Subgroups — C₂×C₆₇×#3370 #30740563

Order 17152.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3370	C₂	1	16	yes	maximal, direct product factor
4	C₂×#490×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#489×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#488×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#478×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#463×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic
13	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
20	#559×C₆₇	—	2	4	no	—
21	#559×C₆₇	C₂²	1	8	yes	complemented
22	#554×C₆₇	—	2	4	no	—
23	#554×C₆₇	C₂²	1	8	yes	complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	—	2	1	no	—
29	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#123×C₆₇	—	2	1	no	—
32	C₂×#123×C₆₇	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	—	2	1	no	—
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
45	#490×C₆₇	C₂²	1	8	yes	complemented
46	#489×C₆₇	C₂²	1	8	yes	complemented
47	#488×C₆₇	C₂²	1	8	yes	complemented
48	#479×C₆₇	C₂²	1	8	yes	complemented
49	#478×C₆₇	C₂²	1	8	yes	complemented
50	#474×C₆₇	C₂²	1	8	yes	complemented
51	#463×C₆₇	C₂²	1	8	yes	complemented
52	#463×C₆₇	C₂²	1	8	yes	complemented
53	#459×C₆₇	C₂²	1	8	yes	—
54	#446×C₆₇	C₂²	1	8	yes	complemented
55	#442×C₆₇	C₂²	1	8	yes	complemented
56	#440×C₆₇	C₂²	1	8	yes	complemented
57	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
58	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₆₇	—	2	1	no	—
78	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₇	—	2	1	no	—
81	C₂²×D₄×C₆₇	—	2	1	no	—
82	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	—	2	1	no	—
86	C₂³×C₄×C₆₇	—	2	1	no	—
87	C₂³×C₄×C₆₇	—	2	1	no	—
88	C₂³×C₄×C₆₇	—	2	1	no	—
89	C₂³×C₄×C₆₇	—	2	1	no	—
90	C₂×SD₁₆×C₆₇	—	2	4	no	—
91	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×D₈×C₆₇	—	2	4	no	—
93	C₂×D₈×C₆₇	—	2	4	no	—
94	C₂×D₈×C₆₇	C₂³	1	4	yes	—
95	C₂×D₈×C₆₇	C₂³	1	4	yes	—
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₇	—	2	2	no	—
101	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
102	#127×C₆₇	—	2	2	no	—
103	#127×C₆₇	C₂³	1	4	yes	—
104	#125×C₆₇	—	2	2	no	—
105	#125×C₆₇	—	2	2	no	—
106	#125×C₆₇	C₂³	1	4	yes	—
107	#125×C₆₇	C₂³	1	4	yes	—
108	#124×C₆₇	—	2	8	no	—
109	#124×C₆₇	—	2	2	no	—
110	#124×C₆₇	—	2	2	no	—
111	#124×C₆₇	C₂³	1	4	yes	—
112	#124×C₆₇	C₂³	1	4	yes	—
113	#123×C₆₇	—	2	8	no	—
114	#123×C₆₇	—	2	8	no	—
115	C₂²⋊Q₈×C₆₇	—	2	8	no	—
116	C₂²⋊Q₈×C₆₇	—	2	8	no	—
117	C₂²⋊Q₈×C₆₇	—	2	8	no	—
118	C₄×Q₈×C₆₇	—	2	2	no	—
119	C₄×Q₈×C₆₇	D₄	1	4	yes	—
120	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
121	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
122	C₄×D₄×C₆₇	—	2	8	no	—
123	C₄×D₄×C₆₇	—	2	2	no	—
124	C₄×D₄×C₆₇	—	2	2	no	—
125	C₄×D₄×C₆₇	—	2	2	no	—
126	C₄×D₄×C₆₇	—	2	2	no	—
127	C₄×D₄×C₆₇	—	2	2	no	—
128	C₄×D₄×C₆₇	C₂³	1	4	yes	—
129	C₄×D₄×C₆₇	C₂³	1	4	yes	—
130	C₄×D₄×C₆₇	C₂³	1	4	yes	—
131	C₄×D₄×C₆₇	C₂³	1	4	yes	—
132	C₄×D₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
140	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂×C₄²×C₆₇	—	2	1	no	—
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	#107×C₆₇	C₂³	1	4	yes	—
161	#107×C₆₇	C₂³	1	4	yes	—
162	#106×C₆₇	C₂³	1	4	yes	—
163	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
165	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
166	#103×C₆₇	C₂³	1	4	yes	—
167	#103×C₆₇	C₂³	1	4	yes	—
168	#103×C₆₇	C₂³	1	4	yes	—
169	#102×C₆₇	C₂³	1	4	yes	—
170	#102×C₆₇	C₂³	1	4	yes	—
171	#102×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	#102×C₆₇	C₂³	1	4	yes	—
