2	yes	—
603	#388	C₂²×C₆₇	1	2	yes	—
604	#387	C₂²×C₆₇	1	2	yes	—
605	#387	C₂²×C₆₇	1	2	yes	—
606	#387	C₂²×C₆₇	1	2	yes	—
607	#387	C₂²×C₆₇	1	2	yes	—
608	#386	C₂²×C₆₇	1	2	yes	—
609	#386	C₂²×C₆₇	1	2	yes	—
610	#386	C₂²×C₆₇	1	2	yes	—
611	#386	C₂²×C₆₇	1	2	yes	—
612	#386	C₂²×C₆₇	1	2	yes	—
613	#385	C₂²×C₆₇	1	2	yes	—
614	#384	C₂²×C₆₇	1	1	yes	characteristic
615	#382	C₂²×C₆₇	1	1	yes	characteristic
616	#381	C₂²×C₆₇	1	2	yes	—
617	#380	C₂²×C₆₇	1	1	yes	characteristic
618	#380	C₂²×C₆₇	1	2	yes	—
619	#380	C₂²×C₆₇	1	1	yes	characteristic
620	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
621	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
622	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
624	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
625	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
627	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
628	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
631	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
632	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
633	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
635	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
636	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
637	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
638	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
640	#376	C₂²×C₆₇	1	1	yes	characteristic
641	#376	C₂²×C₆₇	1	1	yes	characteristic
642	C₄³	C₂²×C₆₇	1	1	yes	characteristic
643	C₄³	C₂²×C₆₇	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
646	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
647	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
648	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
649	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
654	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
656	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
657	#127	—	2	4	no	—
658	#125	—	2	4	no	—
659	#123	—	2	8	no	—
660	#121	—	2	4	no	—
661	#121	—	2	4	no	—
662	#121	—	2	8	no	—
663	C₄×D₄	—	2	4	no	—
664	C₄×D₄	—	2	4	no	—
665	C₄×D₄	—	2	4	no	—
666	C₄×D₄	—	2	4	no	—
667	C₄×D₄	—	4	4	no	—
668	C₄×D₄	—	4	4	no	—
669	C₄×D₄	—	4	4	no	—
670	C₄×D₄	—	4	4	no	—
671	#117	—	2	4	no	—
672	#117	—	2	4	no	—
673	#117	—	4	4	no	—
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄²	—	2	4	no	—
719	C₂×C₄²	—	4	4	no	—
720	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
722	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
731	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
740	#95	C₂³×C₆₇	1	1	yes	characteristic
741	#95	C₂³×C₆₇	1	1	yes	characteristic
742	#95	C₂³×C₆₇	1	1	yes	characteristic
743	#95	C₂³×C₆₇	1	1	yes	characteristic
744	#95	C₂³×C₆₇	1	1	yes	characteristic
745	#95	C₂³×C₆₇	1	1	yes	characteristic
746	#95	C₂³×C₆₇	1	1	yes	characteristic
747	#95	C₂³×C₆₇	1	1	yes	characteristic
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
750	#95	C₂³×C₆₇	1	2	yes	—
751	#95	C₂³×C₆₇	1	2	yes	—
752	#95	C₂³×C₆₇	1	2	yes	—
753	#95	C₂³×C₆₇	1	2	yes	—
754	#95	C₂³×C₆₇	1	2	yes	—
755	#95	C₂³×C₆₇	1	2	yes	—
756	#95	C₂³×C₆₇	1	2	yes	—
757	#95	C₂³×C₆₇	1	2	yes	—
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	2	yes	—
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
763	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	#41×C₆₇	1	4	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	4	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	#41×C₆₇	1	4	yes	—
843	C₄⋊C₄	#41×C₆₇	1	4	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	4	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	4	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	#41×C₆₇	1	4	yes	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	C₂×#41×C₆₇	1	4	yes	—
908	C₂³	C₂×#41×C₆₇	1	2	yes	—
909	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
