Subgroups — C₆₇×#60359 #30739610

Order 17152.

5098 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3007	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3006	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3005	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3004	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3003	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3002	C₂	1	8	yes	maximal, complemented
10	C₆₇×#2896	C₂	1	2	yes	maximal, complemented
11	C₂×#407×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	—	2	16	no	—
13	C₂²×#41×C₆₇	—	2	2	no	—
14	C₂²×#41×C₆₇	—	2	1	no	—
15	C₂²×#41×C₆₇	—	2	2	no	—
16	C₂²×#41×C₆₇	—	2	1	no	—
17	C₂²×#41×C₆₇	C₂²	1	4	yes	—
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₆₇	—	2	1	no	—
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×C₄×C₆₇	—	2	1	no	—
26	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
27	#575×C₆₇	—	2	16	no	—
28	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
29	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
31	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#135×C₆₇	C₂²	1	8	yes	complemented
33	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
34	#525×C₆₇	—	2	2	no	—
35	#525×C₆₇	—	2	1	no	—
36	#525×C₆₇	—	2	1	no	—
37	#525×C₆₇	C₂²	1	2	yes	—
38	#525×C₆₇	C₂²	1	2	yes	complemented
39	#525×C₆₇	C₂²	1	4	yes	complemented
40	C₂×#123×C₆₇	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#120×C₆₇	—	2	1	no	—
44	C₂×C₄×D₄×C₆₇	—	2	2	no	—
45	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#452×C₆₇	C₂²	1	16	yes	complemented
47	#451×C₆₇	C₂²	1	8	yes	complemented
48	#450×C₆₇	C₂²	1	8	yes	complemented
49	#449×C₆₇	C₂²	1	16	yes	complemented
50	#448×C₆₇	C₂²	1	8	yes	complemented
51	#447×C₆₇	C₂²	1	8	yes	complemented
52	#419×C₆₇	C₂²	1	4	yes	complemented
53	#418×C₆₇	C₂²	1	4	yes	complemented
54	#417×C₆₇	C₂²	1	8	yes	complemented
55	#416×C₆₇	C₂²	1	8	yes	complemented
56	#407×C₆₇	C₂²	1	2	yes	complemented
57	#407×C₆₇	C₂²	1	2	yes	complemented
58	#407×C₆₇	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
60	C₂⁵×C₆₇	—	2	1	no	—
61	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
62	C₂×#41×C₆₇	—	2	16	no	—
63	C₂×#41×C₆₇	—	2	32	no	—
64	C₂×#41×C₆₇	—	2	32	no	—
65	C₂×#41×C₆₇	—	2	16	no	—
66	C₂×#41×C₆₇	—	2	32	no	—
67	C₂×#41×C₆₇	—	2	32	no	—
68	C₂×#41×C₆₇	—	2	8	no	—
69	C₂×#41×C₆₇	—	2	8	no	—
70	C₂×#41×C₆₇	—	2	8	no	—
71	C₂×#41×C₆₇	—	2	4	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	—	2	2	no	—
74	C₂×#41×C₆₇	—	2	2	no	—
75	C₂×#41×C₆₇	—	2	4	no	—
76	C₂×#41×C₆₇	—	2	4	no	—
77	C₂×#41×C₆₇	—	2	4	no	—
78	C₂×#41×C₆₇	—	2	1	no	—
79	C₂×#41×C₆₇	—	2	1	no	—
80	C₂×#41×C₆₇	—	2	8	no	—
81	C₂×#41×C₆₇	D₄	1	16	yes	complemented
82	C₂×#41×C₆₇	C₂³	1	8	yes	—
83	C₂×#41×C₆₇	C₂³	1	2	yes	—
84	C₂×#41×C₆₇	C₂³	1	4	yes	—
85	C₂×#41×C₆₇	C₂³	1	4	yes	—
86	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
87	C₂²×Q₈×C₆₇	—	2	8	no	—
88	C₂²×Q₈×C₆₇	—	2	2	no	—
89	C₂²×Q₈×C₆₇	—	2	1	no	—
90	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
91	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
93	C₂²×D₄×C₆₇	—	2	16	no	—
94	C₂²×D₄×C₆₇	—	2	4	no	—
