Subgroups — C₃₇×#60523 #22681776

Order 9472.

2184 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3488	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3099	C₂	1	3	yes	maximal, complemented
4	C₃₇×#3098	C₂	1	3	yes	maximal, complemented
5	C₃₇×#3096	C₂	1	3	yes	maximal, complemented
6	C₃₇×#3096	C₂	1	3	yes	maximal, complemented
7	C₃₇×#3094	C₂	1	3	yes	maximal, complemented
8	C₃₇×#3093	C₂	1	3	yes	maximal, complemented
9	C₃₇×#3091	C₂	1	3	yes	maximal, complemented
10	C₂×C₃₇×#482	C₂	1	3	yes	maximal, complemented
11	C₃₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₃₇	C₂²	1	1	yes	characteristic
20	C₃₇×#550	—	2	1	no	—
21	C₃₇×#548	—	2	1	no	—
22	C₃₇×#546	—	2	3	no	—
23	D₄²×C₃₇	—	2	3	no	—
24	C₃₇×#537	C₂²	1	3	yes	—
25	C₃₇×#535	C₂²	1	3	yes	—
26	C₃₇×#525	C₂²	1	3	yes	—
27	C₂×#121×C₃₇	C₂²	1	3	yes	—
28	C₃₇×#520	C₂²	1	1	yes	characteristic
29	C₃₇×#520	C₂²	1	1	yes	characteristic
30	C₃₇×#520	C₂²	1	1	yes	characteristic
31	C₃₇×#520	C₂²	1	3	yes	complemented
32	C₃₇×#520	C₂²	1	3	yes	complemented
33	C₃₇×#519	—	2	1	no	—
34	C₃₇×#518	—	2	3	no	—
35	C₄×#41×C₃₇	—	2	3	no	—
36	C₄×#41×C₃₇	—	2	1	no	—
37	C₂×#117×C₃₇	C₂²	1	3	yes	complemented
38	C₂×#117×C₃₇	C₂²	1	3	yes	complemented
39	C₃₇×#485	C₂²	1	1	yes	characteristic, complemented
40	C₃₇×#485	C₂²	1	3	yes	complemented
41	C₃₇×#485	C₂²	1	6	yes	complemented
42	C₃₇×#484	C₂²	1	3	yes	complemented
43	C₃₇×#483	C₂²	1	3	yes	complemented
44	C₃₇×#482	C₂²	1	3	yes	complemented
45	C₃₇×#482	C₂²	1	6	yes	complemented
46	C₃₇×#482	C₂²	1	6	yes	complemented
47	C₃₇×#482	C₂²	1	6	yes	complemented
48	C₃₇×#482	C₂²	1	3	yes	complemented
49	C₃₇×#482	C₂²	1	6	yes	complemented
50	C₃₇×#481	C₂²	1	3	yes	complemented
51	C₃₇×#481	C₂²	1	6	yes	complemented
52	C₃₇×#480	C₂²	1	3	yes	complemented
53	C₃₇×#480	C₂²	1	6	yes	complemented
54	C₃₇×#428	C₂²	1	3	yes	complemented
55	C₃₇×#428	C₂²	1	3	yes	complemented
56	C₃₇×#428	C₂²	1	3	yes	complemented
57	C₃₇×#428	C₂²	1	3	yes	complemented
58	C₃₇×#427	C₂²	1	3	yes	complemented
59	C₃₇×#427	C₂²	1	3	yes	complemented
60	C₂×#107×C₃₇	C₂²	1	3	yes	complemented
61	C₂×#106×C₃₇	C₂²	1	3	yes	complemented
62	C₃₇×#418	C₂²	1	3	yes	complemented
63	C₃₇×#418	C₂²	1	3	yes	complemented
