Subgroups — C₂×C₃₇×#3100 #22681780

Order 9472.

2850 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3100	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₇×#480	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#474	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₇×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₇×#447	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₈×C₃₇	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₃₇	—	2	1	no	—
11	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₃₇	—	2	1	no	—
13	C₂²×D₈×C₃₇	C₂²	1	4	yes	—
14	C₃₇×#532	—	2	4	no	—
15	C₃₇×#532	C₂²	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₃₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#124×C₃₇	—	2	1	no	—
19	C₂×#121×C₃₇	—	2	1	no	—
20	C₂×#121×C₃₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₃₇	—	2	1	no	—
22	C₂×C₄×D₄×C₃₇	—	2	4	no	—
23	C₂×C₄×D₄×C₃₇	—	2	1	no	—
24	C₂×C₄×D₄×C₃₇	—	2	1	no	—
25	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₃₇	C₂²	1	8	yes	complemented
28	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	complemented
29	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₃₇	—	2	1	no	—
31	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
32	C₃₇×#480	C₂²	1	16	yes	complemented
33	C₃₇×#474	C₂²	1	16	yes	complemented
34	C₃₇×#459	C₂²	1	16	yes	complemented
35	C₃₇×#447	C₂²	1	16	yes	complemented
36	C₄×D₈×C₃₇	C₂²	1	32	yes	complemented
37	C₃₇×#431	C₂²	1	8	yes	complemented
38	C₂×#107×C₃₇	C₂²	1	4	yes	complemented
39	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	complemented
40	C₂×#102×C₃₇	C₂²	1	4	yes	—
41	C₂×#102×C₃₇	C₂²	1	4	yes	complemented
42	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₃₇	C₂²	1	2	yes	complemented
44	C₂⁵×C₃₇	—	2	1	no	—
45	C₂×#41×C₃₇	—	2	8	no	—
46	C₂×#41×C₃₇	—	4	8	no	—
47	C₂²×Q₈×C₃₇	—	2	1	no	—
48	C₂²×D₄×C₃₇	—	2	8	no	—
49	C₂²×D₄×C₃₇	—	2	2	no	—
50	C₂²×D₄×C₃₇	—	2	1	no	—
51	C₂²×D₄×C₃₇	—	2	2	no	—
52	C₂²×D₄×C₃₇	—	2	1	no	—
53	C₂²×D₄×C₃₇	—	2	1	no	—
54	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
55	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
56	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₃₇	—	2	1	no	—
58	C₂³×C₄×C₃₇	—	2	2	no	—
59	C₂³×C₄×C₃₇	—	2	8	no	—
60	C₂³×C₄×C₃₇	—	2	2	no	—
61	C₂³×C₄×C₃₇	—	2	2	no	—
62	C₂³×C₄×C₃₇	—	4	8	no	—
63	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
66	C₂×D₈×C₃₇	—	2	16	no	—
67	C₂×D₈×C₃₇	C₂³	1	16	yes	—
68	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
69	C₄⋊Q₈×C₃₇	—	2	2	no	—
70	C₄⋊Q₈×C₃₇	C₂³	1	4	yes	complemented
71	#127×C₃₇	—	2	2	no	—
72	#127×C₃₇	C₂³	1	4	yes	complemented
73	#124×C₃₇	—	2	8	no	—
74	#121×C₃₇	—	2	8	no	—
75	#121×C₃₇	—	2	4	no	—
76	#121×C₃₇	C₂³	1	8	yes	—