95	C₂²×D₄×C₆₇	—	2	2	no	—
96	C₂²×D₄×C₆₇	—	2	4	no	—
97	C₂²×D₄×C₆₇	—	2	2	no	—
98	C₂²×D₄×C₆₇	—	2	8	no	—
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	—	2	1	no	—
103	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
104	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
106	C₂³×C₄×C₆₇	—	2	16	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	C₂³×C₄×C₆₇	—	2	4	no	—
109	C₂³×C₄×C₆₇	—	2	2	no	—
110	C₂³×C₄×C₆₇	—	2	2	no	—
111	C₂³×C₄×C₆₇	—	2	4	no	—
112	C₂³×C₄×C₆₇	—	2	8	no	—
113	C₂³×C₄×C₆₇	—	2	1	no	—
114	C₂³×C₄×C₆₇	D₄	1	2	yes	—
115	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	D₄	1	2	yes	—
118	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
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	#137×C₆₇	—	2	16	no	—
125	#137×C₆₇	—	2	16	no	—
126	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
127	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
128	#135×C₆₇	—	2	32	no	—
129	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	complemented
130	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
131	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
132	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
133	C₂×M₁₆×C₆₇	—	2	8	no	—
134	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
135	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
136	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
137	#123×C₆₇	—	2	2	no	—
138	#123×C₆₇	—	2	2	no	—
139	#123×C₆₇	—	2	4	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	2	no	—
142	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	C₂³	1	4	yes	—
147	#121×C₆₇	C₂³	1	4	yes	complemented
148	#120×C₆₇	—	2	2	no	—
149	#120×C₆₇	—	2	2	no	—
150	#120×C₆₇	—	2	4	no	—
151	C₄×D₄×C₆₇	—	2	4	no	—
152	C₄×D₄×C₆₇	—	2	4	no	—
153	C₄×D₄×C₆₇	—	2	4	no	—
154	C₄×D₄×C₆₇	—	2	4	no	—
155	#117×C₆₇	—	2	1	no	—
156	#117×C₆₇	—	2	1	no	—
157	#117×C₆₇	C₂³	1	2	yes	—
158	#117×C₆₇	C₂³	1	2	yes	complemented
159	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
161	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
163	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
164	C₂×C₄²×C₆₇	—	2	1	no	—
165	#103×C₆₇	C₂³	1	16	yes	complemented
166	#102×C₆₇	C₂³	1	16	yes	complemented
167	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
168	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
169	C₂⁴×C₆₇	—	2	8	no	—
170	C₂⁴×C₆₇	—	2	4	no	—
171	C₂⁴×C₆₇	—	2	4	no	—
172	C₂⁴×C₆₇	—	2	2	no	—
173	C₂⁴×C₆₇	—	2	1	no	—
174	C₂⁴×C₆₇	—	4	4	no	—
175	C₂⁴×C₆₇	—	4	8	no	—
176	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
178	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
179	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
181	#41×C₆₇	—	2	32	no	—
182	#41×C₆₇	—	2	32	no	—
183	#41×C₆₇	—	2	32	no	—
184	#41×C₆₇	—	2	32	no	—
185	#41×C₆₇	—	2	32	no	—
186	#41×C₆₇	—	2	16	no	—
187	#41×C₆₇	—	2	16	no	—
188	#41×C₆₇	—	2	16	no	—
189	#41×C₆₇	—	2	16	no	—
190	#41×C₆₇	—	2	8	no	—
191	#41×C₆₇	—	2	8	no	—
192	#41×C₆₇	—	2	8	no	—
193	#41×C₆₇	—	2	8	no	—
194	#41×C₆₇	—	4	4	no	—
195	#41×C₆₇	—	4	4	no	—
196	#41×C₆₇	C₂×D₄	1	16	yes	—
197	#41×C₆₇	C₂×D₄	1	16	yes	complemented
198	C₂×Q₈×C₆₇	—	2	16	no	—