64	C₃₇×#417	C₂²	1	3	yes	complemented
65	C₃₇×#417	C₂²	1	3	yes	complemented
66	C₃₇×#416	C₂²	1	3	yes	complemented
67	C₃₇×#416	C₂²	1	3	yes	complemented
68	C₂×#102×C₃₇	C₂²	1	3	yes	complemented
69	C₂×#102×C₃₇	C₂²	1	3	yes	complemented
70	C₃₇×#408	C₂²	1	3	yes	complemented
71	C₃₇×#408	C₂²	1	3	yes	complemented
72	C₃₇×#407	C₂²	1	3	yes	complemented
73	C₂×C₂²⋊C₈×C₃₇	C₂²	1	3	yes	complemented
74	H(5,𝔽₂)×C₃₇	—	2	4	no	—
75	H(5,𝔽₂)×C₃₇	—	2	4	no	—
76	C₂×#41×C₃₇	—	2	4	no	—
77	C₂×#41×C₃₇	—	2	4	no	—
78	C₂×#41×C₃₇	—	2	1	no	—
79	C₂×#41×C₃₇	D₄	1	3	yes	—
80	C₂×#41×C₃₇	D₄	1	1	yes	characteristic
81	C₂×#41×C₃₇	C₂³	1	3	yes	—
82	C₂×#41×C₃₇	C₂³	1	3	yes	—
83	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₃₇	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₃₇	—	2	3	no	—
86	C₂²×D₄×C₃₇	—	2	3	no	—
87	C₂²×D₄×C₃₇	D₄	1	3	yes	—
88	C₂²×D₄×C₃₇	C₂³	1	3	yes	—
89	C₂³×C₄×C₃₇	C₂³	1	3	yes	—
90	#131×C₃₇	—	2	4	no	—
91	#131×C₃₇	—	2	4	no	—
92	C₂×M₁₆×C₃₇	C₂³	1	3	yes	—
93	C₂×M₁₆×C₃₇	C₂³	1	3	yes	—
94	C₂²×C₈×C₃₇	C₂³	1	3	yes	—
95	C₂²×C₈×C₃₇	C₂³	1	3	yes	—
96	#127×C₃₇	—	2	3	no	—
97	#124×C₃₇	—	2	3	no	—
98	#123×C₃₇	—	2	3	no	—
99	C₂²⋊Q₈×C₃₇	—	2	3	no	—
100	C₂²⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
101	C₂²⋊Q₈×C₃₇	C₂³	1	3	yes	—
102	#121×C₃₇	—	2	6	no	—
103	#121×C₃₇	—	2	3	no	—
104	#121×C₃₇	—	2	3	no	—
105	#121×C₃₇	—	2	3	no	—
106	#121×C₃₇	C₂³	1	3	yes	—
107	#121×C₃₇	C₂³	1	6	yes	—
108	#121×C₃₇	C₂³	1	3	yes	—
109	#120×C₃₇	—	2	3	no	—
110	#120×C₃₇	—	2	6	no	—
111	C₄×Q₈×C₃₇	—	2	1	no	—
112	C₄×Q₈×C₃₇	—	2	1	no	—
113	C₄×Q₈×C₃₇	—	2	3	no	—
114	C₄×Q₈×C₃₇	—	2	3	no	—
115	C₄×Q₈×C₃₇	—	2	1	no	—
116	C₄×D₄×C₃₇	—	2	3	no	—
117	C₄×D₄×C₃₇	—	2	3	no	—
118	C₄×D₄×C₃₇	—	2	3	no	—
119	C₄×D₄×C₃₇	—	2	6	no	—
120	C₄×D₄×C₃₇	—	2	6	no	—
121	C₄×D₄×C₃₇	—	2	3	no	—
122	C₄×D₄×C₃₇	—	2	3	no	—
123	C₄×D₄×C₃₇	—	2	3	no	—
124	C₄×D₄×C₃₇	—	2	3	no	—
125	#117×C₃₇	—	2	3	no	—
126	#117×C₃₇	—	2	3	no	—
127	#117×C₃₇	—	2	3	no	—
128	#117×C₃₇	—	2	3	no	—
129	#117×C₃₇	C₂³	1	3	yes	—
130	#117×C₃₇	C₂³	1	3	yes	—
131	#117×C₃₇	C₂³	1	3	yes	—
132	#117×C₃₇	C₂³	1	6	yes	—
133	#117×C₃₇	C₂³	1	3	yes	—
134	#117×C₃₇	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
136	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