77	C₄×D₄×C₃₇	—	2	4	no	—
78	C₄×D₄×C₃₇	—	2	8	no	—
79	C₄×D₄×C₃₇	—	2	4	no	—
80	C₄×D₄×C₃₇	—	2	4	no	—
81	C₄×D₄×C₃₇	—	2	8	no	—
82	C₄×D₄×C₃₇	—	2	8	no	—
83	C₄×D₄×C₃₇	C₂³	1	8	yes	—
84	C₄×D₄×C₃₇	C₂³	1	8	yes	—
85	C₄×D₄×C₃₇	C₂³	1	8	yes	complemented
86	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₃₇	—	2	8	no	—
97	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₃₇	D₄	1	4	yes	—
99	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
102	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
103	#107×C₃₇	C₂³	1	16	yes	complemented
104	C₄⋊C₈×C₃₇	C₂³	1	8	yes	complemented
105	#102×C₃₇	C₂³	1	16	yes	—
106	#102×C₃₇	C₂³	1	16	yes	complemented
107	C₂²⋊C₈×C₃₇	C₂³	1	8	yes	—
108	C₄×C₈×C₃₇	C₂³	1	8	yes	complemented
109	C₂⁴×C₃₇	—	2	8	no	—
110	C₂⁴×C₃₇	—	2	4	no	—
111	C₂⁴×C₃₇	—	2	2	no	—
112	C₂⁴×C₃₇	—	2	2	no	—
113	C₂⁴×C₃₇	—	4	4	no	—
114	C₂⁴×C₃₇	—	4	4	no	—
115	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
116	#41×C₃₇	—	4	32	no	—
117	C₂×Q₈×C₃₇	—	2	4	no	—
118	C₂×Q₈×C₃₇	—	4	4	no	—
119	C₂×D₄×C₃₇	—	2	8	no	—
120	C₂×D₄×C₃₇	—	2	16	no	—
121	C₂×D₄×C₃₇	—	2	16	no	—
122	C₂×D₄×C₃₇	—	2	8	no	—
123	C₂×D₄×C₃₇	—	2	4	no	—
124	C₂×D₄×C₃₇	—	2	2	no	—
125	C₂×D₄×C₃₇	—	2	2	no	—
126	C₂×D₄×C₃₇	—	2	4	no	—
127	C₂×D₄×C₃₇	—	2	4	no	—
128	C₂×D₄×C₃₇	—	2	4	no	—
129	C₂×D₄×C₃₇	—	2	8	no	—
130	C₂×D₄×C₃₇	—	4	4	no	—
131	C₂×D₄×C₃₇	—	4	8	no	—
132	C₂×D₄×C₃₇	—	4	4	no	—
133	C₂×D₄×C₃₇	#41	1	8	yes	complemented
134	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
135	C₂×D₄×C₃₇	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₃₇	—	2	4	no	—
137	C₂²×C₄×C₃₇	—	2	4	no	—
138	C₂²×C₄×C₃₇	—	2	2	no	—
139	C₂²×C₄×C₃₇	—	2	2	no	—
140	C₂²×C₄×C₃₇	—	2	8	no	—
141	C₂²×C₄×C₃₇	—	2	8	no	—
142	C₂²×C₄×C₃₇	—	2	8	no	—
143	C₂²×C₄×C₃₇	—	4	2	no	—
144	C₂²×C₄×C₃₇	—	4	4	no	—
145	C₂²×C₄×C₃₇	—	4	8	no	—
146	C₂²×C₄×C₃₇	—	4	8	no	—
147	C₂²×C₄×C₃₇	—	4	8	no	—
148	C₂²×C₄×C₃₇	—	4	32	no	—
149	C₂²×C₄×C₃₇	D₈	1	8	yes	complemented
150	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
160	D₈×C₃₇	—	2	32	no	—
161	C₂×C₈×C₃₇	—	2	8	no	—
162	C₂×C₈×C₃₇	C₂⁴	1	8	yes	—
163	C₄⋊C₄×C₃₇	—	2	4	no	—
164	C₄⋊C₄×C₃₇	—	2	2	no	—
165	C₄⋊C₄×C₃₇	—	2	4	no	—
166	C₄⋊C₄×C₃₇	—	2	2	no	—
167	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₃₇	—	2	8	no	—
170	C₂²⋊C₄×C₃₇	—	2	8	no	—
171	C₂²⋊C₄×C₃₇	—	2	8	no	—
172	C₂²⋊C₄×C₃₇	—	2	8	no	—
173	C₄²×C₃₇	C₂×D₄	1	4	yes	—
174	C₄²×C₃₇	C₂×D₄	1	2	yes	—
175	C₄²×C₃₇	C₂×D₄	1	4	yes	—
176	C₄²×C₃₇	C₂×D₄	1	2	yes	—
177	C₄²×C₃₇	C₂⁴	1	2	yes	—
178	C₄²×C₃₇	C₂⁴	1	2	yes	—
179	C₂³×C₃₇	—	2	2	no	—
180	C₂³×C₃₇	—	2	2	no	—
181	C₂³×C₃₇	—	2	16	no	—
182	C₂³×C₃₇	—	2	8	no	—
183	C₂³×C₃₇	—	2	4	no	—
184	C₂³×C₃₇	—	2	4	no	—
185	C₂³×C₃₇	—	4	32	no	—
186	C₂³×C₃₇	—	4	8	no	—
187	C₂³×C₃₇	—	4	8	no	—
188	C₂³×C₃₇	—	4	4	no	—