199	C₂×Q₈×C₆₇	—	2	8	no	—
200	C₂×Q₈×C₆₇	—	2	16	no	—
201	C₂×Q₈×C₆₇	—	2	4	no	—
202	C₂×Q₈×C₆₇	—	2	4	no	—
203	C₂×Q₈×C₆₇	—	2	2	no	—
204	C₂×Q₈×C₆₇	—	2	1	no	—
205	C₂×Q₈×C₆₇	—	2	4	no	—
206	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	complemented
207	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
209	C₂×D₄×C₆₇	—	2	32	no	—
210	C₂×D₄×C₆₇	—	2	32	no	—
211	C₂×D₄×C₆₇	—	2	16	no	—
212	C₂×D₄×C₆₇	—	2	8	no	—
213	C₂×D₄×C₆₇	—	2	16	no	—
214	C₂×D₄×C₆₇	—	2	16	no	—
215	C₂×D₄×C₆₇	—	2	8	no	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	4	no	—
218	C₂×D₄×C₆₇	—	2	16	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	2	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	1	no	—
228	C₂×D₄×C₆₇	—	4	8	no	—
229	C₂×D₄×C₆₇	—	4	4	no	—
230	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	complemented
231	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₆₇	—	2	8	no	—
234	C₂²×C₄×C₆₇	—	2	32	no	—
235	C₂²×C₄×C₆₇	—	2	32	no	—
236	C₂²×C₄×C₆₇	—	2	16	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	16	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	8	no	—
244	C₂²×C₄×C₆₇	—	2	8	no	—
245	C₂²×C₄×C₆₇	—	2	8	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	2	8	no	—
250	C₂²×C₄×C₆₇	—	2	8	no	—
251	C₂²×C₄×C₆₇	—	2	4	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	1	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	2	no	—
256	C₂²×C₄×C₆₇	—	4	4	no	—
257	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	Q₁₆×C₆₇	—	2	16	no	—
277	SD₁₆×C₆₇	—	2	16	no	—
278	SD₁₆×C₆₇	—	2	16	no	—
279	D₈×C₆₇	—	2	16	no	—
280	M₁₆×C₆₇	—	2	8	no	—
281	M₁₆×C₆₇	—	2	8	no	—
282	C₂×C₈×C₆₇	—	2	8	no	—
283	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₄²×C₆₇	—	2	2	no	—
295	C₄²×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	4	no	—
298	C₂³×C₆₇	—	2	16	no	—
299	C₂³×C₆₇	—	2	4	no	—
300	C₂³×C₆₇	—	2	4	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	8	no	—
303	C₂³×C₆₇	—	2	4	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	2	4	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	4	2	no	—
308	C₂³×C₆₇	—	4	2	no	—
309	C₂³×C₆₇	—	4	2	no	—
310	C₂³×C₆₇	—	4	2	no	—
311	C₂³×C₆₇	—	4	16	no	—
312	C₂³×C₆₇	—	4	32	no	—
313	C₂³×C₆₇	—	4	8	no	—
314	C₂³×C₆₇	—	4	8	no	—
315	C₂³×C₆₇	—	4	4	no	—
316	C₂³×C₆₇	—	4	8	no	—
317	C₂³×C₆₇	—	4	2	no	—
318	C₂³×C₆₇	#120	1	4	yes	—
319	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
324	Q₈×C₆₇	—	2	16	no	—
325	Q₈×C₆₇	—	2	8	no	—
326	Q₈×C₆₇	—	2	4	no	—
327	Q₈×C₆₇	—	2	4	no	—
328	Q₈×C₆₇	—	4	2	no	—
329	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
330	D₄×C₆₇	—	2	32	no	—
331	D₄×C₆₇	—	2	16	no	—
332	D₄×C₆₇	—	2	16	no	—
333	D₄×C₆₇	—	2	16	no	—
334	D₄×C₆₇	—	2	8	no	—
335	D₄×C₆₇	—	2	4	no	—
336	D₄×C₆₇	—	2	4	no	—
337	D₄×C₆₇	—	4	8	no	—
338	D₄×C₆₇	—	4	4	no	—
339	D₄×C₆₇	—	4	4	no	—
340	D₄×C₆₇	—	4	8	no	—
341	D₄×C₆₇	—	4	2	no	—
342	D₄×C₆₇	C₂²×D₄	1	8	yes	—
343	C₂×C₄×C₆₇	—	2	16	no	—
344	C₂×C₄×C₆₇	—	2	32	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	8	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	2	4	no	—
352	C₂×C₄×C₆₇	—	2	4	no	—
353	C₂×C₄×C₆₇	—	2	16	no	—
354	C₂×C₄×C₆₇	—	2	16	no	—
355	C₂×C₄×C₆₇	—	2	4	no	—