174	#102×C₆₇	C₂³	1	4	yes	—
175	#102×C₆₇	C₂³	1	4	yes	—
176	#97×C₆₇	C₂³	1	4	yes	—
177	#97×C₆₇	C₂³	1	4	yes	—
178	C₄×C₈×C₆₇	C₂³	1	4	yes	—
179	C₂⁴×C₆₇	—	2	1	no	—
180	C₂⁴×C₆₇	—	2	1	no	—
181	C₂⁴×C₆₇	—	2	1	no	—
182	C₂×Q₈×C₆₇	—	2	1	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	—	4	2	no	—
187	C₂×Q₈×C₆₇	—	8	2	no	—
188	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
189	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
190	C₂×D₄×C₆₇	—	2	1	no	—
191	C₂×D₄×C₆₇	—	2	1	no	—
192	C₂×D₄×C₆₇	—	2	1	no	—
193	C₂×D₄×C₆₇	—	2	4	no	—
194	C₂×D₄×C₆₇	—	2	4	no	—
195	C₂×D₄×C₆₇	—	2	2	no	—
196	C₂×D₄×C₆₇	—	2	2	no	—
197	C₂×D₄×C₆₇	—	2	2	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	2	2	no	—
200	C₂×D₄×C₆₇	—	4	4	no	—
201	C₂×D₄×C₆₇	—	8	2	no	—
202	C₂×D₄×C₆₇	#41	1	4	yes	—
203	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
204	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
205	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₇	—	2	1	no	—
207	C₂²×C₄×C₆₇	—	2	1	no	—
208	C₂²×C₄×C₆₇	—	2	1	no	—
209	C₂²×C₄×C₆₇	—	2	1	no	—
210	C₂²×C₄×C₆₇	—	2	1	no	—
211	C₂²×C₄×C₆₇	—	2	4	no	—
212	C₂²×C₄×C₆₇	—	2	4	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	4	4	no	—
217	C₂²×C₄×C₆₇	—	8	2	no	—
218	C₂²×C₄×C₆₇	—	8	2	no	—
219	C₂²×C₄×C₆₇	—	8	2	no	—
220	C₂²×C₄×C₆₇	—	8	2	no	—
221	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₆₇	—	2	8	no	—
229	D₈×C₆₇	—	2	8	no	—
230	D₈×C₆₇	—	2	8	no	—
231	C₂×C₈×C₆₇	—	2	2	no	—
232	C₂×C₈×C₆₇	—	2	2	no	—
233	C₂×C₈×C₆₇	—	2	2	no	—
234	C₂×C₈×C₆₇	—	2	2	no	—
235	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
236	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	4	no	—
243	C₄⋊C₄×C₆₇	—	2	4	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	1	no	—
246	C₄⋊C₄×C₆₇	—	2	1	no	—
247	C₄⋊C₄×C₆₇	—	2	1	no	—
248	C₄⋊C₄×C₆₇	—	2	1	no	—
249	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₆₇	—	2	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	4	no	—
258	C₂²⋊C₄×C₆₇	—	2	4	no	—
259	C₂²⋊C₄×C₆₇	—	2	4	no	—
260	C₂²⋊C₄×C₆₇	—	2	4	no	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	4	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₄²×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	C₂×D₄	1	2	yes	—
267	C₄²×C₆₇	C₂×D₄	1	2	yes	—
268	C₄²×C₆₇	C₂×D₄	1	2	yes	—
269	C₄²×C₆₇	C₂⁴	1	2	yes	—
270	C₄²×C₆₇	C₂⁴	1	2	yes	—
271	C₄²×C₆₇	C₂⁴	1	2	yes	—
272	C₂³×C₆₇	—	2	4	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	—	2	2	no	—
275	C₂³×C₆₇	—	2	2	no	—
276	C₂³×C₆₇	—	4	2	no	—
277	C₂³×C₆₇	—	4	2	no	—
278	C₂³×C₆₇	—	4	2	no	—
279	C₂³×C₆₇	—	4	2	no	—
280	C₂³×C₆₇	—	4	2	no	—
281	C₂³×C₆₇	—	4	2	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	4	2	no	—
284	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₆₇	—	2	2	no	—
286	Q₈×C₆₇	—	2	2	no	—
287	Q₈×C₆₇	—	4	4	no	—
288	Q₈×C₆₇	—	4	2	no	—
289	Q₈×C₆₇	—	8	4	no	—
290	D₄×C₆₇	—	2	4	no	—
291	D₄×C₆₇	—	2	2	no	—
292	D₄×C₆₇	—	2	2	no	—
293	D₄×C₆₇	—	2	2	no	—
294	D₄×C₆₇	—	2	2	no	—
295	D₄×C₆₇	—	2	2	no	—
296	D₄×C₆₇	—	4	8	no	—
297	D₄×C₆₇	—	4	2	no	—
298	D₄×C₆₇	—	4	2	no	—
299	D₄×C₆₇	—	8	4	no	—
300	D₄×C₆₇	C₂×#41	1	4	yes	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	4	8	no	—
313	C₂×C₄×C₆₇	—	4	2	no	—
314	C₂×C₄×C₆₇	—	4	2	no	—
315	C₂×C₄×C₆₇	—	4	2	no	—
316	C₂×C₄×C₆₇	—	4	2	no	—
317	C₂×C₄×C₆₇	—	4	2	no	—
318	C₂×C₄×C₆₇	—	8	4	no	—
319	C₂×C₄×C₆₇	—	8	4	no	—
320	C₂×C₄×C₆₇	—	8	4	no	—
321	C₂×C₄×C₆₇	—	8	4	no	—
322	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
330	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