189	C₂³×C₃₇	—	4	4	no	—
190	C₂³×C₃₇	—	4	4	no	—
191	C₂³×C₃₇	—	4	4	no	—
192	C₂³×C₃₇	—	4	4	no	—
193	C₂³×C₃₇	C₂×D₈	1	4	yes	—
194	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
195	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₃₇	—	4	8	no	—
197	D₄×C₃₇	—	2	16	no	—
198	D₄×C₃₇	—	2	8	no	—
199	D₄×C₃₇	—	2	4	no	—
200	D₄×C₃₇	—	2	8	no	—
201	D₄×C₃₇	—	4	8	no	—
202	D₄×C₃₇	—	4	16	no	—
203	D₄×C₃₇	—	4	4	no	—
204	D₄×C₃₇	—	4	8	no	—
205	D₄×C₃₇	C₂×#41	1	8	yes	complemented
206	C₂×C₄×C₃₇	—	2	2	no	—
207	C₂×C₄×C₃₇	—	2	2	no	—
208	C₂×C₄×C₃₇	—	2	2	no	—
209	C₂×C₄×C₃₇	—	2	4	no	—
210	C₂×C₄×C₃₇	—	2	4	no	—
211	C₂×C₄×C₃₇	—	2	4	no	—
212	C₂×C₄×C₃₇	—	2	4	no	—
213	C₂×C₄×C₃₇	—	4	4	no	—
214	C₂×C₄×C₃₇	—	4	8	no	—
215	C₂×C₄×C₃₇	—	4	4	no	—
216	C₂×C₄×C₃₇	—	4	4	no	—
217	C₂×C₄×C₃₇	—	4	16	no	—
218	C₂×C₄×C₃₇	—	4	16	no	—
219	C₂×C₄×C₃₇	—	4	16	no	—
220	C₂×C₄×C₃₇	C₂×D₈	1	4	yes	—
221	C₂×C₄×C₃₇	C₂×D₈	1	4	yes	—
222	C₂×C₄×C₃₇	C₂×D₈	1	16	yes	complemented
223	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
230	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
231	C₈×C₃₇	—	2	8	no	—
232	C₂×#3100	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₃₇	—	2	8	no	—
234	C₂²×C₃₇	—	2	2	no	—
235	C₂²×C₃₇	—	2	2	no	—
236	C₂²×C₃₇	—	2	8	no	—
237	C₂²×C₃₇	—	4	32	no	—
238	C₂²×C₃₇	—	4	16	no	—
239	C₂²×C₃₇	—	4	4	no	—
240	C₂²×C₃₇	—	4	4	no	—
241	C₂²×C₃₇	—	4	4	no	—
242	C₂²×C₃₇	—	4	4	no	—
243	C₂²×C₃₇	—	4	4	no	—
244	C₂²×C₃₇	—	8	8	no	—
245	C₂²×C₃₇	#525	1	2	yes	—
246	C₂²×C₃₇	C₂²×D₈	1	4	yes	—
247	C₂²×C₃₇	C₂²×D₈	1	2	yes	—
248	C₂²×C₃₇	#575	1	2	yes	—
249	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₃₇	—	2	2	no	—
251	C₄×C₃₇	—	2	2	no	—
252	C₄×C₃₇	—	2	2	no	—
253	C₄×C₃₇	—	4	4	no	—
254	C₄×C₃₇	—	4	4	no	—
255	C₄×C₃₇	#525	1	2	yes	—
256	C₄×C₃₇	C₂²×D₈	1	4	yes	—
257	C₄×C₃₇	C₂²×D₈	1	4	yes	—
258	C₄×C₃₇	C₂²×#41	1	2	yes	—
259	C₂×#532	C₂×C₃₇	1	1	yes	characteristic, complemented
260	C₂²×C₄×D₄	C₂×C₃₇	1	1	yes	characteristic, complemented
261	#3100	C₂×C₃₇	1	16	yes	direct product factor
262	C₂×#480	C₂×C₃₇	1	2	yes	complemented
263	C₂×#474	C₂×C₃₇	1	2	yes	complemented
264	C₂×#459	C₂×C₃₇	1	2	yes	complemented
265	C₂×#447	C₂×C₃₇	1	2	yes	complemented
266	C₂×C₄×D₈	C₂×C₃₇	1	4	yes	complemented
267	C₂×#431	C₂×C₃₇	1	1	yes	characteristic, complemented
268	C₂×C₃₇	—	2	4	no	—
269	C₂×C₃₇	—	4	8	no	—
270	C₂×C₃₇	—	8	4	no	—
271	C₂×C₃₇	#3100	1	4	yes	direct product factor
272	C₂×C₃₇	C₂×#525	1	1	yes	characteristic
273	C₂×C₃₇	C₂³×D₈	1	1	yes	characteristic
274	C₂×C₃₇	C₂×#575	1	1	yes	characteristic
275	C₂²×#41	—	2	1	no	—
276	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
277	C₂⁴×C₄	—	2	1	no	—
278	C₂²×D₈	C₂²×C₃₇	1	4	yes	—
279	#532	—	2	4	no	—
280	#532	C₂²×C₃₇	1	8	yes	complemented