356	C₂×C₄×C₆₇	—	2	4	no	—
357	C₂×C₄×C₆₇	—	2	4	no	—
358	C₂×C₄×C₆₇	—	2	4	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	2	4	no	—
361	C₂×C₄×C₆₇	—	2	4	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	4	no	—
367	C₂×C₄×C₆₇	#120	1	4	yes	—
368	C₂×C₄×C₆₇	#120	1	4	yes	—
369	C₂×C₄×C₆₇	#120	1	4	yes	—
370	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
376	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
379	C₈×C₆₇	—	2	8	no	—
380	C₂²×C₆₇	—	2	8	no	—
381	C₂²×C₆₇	—	2	2	no	—
382	C₂²×C₆₇	—	2	2	no	—
383	C₂²×C₆₇	—	2	2	no	—
384	C₂²×C₆₇	—	2	2	no	—
385	C₂²×C₆₇	—	2	2	no	—
386	C₂²×C₆₇	—	2	2	no	—
387	C₂²×C₆₇	—	2	8	no	—
388	C₂²×C₆₇	—	2	2	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	4	4	no	—
391	C₂²×C₆₇	—	4	8	no	—
392	C₂²×C₆₇	—	4	8	no	—
393	C₂²×C₆₇	—	4	4	no	—
394	C₂²×C₆₇	—	4	16	no	—
395	C₂²×C₆₇	—	4	32	no	—
396	C₂²×C₆₇	—	4	8	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	4	no	—
399	C₂²×C₆₇	—	8	4	no	—
400	C₂²×C₆₇	C₂×#120	1	2	yes	—
401	C₂²×C₆₇	C₂×#120	1	2	yes	—
402	C₂²×C₆₇	C₂×#120	1	2	yes	—
403	C₂²×C₆₇	#575	1	4	yes	complemented
404	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
405	C₄×C₆₇	—	2	2	no	—
406	C₄×C₆₇	—	2	8	no	—
407	C₄×C₆₇	—	2	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	—	4	4	no	—
410	C₄×C₆₇	C₂×#120	1	2	yes	—
411	C₄×C₆₇	C₂×#120	1	2	yes	—
412	C₄×C₆₇	C₂×#120	1	2	yes	—
413	C₄×C₆₇	C₂³×D₄	1	2	yes	—
414	#60359	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₆₇	—	2	2	no	—
416	C₂×C₆₇	—	2	4	no	—
417	C₂×C₆₇	—	2	2	no	—
418	C₂×C₆₇	—	2	2	no	—
419	C₂×C₆₇	—	4	2	no	—
420	C₂×C₆₇	—	4	8	no	—
421	C₂×C₆₇	—	8	2	no	—
422	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
423	C₂×C₆₇	C₂×#575	1	2	yes	—
424	C₂³×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#575	C₂×C₆₇	1	2	yes	complemented
426	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#3007	C₂×C₆₇	1	4	yes	complemented
428	#3006	C₂×C₆₇	1	4	yes	complemented
429	#3005	C₂×C₆₇	1	4	yes	complemented
430	#3004	C₂×C₆₇	1	2	yes	complemented
431	#3003	C₂×C₆₇	1	2	yes	complemented
432	#3002	C₂×C₆₇	1	8	yes	complemented
433	#2896	C₂×C₆₇	1	2	yes	complemented
434	C₂×#407	C₂×C₆₇	1	1	yes	characteristic, complemented
435	C₆₇	#60359	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²×#41	—	2	16	no	—
437	C₂²×#41	—	2	2	no	—
438	C₂²×#41	—	2	1	no	—
439	C₂²×#41	—	2	2	no	—
440	C₂²×#41	—	2	1	no	—
441	C₂²×#41	C₂²×C₆₇	1	4	yes	—
442	C₂²×#41	C₂²×C₆₇	1	2	yes	—
443	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
444	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
445	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
447	C₂³×D₄	—	2	1	no	—
448	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
449	C₂⁴×C₄	—	2	1	no	—
450	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
451	#575	—	2	16	no	—
452	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
453	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
454	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
455	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
456	C₂×#135	C₂²×C₆₇	1	8	yes	complemented
457	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
458	#525	—	2	2	no	—