910	D₄	—	2	8	no	—
911	D₄	—	4	8	no	—
912	D₄	—	4	8	no	—
913	D₄	—	4	8	no	—
914	D₄	—	4	8	no	—
915	D₄	—	4	4	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	8	no	—
965	C₂×C₄	—	4	8	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	8	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
971	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
972	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
973	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
974	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
975	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
976	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
977	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
978	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
979	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
980	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
981	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
982	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
983	C₂²	—	2	4	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	4	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1005	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1006	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1007	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1008	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1009	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1010	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	4	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	#529×C₆₇	1	4	yes	—
1030	C₄	#540×C₆₇	1	4	yes	—
1031	C₂	—	4	4	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
1035	C₂	C₆₇×#3444	1	1	yes	characteristic
1036	C₂	C₂×#540×C₆₇	1	1	yes	characteristic
1037	C₂	C₆₇×#3481	1	1	yes	characteristic
1038	C₂	C₆₇×#3481	1	1	yes	characteristic
1039	C₂	C₆₇×#3481	1	1	yes	characteristic
1040	C₂	C₆₇×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₆₇×#2428	C₂
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×#2531	C₂	semidirect
2. C₆₇×#2526	C₂	semidirect
3. C₆₇×#2513	C₂	semidirect
4. C₆₇×#2507	C₂	semidirect
5. C₆₇×#2497	C₂	semidirect
6. C₆₇×#2490	C₂	semidirect
7. C₆₇×#2476	C₂	semidirect
8. C₆₇×#2471	C₂	semidirect
9. C₆₇×#2454	C₂	semidirect
10. C₆₇×#2445	C₂	semidirect
12. C₆₇×#2420	C₂	semidirect
13. C₆₇×#2395	C₂	semidirect
14. C₆₇×#2392	C₂	semidirect
15. C₄×#127×C₆₇	C₂	semidirect
16. C₄×#125×C₆₇	C₂	semidirect
17. C₄×#123×C₆₇	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₄×#121×C₆₇	C₂	semidirect
20. C₄×#121×C₆₇	C₂	semidirect
21. C₆₇×#2293	C₂	semidirect
22. C₄²×D₄×C₆₇	C₂	semidirect
23. C₄×#117×C₆₇	C₂	semidirect
510. #34970	C₆₇	direct (N × H)
521. #2531	C₂×C₆₇	semidirect
522. #2526	C₂×C₆₇	semidirect
523. #2513	C₂×C₆₇	semidirect
524. #2507	C₂×C₆₇	semidirect
525. #2497	C₂×C₆₇	semidirect
526. #2490	C₂×C₆₇	semidirect
527. #2476	C₂×C₆₇	semidirect
528. #2471	C₂×C₆₇	semidirect
529. #2454	C₂×C₆₇	semidirect
530. #2445	C₂×C₆₇	semidirect
532. #2420	C₂×C₆₇	semidirect
533. #2395	C₂×C₆₇	semidirect
534. #2392	C₂×C₆₇	semidirect
535. C₄×#127	C₂×C₆₇	semidirect
536. C₄×#125	C₂×C₆₇	semidirect
537. C₄×#123	C₂×C₆₇	semidirect
538. C₄×#121	C₂×C₆₇	semidirect
539. C₄×#121	C₂×C₆₇	semidirect
540. C₄×#121	C₂×C₆₇	semidirect
541. #2293	C₂×C₆₇	semidirect
542. C₄²×D₄	C₂×C₆₇	semidirect
543. C₄×#117	C₂×C₆₇	semidirect
544. C₆₇	#34970	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×#2531	2
C₆₇×#2526	2
C₆₇×#2513	2
C₆₇×#2507	2
C₆₇×#2497	2
C₆₇×#2490	2
C₆₇×#2476	2
C₆₇×#2471	2
C₆₇×#2454	2
C₆₇×#2445	2
C₆₇×#2428	2
C₆₇×#2420	2
C₆₇×#2395	2
C₆₇×#2392	2
C₄×#127×C₆₇	2
C₄×#125×C₆₇	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2293	2
C₄²×D₄×C₆₇	2
C₄×#117×C₆₇	2
#34970	67

Subgroups — C67×#34970 #30714221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34970 #30714221