137	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
138	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
139	C₂×C₄⋊C₄×C₃₇	C₂³	1	3	yes	—
140	C₂×C₂²⋊C₄×C₃₇	—	2	3	no	—
141	C₂×C₂²⋊C₄×C₃₇	—	2	3	no	—
142	C₂×C₂²⋊C₄×C₃₇	—	2	3	no	—
143	C₂×C₄²×C₃₇	—	2	3	no	—
144	C₂×C₄²×C₃₇	—	2	3	no	—
145	#107×C₃₇	C₂³	1	3	yes	—
146	#107×C₃₇	C₂³	1	6	yes	—
147	#107×C₃₇	C₂³	1	1	yes	characteristic
148	#107×C₃₇	C₂³	1	3	yes	—
149	#107×C₃₇	C₂³	1	3	yes	—
150	#106×C₃₇	C₂³	1	3	yes	—
151	#106×C₃₇	C₂³	1	6	yes	—
152	#106×C₃₇	C₂³	1	1	yes	characteristic
153	#106×C₃₇	C₂³	1	3	yes	—
154	#106×C₃₇	C₂³	1	3	yes	—
155	#103×C₃₇	C₂³	1	1	yes	characteristic
156	#103×C₃₇	C₂³	1	1	yes	characteristic
157	#103×C₃₇	C₂³	1	3	yes	—
158	#103×C₃₇	C₂³	1	3	yes	—
159	#102×C₃₇	C₂³	1	3	yes	—
160	#102×C₃₇	C₂³	1	3	yes	—
161	#102×C₃₇	C₂³	1	6	yes	—
162	#102×C₃₇	C₂³	1	6	yes	—
163	#102×C₃₇	C₂³	1	3	yes	—
164	#102×C₃₇	C₂³	1	3	yes	—
165	C₂²⋊C₈×C₃₇	C₂³	1	1	yes	characteristic
166	C₂²⋊C₈×C₃₇	C₂³	1	3	yes	—
167	C₂²⋊C₈×C₃₇	C₂³	1	3	yes	—
168	C₂²⋊C₈×C₃₇	C₂³	1	3	yes	—
169	C₂²⋊C₈×C₃₇	C₂³	1	6	yes	—
170	C₂⁴×C₃₇	—	2	3	no	—
171	C₂⁴×C₃₇	C₂×D₄	1	3	yes	—
172	#41×C₃₇	—	2	4	no	—
173	#41×C₃₇	—	2	12	no	—
174	#41×C₃₇	—	2	6	no	—
175	#41×C₃₇	—	2	6	no	—
176	#41×C₃₇	—	2	6	no	—
177	#41×C₃₇	—	2	6	no	—
178	#41×C₃₇	—	4	4	no	—
179	#41×C₃₇	#41	1	4	yes	—
180	#41×C₃₇	#41	1	4	yes	—
181	C₂×Q₈×C₃₇	—	2	4	no	—
182	C₂×Q₈×C₃₇	C₂×D₄	1	3	yes	—
183	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₃₇	C₂⁴	1	1	yes	characteristic
185	C₂×D₄×C₃₇	—	2	12	no	—
186	C₂×D₄×C₃₇	—	2	3	no	—
187	C₂×D₄×C₃₇	—	2	3	no	—
188	C₂×D₄×C₃₇	—	2	3	no	—
189	C₂×D₄×C₃₇	—	2	6	no	—
190	C₂×D₄×C₃₇	—	2	3	no	—
191	C₂×D₄×C₃₇	—	2	6	no	—
192	C₂×D₄×C₃₇	—	2	6	no	—
193	C₂×D₄×C₃₇	—	4	12	no	—
194	C₂×D₄×C₃₇	—	8	6	no	—
195	C₂×D₄×C₃₇	C₂×D₄	1	6	yes	—
196	C₂×D₄×C₃₇	C₂×D₄	1	3	yes	—
197	C₂×D₄×C₃₇	C₂×D₄	1	3	yes	—
198	C₂×D₄×C₃₇	C₂⁴	1	3	yes	—
199	C₂²×C₄×C₃₇	—	2	6	no	—
200	C₂²×C₄×C₃₇	—	2	6	no	—
201	C₂²×C₄×C₃₇	—	2	3	no	—
202	C₂²×C₄×C₃₇	—	2	3	no	—
203	C₂²×C₄×C₃₇	—	2	3	no	—
204	C₂²×C₄×C₃₇	—	2	3	no	—
205	C₂²×C₄×C₃₇	—	2	3	no	—
206	C₂²×C₄×C₃₇	—	2	3	no	—
207	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
208	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