459	#525	—	2	1	no	—
460	#525	—	2	1	no	—
461	#525	C₂²×C₆₇	1	2	yes	—
462	#525	C₂²×C₆₇	1	2	yes	complemented
463	#525	C₂²×C₆₇	1	4	yes	complemented
464	C₂×#123	—	2	1	no	—
465	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
466	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
467	C₂×#120	—	2	1	no	—
468	C₂×C₄×D₄	—	2	2	no	—
469	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	#452	C₂²×C₆₇	1	16	yes	complemented
471	#451	C₂²×C₆₇	1	8	yes	complemented
472	#450	C₂²×C₆₇	1	8	yes	complemented
473	#449	C₂²×C₆₇	1	16	yes	complemented
474	#448	C₂²×C₆₇	1	8	yes	complemented
475	#447	C₂²×C₆₇	1	8	yes	complemented
476	#419	C₂²×C₆₇	1	4	yes	complemented
477	#418	C₂²×C₆₇	1	4	yes	complemented
478	#417	C₂²×C₆₇	1	8	yes	complemented
479	#416	C₂²×C₆₇	1	8	yes	complemented
480	#407	C₂²×C₆₇	1	2	yes	complemented
481	#407	C₂²×C₆₇	1	4	yes	complemented
482	#407	C₂²×C₆₇	1	2	yes	complemented
483	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
484	C₂⁵	—	2	1	no	—
485	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
486	C₂×#41	—	2	16	no	—
487	C₂×#41	—	2	32	no	—
488	C₂×#41	—	2	32	no	—
489	C₂×#41	—	2	16	no	—
490	C₂×#41	—	2	32	no	—
491	C₂×#41	—	2	32	no	—
492	C₂×#41	—	2	8	no	—
493	C₂×#41	—	2	8	no	—
494	C₂×#41	—	2	8	no	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	4	no	—
500	C₂×#41	—	2	4	no	—
501	C₂×#41	—	2	4	no	—
502	C₂×#41	—	2	1	no	—
503	C₂×#41	—	2	1	no	—
504	C₂×#41	—	2	8	no	—
505	C₂×#41	D₄×C₆₇	1	16	yes	complemented
506	C₂×#41	C₂³×C₆₇	1	2	yes	—
507	C₂×#41	C₂³×C₆₇	1	8	yes	—
508	C₂×#41	C₂³×C₆₇	1	4	yes	—
509	C₂×#41	C₂³×C₆₇	1	4	yes	—
510	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
511	C₂²×Q₈	—	2	8	no	—
512	C₂²×Q₈	—	2	2	no	—
513	C₂²×Q₈	—	2	1	no	—
514	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
515	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
516	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
517	C₂²×D₄	—	2	16	no	—
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	2	no	—
520	C₂²×D₄	—	2	4	no	—
521	C₂²×D₄	—	2	2	no	—
522	C₂²×D₄	—	2	8	no	—
523	C₂²×D₄	—	2	2	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
528	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
529	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
530	C₂³×C₄	—	2	16	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	4	no	—
533	C₂³×C₄	—	2	2	no	—
534	C₂³×C₄	—	2	4	no	—
535	C₂³×C₄	—	2	2	no	—
536	C₂³×C₄	—	2	8	no	—
537	C₂³×C₄	—	2	1	no	—
538	C₂³×C₄	D₄×C₆₇	1	2	yes	—
539	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
541	C₂³×C₄	D₄×C₆₇	1	2	yes	—
542	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
544	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
546	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
548	#137	—	2	16	no	—
549	#137	—	2	16	no	—
550	AGL(1,ℤ/8)	—	2	16	no	—
551	AGL(1,ℤ/8)	—	2	16	no	—
552	#135	—	2	32	no	—
553	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	complemented
554	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
555	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
556	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
557	C₂×M₁₆	—	2	8	no	—