331	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
332	C₈×C₆₇	—	2	2	no	—
333	C₈×C₆₇	—	2	2	no	—
334	C₈×C₆₇	—	2	2	no	—
335	C₈×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	4	no	—
337	C₂²×C₆₇	—	4	8	no	—
338	C₂²×C₆₇	—	4	2	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	4	2	no	—
341	C₂²×C₆₇	—	4	2	no	—
342	C₂²×C₆₇	—	4	2	no	—
343	C₂²×C₆₇	—	4	2	no	—
344	C₂²×C₆₇	—	4	2	no	—
345	C₂²×C₆₇	—	4	2	no	—
346	C₂²×C₆₇	—	8	4	no	—
347	C₂²×C₆₇	—	8	4	no	—
348	C₂²×C₆₇	#548	1	2	yes	—
349	C₂²×C₆₇	#575	1	2	yes	—
350	C₂²×C₆₇	#576	1	2	yes	—
351	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₆₇	—	2	2	no	—
353	C₄×C₆₇	—	2	2	no	—
354	C₄×C₆₇	—	2	2	no	—
355	C₄×C₆₇	—	2	2	no	—
356	C₄×C₆₇	—	2	2	no	—
357	C₄×C₆₇	—	2	2	no	—
358	C₄×C₆₇	—	4	2	no	—
359	C₄×C₆₇	—	4	2	no	—
360	C₄×C₆₇	—	4	2	no	—
361	C₄×C₆₇	—	4	2	no	—
362	C₄×C₆₇	—	4	2	no	—
363	C₄×C₆₇	#548	1	2	yes	—
364	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
365	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
366	C₂×#3370	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂×C₆₇	—	4	4	no	—
368	C₂×C₆₇	—	8	2	no	—
369	C₂×C₆₇	—	8	2	no	—
370	C₂×C₆₇	#3370	1	4	yes	direct product factor
371	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
372	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
373	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
374	C₂×#559	C₂×C₆₇	1	1	yes	characteristic, complemented
375	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
376	#3370	C₂×C₆₇	1	16	yes	direct product factor
377	C₂×#490	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₂×#489	C₂×C₆₇	1	1	yes	characteristic, complemented
379	C₂×#488	C₂×C₆₇	1	1	yes	characteristic, complemented
380	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
381	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
382	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
383	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
385	C₂×#459	C₂×C₆₇	1	1	yes	characteristic
386	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
387	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
388	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
389	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
390	C₆₇	C₂×#3370	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
392	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
393	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
394	#559	—	2	4	no	—
395	#559	C₂²×C₆₇	1	8	yes	complemented
396	#554	—	2	4	no	—
397	#554	C₂²×C₆₇	1	8	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
399	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
400	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
401	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
402	C₂×#124	—	2	1	no	—
403	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
404	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
405	C₂×#123	—	2	1	no	—
406	C₂×#123	—	2	1	no	—
407	C₂×C₂²⋊Q₈	—	2	1	no	—
408	C₂×C₂²⋊Q₈	—	2	1	no	—
409	C₂×C₂²⋊Q₈	—	2	1	no	—
410	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	—	2	1	no	—
419	#490	C₂²×C₆₇	1	8	yes	complemented
420	#489	C₂²×C₆₇	1	8	yes	complemented
421	#488	C₂²×C₆₇	1	8	yes	complemented
422	#479	C₂²×C₆₇	1	8	yes	complemented
423	#478	C₂²×C₆₇	1	8	yes	complemented
424	#474	C₂²×C₆₇	1	8	yes	complemented
425	#463	C₂²×C₆₇	1	8	yes	complemented
426	#463	C₂²×C₆₇	1	8	yes	complemented
427	#459	C₂²×C₆₇	1	8	yes	—
428	#446	C₂²×C₆₇	1	8	yes	complemented
429	#442	C₂²×C₆₇	1	8	yes	complemented
430	#440	C₂²×C₆₇	1	8	yes	complemented