209	C₂²×C₄×C₃₇	C₂×D₄	1	3	yes	—
210	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
211	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₃₇	C₂⁴	1	3	yes	—
213	M₁₆×C₃₇	—	2	6	no	—
214	M₁₆×C₃₇	—	2	6	no	—
215	C₂×C₈×C₃₇	—	2	6	no	—
216	C₂×C₈×C₃₇	—	2	6	no	—
217	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₈×C₃₇	C₂⁴	1	3	yes	—
219	C₂×C₈×C₃₇	C₂⁴	1	3	yes	—
220	C₂×C₈×C₃₇	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₃₇	—	2	3	no	—
222	C₄⋊C₄×C₃₇	—	2	3	no	—
223	C₄⋊C₄×C₃₇	—	2	3	no	—
224	C₄⋊C₄×C₃₇	—	2	3	no	—
225	C₄⋊C₄×C₃₇	—	2	3	no	—
226	C₄⋊C₄×C₃₇	—	2	1	no	—
227	C₄⋊C₄×C₃₇	—	2	3	no	—
228	C₄⋊C₄×C₃₇	C₂⁴	1	3	yes	—
229	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₃₇	C₂⁴	1	3	yes	—
231	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₃₇	C₂⁴	1	3	yes	—
233	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
234	C₂²⋊C₄×C₃₇	—	2	3	no	—
235	C₂²⋊C₄×C₃₇	—	2	1	no	—
236	C₂²⋊C₄×C₃₇	—	2	6	no	—
237	C₂²⋊C₄×C₃₇	—	2	3	no	—
238	C₂²⋊C₄×C₃₇	—	2	3	no	—
239	C₂²⋊C₄×C₃₇	—	2	3	no	—
240	C₂²⋊C₄×C₃₇	—	2	1	no	—
241	C₂²⋊C₄×C₃₇	—	2	3	no	—
242	C₂²⋊C₄×C₃₇	—	2	3	no	—
243	C₂²⋊C₄×C₃₇	—	2	6	no	—
244	C₂²⋊C₄×C₃₇	—	2	3	no	—
245	C₄²×C₃₇	—	2	3	no	—
246	C₄²×C₃₇	—	2	1	no	—
247	C₄²×C₃₇	—	2	6	no	—
248	C₄²×C₃₇	—	2	3	no	—
249	C₄²×C₃₇	—	2	3	no	—
250	C₄²×C₃₇	—	2	3	no	—
251	C₂³×C₃₇	—	2	6	no	—
252	C₂³×C₃₇	—	2	3	no	—
253	C₂³×C₃₇	—	4	3	no	—
254	C₂³×C₃₇	—	4	3	no	—
255	C₂³×C₃₇	—	4	6	no	—
256	C₂³×C₃₇	—	8	3	no	—
257	C₂³×C₃₇	—	8	3	no	—
258	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
259	C₂³×C₃₇	C₂²×D₄	1	3	yes	—
260	C₂³×C₃₇	C₂²×D₄	1	3	yes	—
261	Q₈×C₃₇	—	2	6	no	—
262	Q₈×C₃₇	—	2	1	no	—
263	Q₈×C₃₇	—	2	1	no	—
264	Q₈×C₃₇	#123	1	4	yes	—
265	D₄×C₃₇	—	2	12	no	—
266	D₄×C₃₇	—	2	6	no	—
267	D₄×C₃₇	—	2	3	no	—
268	D₄×C₃₇	—	2	3	no	—
269	D₄×C₃₇	—	4	6	no	—
270	D₄×C₃₇	—	4	6	no	—
271	D₄×C₃₇	—	4	6	no	—
272	D₄×C₃₇	—	8	3	no	—
273	D₄×C₃₇	—	8	6	no	—
274	D₄×C₃₇	#123	1	12	yes	—
275	C₂×C₄×C₃₇	—	2	6	no	—
276	C₂×C₄×C₃₇	—	2	6	no	—
277	C₂×C₄×C₃₇	—	2	6	no	—
278	C₂×C₄×C₃₇	—	2	1	no	—
279	C₂×C₄×C₃₇	—	2	1	no	—
280	C₂×C₄×C₃₇	—	2	3	no	—
281	C₂×C₄×C₃₇	—	2	3	no	—
282	C₂×C₄×C₃₇	—	2	3	no	—
283	C₂×C₄×C₃₇	—	2	1	no	—
284	C₂×C₄×C₃₇	—	2	3	no	—