558	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
559	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
560	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
567	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	C₂³×C₆₇	1	4	yes	—
571	#121	C₂³×C₆₇	1	4	yes	complemented
572	#120	—	2	2	no	—
573	#120	—	2	2	no	—
574	#120	—	2	4	no	—
575	C₄×D₄	—	2	4	no	—
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	#117	—	2	1	no	—
580	#117	—	2	1	no	—
581	#117	C₂³×C₆₇	1	2	yes	—
582	#117	C₂³×C₆₇	1	2	yes	complemented
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₄²	—	2	1	no	—
589	#103	C₂³×C₆₇	1	16	yes	complemented
590	#102	C₂³×C₆₇	1	16	yes	complemented
591	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
592	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
593	C₂⁴	—	2	8	no	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	4	4	no	—
599	C₂⁴	—	4	8	no	—
600	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
601	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
602	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
603	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
605	#41	—	2	32	no	—
606	#41	—	2	32	no	—
607	#41	—	2	32	no	—
608	#41	—	2	32	no	—
609	#41	—	2	32	no	—
610	#41	—	2	16	no	—
611	#41	—	2	16	no	—
612	#41	—	2	16	no	—
613	#41	—	2	16	no	—
614	#41	—	2	8	no	—
615	#41	—	2	8	no	—
616	#41	—	2	8	no	—
617	#41	—	2	8	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	#41	C₂×D₄×C₆₇	1	16	yes	—
621	#41	C₂×D₄×C₆₇	1	16	yes	complemented
622	C₂×Q₈	—	2	16	no	—
623	C₂×Q₈	—	2	8	no	—
624	C₂×Q₈	—	2	16	no	—
625	C₂×Q₈	—	2	4	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	complemented
631	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
632	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
633	C₂×D₄	—	2	32	no	—
634	C₂×D₄	—	2	32	no	—
635	C₂×D₄	—	2	16	no	—
636	C₂×D₄	—	2	8	no	—
637	C₂×D₄	—	2	16	no	—
638	C₂×D₄	—	2	16	no	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	16	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	complemented
655	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
656	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
657	C₂²×C₄	—	2	8	no	—
658	C₂²×C₄	—	2	32	no	—
659	C₂²×C₄	—	2	32	no	—
660	C₂²×C₄	—	2	16	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	16	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	8	no	—
669	C₂²×C₄	—	2	8	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	8	no	—
675	C₂²×C₄	—	2	8	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	4	4	no	—
681	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
695	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
700	Q₁₆	—	2	16	no	—
701	SD₁₆	—	2	16	no	—
702	SD₁₆	—	2	16	no	—
703	D₈	—	2	16	no	—
704	M₁₆	—	2	8	no	—
705	M₁₆	—	2	8	no	—
706	C₂×C₈	—	2	8	no	—
707	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	16	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	8	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	16	no	—
736	C₂³	—	4	32	no	—
737	C₂³	—	4	8	no	—
738	C₂³	—	4	8	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	2	no	—
742	C₂³	#120×C₆₇	1	4	yes	—