281	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
282	C₂×#127	C₂²×C₃₇	1	1	yes	characteristic, complemented
283	C₂×#124	—	2	1	no	—
284	C₂×#121	—	2	1	no	—
285	C₂×#121	C₂²×C₃₇	1	2	yes	—
286	C₂×C₄×D₄	—	2	1	no	—
287	C₂×C₄×D₄	—	2	1	no	—
288	C₂×C₄×D₄	—	2	4	no	—
289	C₂×C₄×D₄	—	2	1	no	—
290	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
291	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
292	C₂×C₄×D₄	C₂²×C₃₇	1	8	yes	complemented
293	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	complemented
294	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	—	2	1	no	—
296	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
297	#480	C₂²×C₃₇	1	16	yes	complemented
298	#474	C₂²×C₃₇	1	16	yes	complemented
299	#459	C₂²×C₃₇	1	16	yes	complemented
300	#447	C₂²×C₃₇	1	16	yes	complemented
301	C₄×D₈	C₂²×C₃₇	1	32	yes	complemented
302	#431	C₂²×C₃₇	1	8	yes	complemented
303	C₂×#107	C₂²×C₃₇	1	4	yes	complemented
304	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	complemented
305	C₂×#102	C₂²×C₃₇	1	4	yes	—
306	C₂×#102	C₂²×C₃₇	1	4	yes	complemented
307	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
308	C₂×C₄×C₈	C₂²×C₃₇	1	2	yes	complemented
309	C₃₇	C₂×#3100	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁵	—	2	1	no	—
311	C₂×#41	—	2	8	no	—
312	C₂×#41	—	4	8	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×D₄	—	2	8	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
321	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
322	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	2	no	—
326	C₂³×C₄	—	2	8	no	—
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	4	8	no	—
329	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
330	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
332	C₂×D₈	—	2	16	no	—
333	C₂×D₈	C₂³×C₃₇	1	16	yes	—
334	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	C₂³×C₃₇	1	4	yes	complemented
337	#127	—	2	2	no	—
338	#127	C₂³×C₃₇	1	4	yes	complemented
339	#124	—	2	8	no	—
340	#121	—	2	8	no	—
341	#121	—	2	4	no	—
342	#121	C₂³×C₃₇	1	8	yes	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	—	2	8	no	—
346	C₄×D₄	—	2	8	no	—
347	C₄×D₄	—	2	8	no	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	C₂³×C₃₇	1	8	yes	—
350	C₄×D₄	C₂³×C₃₇	1	8	yes	—
351	C₄×D₄	C₂³×C₃₇	1	8	yes	complemented
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	8	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₃₇	1	4	yes	—
366	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
369	#107	C₂³×C₃₇	1	16	yes	complemented
370	C₄⋊C₈	C₂³×C₃₇	1	8	yes	complemented
371	#102	C₂³×C₃₇	1	16	yes	—
372	#102	C₂³×C₃₇	1	16	yes	complemented
373	C₂²⋊C₈	C₂³×C₃₇	1	8	yes	—
374	C₄×C₈	C₂³×C₃₇	1	8	yes	complemented