431	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
432	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
433	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
440	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
441	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
443	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
444	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
448	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
449	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
450	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
451	C₂²×Q₈	—	2	1	no	—
452	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	—	2	1	no	—
464	C₂×SD₁₆	—	2	4	no	—
465	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
466	C₂×D₈	—	2	4	no	—
467	C₂×D₈	—	2	4	no	—
468	C₂×D₈	C₂³×C₆₇	1	4	yes	—
469	C₂×D₈	C₂³×C₆₇	1	4	yes	—
470	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
476	#127	—	2	2	no	—
477	#127	C₂³×C₆₇	1	4	yes	—
478	#125	—	2	2	no	—
479	#125	—	2	2	no	—
480	#125	C₂³×C₆₇	1	4	yes	—
481	#125	C₂³×C₆₇	1	4	yes	—
482	#124	—	2	8	no	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	C₂³×C₆₇	1	4	yes	—
486	#124	C₂³×C₆₇	1	4	yes	—
487	#123	—	2	8	no	—
488	#123	—	2	8	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	C₂²⋊Q₈	—	2	8	no	—
491	C₂²⋊Q₈	—	2	8	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	D₄×C₆₇	1	4	yes	—
494	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
495	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	C₂³×C₆₇	1	4	yes	—
503	C₄×D₄	C₂³×C₆₇	1	4	yes	—
504	C₄×D₄	C₂³×C₆₇	1	4	yes	—
505	C₄×D₄	C₂³×C₆₇	1	4	yes	—
506	C₄×D₄	C₂³×C₆₇	1	4	yes	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	8	no	—
514	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
534	#107	C₂³×C₆₇	1	4	yes	—
535	#107	C₂³×C₆₇	1	4	yes	—
536	#106	C₂³×C₆₇	1	4	yes	—
537	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
538	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
539	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
540	#103	C₂³×C₆₇	1	4	yes	—
541	#103	C₂³×C₆₇	1	4	yes	—
542	#103	C₂³×C₆₇	1	4	yes	—
543	#102	C₂³×C₆₇	1	4	yes	—
544	#102	C₂³×C₆₇	1	4	yes	—
545	#102	C₂³×C₆₇	1	4	yes	—
546	#102	C₂³×C₆₇	1	4	yes	—
547	#102	C₂³×C₆₇	1	4	yes	—
548	#102	C₂³×C₆₇	1	4	yes	—
549	#102	C₂³×C₆₇	1	4	yes	—
550	#97	C₂³×C₆₇	1	4	yes	—
551	#97	C₂³×C₆₇	1	4	yes	—
552	C₄×C₈	C₂³×C₆₇	1	4	yes	—
553	C₂⁴	—	2	1	no	—
554	C₂⁴	—	2	1	no	—
555	C₂⁴	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	8	2	no	—
562	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
563	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	8	2	no	—
576	C₂×D₄	#41×C₆₇	1	4	yes	—
577	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
578	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
579	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	—	8	2	no	—
593	C₂²×C₄	—	8	2	no	—
594	C₂²×C₄	—	8	2	no	—
595	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
602	SD₁₆	—	2	8	no	—
603	D₈	—	2	8	no	—
604	D₈	—	2	8	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
610	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
611	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
612	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
624	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
625	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
626	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	C₂×D₄×C₆₇	1	2	yes	—
641	C₄²	C₂×D₄×C₆₇	1	2	yes	—
642	C₄²	C₂×D₄×C₆₇	1	2	yes	—
643	C₄²	C₂⁴×C₆₇	1	2	yes	—