743	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
744	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
745	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
747	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
748	Q₈	—	2	16	no	—
749	Q₈	—	2	8	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	4	2	no	—
753	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
754	D₄	—	2	32	no	—
755	D₄	—	2	16	no	—
756	D₄	—	2	16	no	—
757	D₄	—	2	16	no	—
758	D₄	—	2	8	no	—
759	D₄	—	2	4	no	—
760	D₄	—	2	4	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	2	no	—
766	D₄	C₂²×D₄×C₆₇	1	8	yes	—
767	C₂×C₄	—	2	16	no	—
768	C₂×C₄	—	2	32	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	16	no	—
778	C₂×C₄	—	2	16	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	#120×C₆₇	1	4	yes	—
792	C₂×C₄	#120×C₆₇	1	4	yes	—
793	C₂×C₄	#120×C₆₇	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
800	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
801	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
802	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
803	C₈	—	2	8	no	—
804	C₂²	—	2	8	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	8	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	8	no	—
816	C₂²	—	4	8	no	—
817	C₂²	—	4	4	no	—
818	C₂²	—	4	16	no	—
819	C₂²	—	4	32	no	—
820	C₂²	—	4	8	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	8	4	no	—
824	C₂²	C₂×#120×C₆₇	1	2	yes	—
825	C₂²	C₂×#120×C₆₇	1	2	yes	—
826	C₂²	C₂×#120×C₆₇	1	2	yes	—
827	C₂²	#575×C₆₇	1	4	yes	complemented
828	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
829	C₄	—	2	2	no	—
830	C₄	—	2	8	no	—
831	C₄	—	2	2	no	—
832	C₄	—	4	4	no	—
833	C₄	—	4	2	no	—
834	C₄	C₂×#120×C₆₇	1	2	yes	—
835	C₄	C₂×#120×C₆₇	1	2	yes	—
836	C₄	C₂×#120×C₆₇	1	2	yes	—
837	C₄	C₂³×D₄×C₆₇	1	2	yes	—
838	C₂	—	2	2	no	—
839	C₂	—	2	4	no	—
840	C₂	—	2	2	no	—
841	C₂	—	2	2	no	—
842	C₂	—	4	2	no	—
843	C₂	—	4	8	no	—
844	C₂	—	8	2	no	—
845	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
846	C₂	C₂×#575×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₂×#525×C₆₇	C₂	semidirect
4. C₆₇×#3007	C₂	semidirect
5. C₆₇×#3006	C₂	semidirect
6. C₆₇×#3005	C₂	semidirect
7. C₆₇×#3004	C₂	semidirect
8. C₆₇×#3003	C₂	semidirect
9. C₆₇×#3002	C₂	semidirect
10. C₆₇×#2896	C₂	semidirect
11. C₂×#407×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂³×Q₈×C₆₇	C₂²	semidirect
24. C₂³×D₄×C₆₇	C₂²	semidirect
28. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
32. C₂×#135×C₆₇	C₂²	semidirect
33. C₂²×M₁₆×C₆₇	C₂²	semidirect
38. #525×C₆₇	C₂²	semidirect
39. #525×C₆₇	C₂²	semidirect
41. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
42. C₂×#121×C₆₇	C₂²	semidirect
45. C₂×#117×C₆₇	C₂²	semidirect
46. #452×C₆₇	C₂²	semidirect
47. #451×C₆₇	C₂²	semidirect
48. #450×C₆₇	C₂²	semidirect
49. #449×C₆₇	C₂²	semidirect
50. #448×C₆₇	C₂²	semidirect
51. #447×C₆₇	C₂²	semidirect
52. #419×C₆₇	C₂²	semidirect
53. #418×C₆₇	C₂²	semidirect
54. #417×C₆₇	C₂²	semidirect
55. #416×C₆₇	C₂²	semidirect
56. #407×C₆₇	C₂²	semidirect
57. #407×C₆₇	C₂²	semidirect
58. #407×C₆₇	C₂²	semidirect
59. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