375	C₂⁴	—	2	8	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	—	4	4	no	—
381	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
382	#41	—	4	32	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	2	16	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	#41×C₃₇	1	8	yes	complemented
400	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
401	C₂×D₄	C₂⁴×C₃₇	1	4	yes	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	8	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	—	4	32	no	—
415	C₂²×C₄	D₈×C₃₇	1	8	yes	complemented
416	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
421	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
426	D₈	—	2	32	no	—
427	C₂×C₈	—	2	8	no	—
428	C₂×C₈	C₂⁴×C₃₇	1	8	yes	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
434	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₄²	C₂×D₄×C₃₇	1	4	yes	—
440	C₄²	C₂×D₄×C₃₇	1	2	yes	—
441	C₄²	C₂×D₄×C₃₇	1	4	yes	—
442	C₄²	C₂×D₄×C₃₇	1	2	yes	—
443	C₄²	C₂⁴×C₃₇	1	2	yes	—
444	C₄²	C₂⁴×C₃₇	1	2	yes	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	16	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	32	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	C₂×D₈×C₃₇	1	4	yes	—
460	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
461	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
462	Q₈	—	4	8	no	—
463	D₄	—	2	16	no	—
464	D₄	—	2	8	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	8	no	—
467	D₄	—	4	8	no	—
468	D₄	—	4	16	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	8	no	—
471	D₄	C₂×#41×C₃₇	1	8	yes	complemented
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	8	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	16	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	C₂×D₈×C₃₇	1	4	yes	—
487	C₂×C₄	C₂×D₈×C₃₇	1	4	yes	—
488	C₂×C₄	C₂×D₈×C₃₇	1	16	yes	complemented
489	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
495	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
496	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
497	C₈	—	2	8	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	8	no	—
502	C₂²	—	4	32	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	8	8	no	—
510	C₂²	C₃₇×#525	1	2	yes	—
511	C₂²	C₂²×D₈×C₃₇	1	4	yes	—
512	C₂²	C₂²×D₈×C₃₇	1	2	yes	—
513	C₂²	C₃₇×#575	1	2	yes	—
514	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	C₃₇×#525	1	2	yes	—
521	C₄	C₂²×D₈×C₃₇	1	4	yes	—
522	C₄	C₂²×D₈×C₃₇	1	4	yes	—
523	C₄	C₂²×#41×C₃₇	1	2	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	4	8	no	—
526	C₂	—	8	4	no	—
527	C₂	C₃₇×#3100	1	4	yes	direct product factor
528	C₂	C₂×C₃₇×#525	1	1	yes	characteristic
529	C₂	C₂³×D₈×C₃₇	1	1	yes	characteristic
530	C₂	C₂×C₃₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