644	C₄²	C₂⁴×C₆₇	1	2	yes	—
645	C₄²	C₂⁴×C₆₇	1	2	yes	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	4	2	no	—
657	C₂³	—	4	2	no	—
658	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	4	4	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	8	4	no	—
664	D₄	—	2	4	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	2	no	—
673	D₄	—	8	4	no	—
674	D₄	C₂×#41×C₆₇	1	4	yes	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
704	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
705	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	8	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	8	4	no	—
721	C₂²	—	8	4	no	—
722	C₂²	#548×C₆₇	1	2	yes	—
723	C₂²	#575×C₆₇	1	2	yes	—
724	C₂²	#576×C₆₇	1	2	yes	—
725	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	#548×C₆₇	1	2	yes	—
738	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
739	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
740	C₂	—	4	4	no	—
741	C₂	—	8	2	no	—
742	C₂	—	8	2	no	—
743	C₂	C₆₇×#3370	1	4	yes	direct product factor
744	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
745	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
746	C₂	C₂×#576×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#459×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₆₇	C₂	semidirect
2. C₂×#554×C₆₇	C₂	semidirect
3. C₆₇×#3370	C₂	direct (N × H)
4. C₂×#490×C₆₇	C₂	semidirect
5. C₂×#489×C₆₇	C₂	semidirect
6. C₂×#488×C₆₇	C₂	semidirect
7. C₂×#479×C₆₇	C₂	semidirect
8. C₂×#478×C₆₇	C₂	semidirect
9. C₂×#474×C₆₇	C₂	semidirect
10. C₂×#463×C₆₇	C₂	semidirect
11. C₂×#463×C₆₇	C₂	semidirect
13. C₂×#446×C₆₇	C₂	semidirect
14. C₂×#442×C₆₇	C₂	semidirect
15. C₂×#440×C₆₇	C₂	semidirect
16. C₂×C₄×D₈×C₆₇	C₂	semidirect
21. #559×C₆₇	C₂²	semidirect
23. #554×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #488×C₆₇	C₂²	semidirect
48. #479×C₆₇	C₂²	semidirect
49. #478×C₆₇	C₂²	semidirect
50. #474×C₆₇	C₂²	semidirect
51. #463×C₆₇	C₂²	semidirect
52. #463×C₆₇	C₂²	semidirect
54. #446×C₆₇	C₂²	semidirect
55. #442×C₆₇	C₂²	semidirect
56. #440×C₆₇	C₂²	semidirect
57. C₄×D₈×C₆₇	C₂²	semidirect
366. C₂×#3370	C₆₇	direct (N × H)
370. C₂×C₆₇	#3370	direct (N × H)
374. C₂×#559	C₂×C₆₇	semidirect
375. C₂×#554	C₂×C₆₇	semidirect
376. #3370	C₂×C₆₇	direct (N × H)
377. C₂×#490	C₂×C₆₇	semidirect
378. C₂×#489	C₂×C₆₇	semidirect
379. C₂×#488	C₂×C₆₇	semidirect
380. C₂×#479	C₂×C₆₇	semidirect
381. C₂×#478	C₂×C₆₇	semidirect
382. C₂×#474	C₂×C₆₇	semidirect
383. C₂×#463	C₂×C₆₇	semidirect
384. C₂×#463	C₂×C₆₇	semidirect
386. C₂×#446	C₂×C₆₇	semidirect
387. C₂×#442	C₂×C₆₇	semidirect
388. C₂×#440	C₂×C₆₇	semidirect
389. C₂×C₄×D₈	C₂×C₆₇	semidirect
390. C₆₇	C₂×#3370	direct (N × H)
395. #559	C₂²×C₆₇	semidirect
397. #554	C₂²×C₆₇	semidirect
419. #490	C₂²×C₆₇	semidirect
420. #489	C₂²×C₆₇	semidirect
421. #488	C₂²×C₆₇	semidirect
422. #479	C₂²×C₆₇	semidirect
423. #478	C₂²×C₆₇	semidirect
424. #474	C₂²×C₆₇	semidirect
425. #463	C₂²×C₆₇	semidirect
426. #463	C₂²×C₆₇	semidirect
428. #446	C₂²×C₆₇	semidirect
429. #442	C₂²×C₆₇	semidirect
430. #440	C₂²×C₆₇	semidirect
431. C₄×D₈	C₂²×C₆₇	semidirect
743. C₂	C₆₇×#3370	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#559×C₆₇	2
C₂×#554×C₆₇	2
C₆₇×#3370	2
C₂×#490×C₆₇	2
C₂×#489×C₆₇	2
C₂×#488×C₆₇	2
C₂×#479×C₆₇	2
C₂×#478×C₆₇	2
C₂×#474×C₆₇	2
C₂×#463×C₆₇	2
C₂×#459×C₆₇	2
C₂×#446×C₆₇	2
C₂×#442×C₆₇	2
C₂×#440×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#3370	67

Subgroups — C2×C67×#3370 #30740563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3370 #30740563