285	C₂×C₄×C₃₇	—	2	1	no	—
286	C₂×C₄×C₃₇	—	2	1	no	—
287	C₂×C₄×C₃₇	—	2	3	no	—
288	C₂×C₄×C₃₇	—	2	1	no	—
289	C₂×C₄×C₃₇	—	4	6	no	—
290	C₂×C₄×C₃₇	—	8	3	no	—
291	C₂×C₄×C₃₇	—	8	3	no	—
292	C₂×C₄×C₃₇	—	8	3	no	—
293	C₂×C₄×C₃₇	—	8	3	no	—
294	C₂×C₄×C₃₇	—	8	3	no	—
295	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
297	C₂×C₄×C₃₇	C₂²×D₄	1	3	yes	—
298	C₂×C₄×C₃₇	C₂×#41	1	6	yes	—
299	C₂×C₄×C₃₇	C₂×#41	1	6	yes	—
300	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
301	C₈×C₃₇	—	2	1	no	—
302	C₈×C₃₇	—	2	1	no	—
303	C₈×C₃₇	—	2	3	no	—
304	C₈×C₃₇	—	2	3	no	—
305	#60523	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₃₇	—	2	3	no	—
307	C₂²×C₃₇	—	2	3	no	—
308	C₂²×C₃₇	—	2	3	no	—
309	C₂²×C₃₇	—	2	1	no	—
310	C₂²×C₃₇	—	2	3	no	—
311	C₂²×C₃₇	—	2	1	no	—
312	C₂²×C₃₇	—	2	1	no	—
313	C₂²×C₃₇	—	2	3	no	—
314	C₂²×C₃₇	—	4	3	no	—
315	C₂²×C₃₇	—	4	3	no	—
316	C₂²×C₃₇	—	4	3	no	—
317	C₂²×C₃₇	—	8	6	no	—
318	C₂²×C₃₇	—	16	6	no	—
319	C₂²×C₃₇	C₂×#123	1	6	yes	—
320	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₃₇	—	2	1	no	—
322	C₄×C₃₇	—	2	3	no	—
323	C₄×C₃₇	—	4	3	no	—
324	C₄×C₃₇	—	4	1	no	—
325	C₄×C₃₇	—	4	1	no	—
326	C₄×C₃₇	—	4	3	no	—
327	C₄×C₃₇	—	4	1	no	—
328	C₄×C₃₇	—	4	3	no	—
329	C₄×C₃₇	—	4	1	no	—
330	C₄×C₃₇	C₂×#123	1	6	yes	—
331	C₄×C₃₇	C₂²×#41	1	1	yes	characteristic
332	C₄×C₃₇	C₂²×#41	1	1	yes	characteristic
333	#3488	C₂×C₃₇	1	1	yes	characteristic
334	#3428	C₂×C₃₇	1	1	yes	characteristic, complemented
335	#3099	C₂×C₃₇	1	3	yes	complemented
336	#3098	C₂×C₃₇	1	3	yes	complemented
337	#3096	C₂×C₃₇	1	3	yes	complemented
338	#3096	C₂×C₃₇	1	3	yes	complemented
339	#3094	C₂×C₃₇	1	3	yes	complemented
340	#3093	C₂×C₃₇	1	3	yes	complemented
341	#3091	C₂×C₃₇	1	3	yes	complemented
342	C₂×#482	C₂×C₃₇	1	3	yes	complemented
343	#2913	C₂×C₃₇	1	1	yes	characteristic, complemented
344	#2912	C₂×C₃₇	1	1	yes	characteristic, complemented
345	#2897	C₂×C₃₇	1	1	yes	characteristic, complemented
346	#2897	C₂×C₃₇	1	1	yes	characteristic, complemented
347	#2880	C₂×C₃₇	1	1	yes	characteristic, complemented
348	C₂×C₃₇	—	2	6	no	—
349	C₂×C₃₇	—	4	3	no	—
350	C₂×C₃₇	—	4	1	no	—
351	C₂×C₃₇	—	8	3	no	—
352	C₂×C₃₇	C₂²×#123	1	1	yes	characteristic
353	C₂×C₃₇	#3584	1	1	yes	characteristic