socle	C₂³×C₃₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#532	C₂	semidirect
2. C₂²×C₄×D₄×C₃₇	C₂	semidirect
3. C₃₇×#3100	C₂	direct (N × H)
4. C₂×C₃₇×#480	C₂	semidirect
5. C₂×C₃₇×#474	C₂	semidirect
6. C₂×C₃₇×#459	C₂	semidirect
7. C₂×C₃₇×#447	C₂	semidirect
8. C₂×C₄×D₈×C₃₇	C₂	semidirect
9. C₂×C₃₇×#431	C₂	semidirect
15. C₃₇×#532	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
17. C₂×#127×C₃₇	C₂²	semidirect
27. C₂×C₄×D₄×C₃₇	C₂²	semidirect
28. C₂×C₄×D₄×C₃₇	C₂²	semidirect
32. C₃₇×#480	C₂²	semidirect
33. C₃₇×#474	C₂²	semidirect
34. C₃₇×#459	C₂²	semidirect
35. C₃₇×#447	C₂²	semidirect
36. C₄×D₈×C₃₇	C₂²	semidirect
37. C₃₇×#431	C₂²	semidirect
38. C₂×#107×C₃₇	C₂²	semidirect
39. C₂×C₄⋊C₈×C₃₇	C₂²	semidirect
41. C₂×#102×C₃₇	C₂²	semidirect
43. C₂×C₄×C₈×C₃₇	C₂²	semidirect
70. C₄⋊Q₈×C₃₇	C₂³	semidirect
72. #127×C₃₇	C₂³	semidirect
85. C₄×D₄×C₃₇	C₂³	semidirect
103. #107×C₃₇	C₂³	semidirect
104. C₄⋊C₈×C₃₇	C₂³	semidirect
106. #102×C₃₇	C₂³	semidirect
108. C₄×C₈×C₃₇	C₂³	semidirect
133. C₂×D₄×C₃₇	#41	semidirect
149. C₂²×C₄×C₃₇	D₈	semidirect
205. D₄×C₃₇	C₂×#41	semidirect
222. C₂×C₄×C₃₇	C₂×D₈	semidirect
232. C₂×#3100	C₃₇	direct (N × H)
259. C₂×#532	C₂×C₃₇	semidirect
260. C₂²×C₄×D₄	C₂×C₃₇	semidirect
261. #3100	C₂×C₃₇	direct (N × H)
262. C₂×#480	C₂×C₃₇	semidirect
263. C₂×#474	C₂×C₃₇	semidirect
264. C₂×#459	C₂×C₃₇	semidirect
265. C₂×#447	C₂×C₃₇	semidirect
266. C₂×C₄×D₈	C₂×C₃₇	semidirect
267. C₂×#431	C₂×C₃₇	semidirect
271. C₂×C₃₇	#3100	direct (N × H)
280. #532	C₂²×C₃₇	semidirect
281. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
282. C₂×#127	C₂²×C₃₇	semidirect
292. C₂×C₄×D₄	C₂²×C₃₇	semidirect
293. C₂×C₄×D₄	C₂²×C₃₇	semidirect
297. #480	C₂²×C₃₇	semidirect
298. #474	C₂²×C₃₇	semidirect
299. #459	C₂²×C₃₇	semidirect
300. #447	C₂²×C₃₇	semidirect
301. C₄×D₈	C₂²×C₃₇	semidirect
302. #431	C₂²×C₃₇	semidirect
303. C₂×#107	C₂²×C₃₇	semidirect
304. C₂×C₄⋊C₈	C₂²×C₃₇	semidirect
306. C₂×#102	C₂²×C₃₇	semidirect
308. C₂×C₄×C₈	C₂²×C₃₇	semidirect
309. C₃₇	C₂×#3100	direct (N × H)
336. C₄⋊Q₈	C₂³×C₃₇	semidirect
338. #127	C₂³×C₃₇	semidirect
351. C₄×D₄	C₂³×C₃₇	semidirect
369. #107	C₂³×C₃₇	semidirect
370. C₄⋊C₈	C₂³×C₃₇	semidirect
372. #102	C₂³×C₃₇	semidirect
374. C₄×C₈	C₂³×C₃₇	semidirect
399. C₂×D₄	#41×C₃₇	semidirect
415. C₂²×C₄	D₈×C₃₇	semidirect
471. D₄	C₂×#41×C₃₇	semidirect
488. C₂×C₄	C₂×D₈×C₃₇	semidirect
527. C₂	C₃₇×#3100	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×C₃₇×#532	2
C₂²×C₄×D₄×C₃₇	2
C₃₇×#3100	2
C₂×C₃₇×#480	2
C₂×C₃₇×#474	2
C₂×C₃₇×#459	2
C₂×C₃₇×#447	2
C₂×C₄×D₈×C₃₇	2
C₂×C₃₇×#431	2
C₂×#3100	37

Subgroups — C2×C37×#3100 #22681780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#3100 #22681780