81. C₂×#41×C₆₇	D₄	semidirect
86. C₂×#41×C₆₇	C₂³	semidirect
92. C₂²×Q₈×C₆₇	C₂³	semidirect
105. C₂²×D₄×C₆₇	C₂³	semidirect
129. C₂×Q₁₆×C₆₇	C₂³	semidirect
130. C₂×SD₁₆×C₆₇	C₂³	semidirect
131. C₂×SD₁₆×C₆₇	C₂³	semidirect
132. C₂×D₈×C₆₇	C₂³	semidirect
135. C₂×M₁₆×C₆₇	C₂³	semidirect
136. C₂²×C₈×C₆₇	C₂³	semidirect
143. C₂²⋊Q₈×C₆₇	C₂³	semidirect
147. #121×C₆₇	C₂³	semidirect
158. #117×C₆₇	C₂³	semidirect
160. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
165. #103×C₆₇	C₂³	semidirect
166. #102×C₆₇	C₂³	semidirect
168. C₂²⋊C₈×C₆₇	C₂³	semidirect
197. #41×C₆₇	C₂×D₄	semidirect
206. C₂×Q₈×C₆₇	C₂×D₄	semidirect
230. C₂×D₄×C₆₇	C₂×D₄	semidirect
403. C₂²×C₆₇	#575	semidirect
414. #60359	C₆₇	direct (N × H)
424. C₂³×#41	C₂×C₆₇	semidirect
425. C₂×#575	C₂×C₆₇	semidirect
426. C₂×#525	C₂×C₆₇	semidirect
427. #3007	C₂×C₆₇	semidirect
428. #3006	C₂×C₆₇	semidirect
429. #3005	C₂×C₆₇	semidirect
430. #3004	C₂×C₆₇	semidirect
431. #3003	C₂×C₆₇	semidirect
432. #3002	C₂×C₆₇	semidirect
433. #2896	C₂×C₆₇	semidirect
434. C₂×#407	C₂×C₆₇	semidirect
435. C₆₇	#60359	direct (N × H)
443. C₂²×#41	C₂²×C₆₇	semidirect
444. C₂²×#41	C₂²×C₆₇	semidirect
445. C₂²×#41	C₂²×C₆₇	semidirect
446. C₂³×Q₈	C₂²×C₆₇	semidirect
448. C₂³×D₄	C₂²×C₆₇	semidirect
452. C₂×#137	C₂²×C₆₇	semidirect
453. C₂×#137	C₂²×C₆₇	semidirect
454. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
455. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
456. C₂×#135	C₂²×C₆₇	semidirect
457. C₂²×M₁₆	C₂²×C₆₇	semidirect
462. #525	C₂²×C₆₇	semidirect
463. #525	C₂²×C₆₇	semidirect
465. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
466. C₂×#121	C₂²×C₆₇	semidirect
469. C₂×#117	C₂²×C₆₇	semidirect
470. #452	C₂²×C₆₇	semidirect
471. #451	C₂²×C₆₇	semidirect
472. #450	C₂²×C₆₇	semidirect
473. #449	C₂²×C₆₇	semidirect
474. #448	C₂²×C₆₇	semidirect
475. #447	C₂²×C₆₇	semidirect
476. #419	C₂²×C₆₇	semidirect
477. #418	C₂²×C₆₇	semidirect
478. #417	C₂²×C₆₇	semidirect
479. #416	C₂²×C₆₇	semidirect
480. #407	C₂²×C₆₇	semidirect
481. #407	C₂²×C₆₇	semidirect
482. #407	C₂²×C₆₇	semidirect
483. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
505. C₂×#41	D₄×C₆₇	semidirect
510. C₂×#41	C₂³×C₆₇	semidirect
516. C₂²×Q₈	C₂³×C₆₇	semidirect
529. C₂²×D₄	C₂³×C₆₇	semidirect
553. C₂×Q₁₆	C₂³×C₆₇	semidirect
554. C₂×SD₁₆	C₂³×C₆₇	semidirect
555. C₂×SD₁₆	C₂³×C₆₇	semidirect
556. C₂×D₈	C₂³×C₆₇	semidirect
559. C₂×M₁₆	C₂³×C₆₇	semidirect
560. C₂²×C₈	C₂³×C₆₇	semidirect
567. C₂²⋊Q₈	C₂³×C₆₇	semidirect
571. #121	C₂³×C₆₇	semidirect
582. #117	C₂³×C₆₇	semidirect
584. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
589. #103	C₂³×C₆₇	semidirect
590. #102	C₂³×C₆₇	semidirect
592. C₂²⋊C₈	C₂³×C₆₇	semidirect
621. #41	C₂×D₄×C₆₇	semidirect
630. C₂×Q₈	C₂×D₄×C₆₇	semidirect
654. C₂×D₄	C₂×D₄×C₆₇	semidirect
827. C₂²	#575×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₆₇	2
C₂×#575×C₆₇	2
C₂×#525×C₆₇	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#3005	2
C₆₇×#3004	2
C₆₇×#3003	2
C₆₇×#3002	2
C₆₇×#2896	2
C₂×#407×C₆₇	2
#60359	67

Subgroups — C67×#60359 #30739610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60359 #30739610