354	C₂×C₃₇	#3585	1	1	yes	characteristic
355	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	1	yes	characteristic
356	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic
357	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
358	C₂×#131	C₂²×C₃₇	1	1	yes	characteristic
359	#550	—	2	1	no	—
360	#548	—	2	1	no	—
361	#546	—	2	3	no	—
362	D₄²	—	2	3	no	—
363	#537	C₂²×C₃₇	1	3	yes	—
364	#535	C₂²×C₃₇	1	3	yes	—
365	#525	C₂²×C₃₇	1	3	yes	—
366	C₂×#121	C₂²×C₃₇	1	3	yes	—
367	#520	C₂²×C₃₇	1	1	yes	characteristic
368	#520	C₂²×C₃₇	1	1	yes	characteristic
369	#520	C₂²×C₃₇	1	1	yes	characteristic
370	#520	C₂²×C₃₇	1	3	yes	complemented
371	#520	C₂²×C₃₇	1	3	yes	complemented
372	#519	—	2	1	no	—
373	#518	—	2	3	no	—
374	C₄×#41	—	2	3	no	—
375	C₄×#41	—	2	1	no	—
376	C₂×#117	C₂²×C₃₇	1	3	yes	complemented
377	C₂×#117	C₂²×C₃₇	1	3	yes	complemented
378	#485	C₂²×C₃₇	1	1	yes	characteristic, complemented
379	#485	C₂²×C₃₇	1	3	yes	complemented
380	#485	C₂²×C₃₇	1	6	yes	complemented
381	#484	C₂²×C₃₇	1	3	yes	complemented
382	#483	C₂²×C₃₇	1	3	yes	complemented
383	#482	C₂²×C₃₇	1	3	yes	complemented
384	#482	C₂²×C₃₇	1	6	yes	complemented
385	#482	C₂²×C₃₇	1	6	yes	complemented
386	#482	C₂²×C₃₇	1	6	yes	complemented
387	#482	C₂²×C₃₇	1	3	yes	complemented
388	#482	C₂²×C₃₇	1	6	yes	complemented
389	#481	C₂²×C₃₇	1	3	yes	complemented
390	#481	C₂²×C₃₇	1	6	yes	complemented
391	#480	C₂²×C₃₇	1	3	yes	complemented
392	#480	C₂²×C₃₇	1	6	yes	complemented
393	#428	C₂²×C₃₇	1	3	yes	complemented
394	#428	C₂²×C₃₇	1	3	yes	complemented
395	#428	C₂²×C₃₇	1	3	yes	complemented
396	#428	C₂²×C₃₇	1	3	yes	complemented
397	#427	C₂²×C₃₇	1	3	yes	complemented
398	#427	C₂²×C₃₇	1	3	yes	complemented
399	C₂×#107	C₂²×C₃₇	1	3	yes	complemented
400	C₂×#106	C₂²×C₃₇	1	3	yes	complemented
401	#418	C₂²×C₃₇	1	3	yes	complemented
402	#418	C₂²×C₃₇	1	3	yes	complemented
403	#417	C₂²×C₃₇	1	3	yes	complemented
404	#417	C₂²×C₃₇	1	3	yes	complemented
405	#416	C₂²×C₃₇	1	3	yes	complemented
406	#416	C₂²×C₃₇	1	3	yes	complemented
407	C₂×#102	C₂²×C₃₇	1	3	yes	complemented
408	C₂×#102	C₂²×C₃₇	1	3	yes	complemented
409	#408	C₂²×C₃₇	1	3	yes	complemented
410	#408	C₂²×C₃₇	1	3	yes	complemented
411	#407	C₂²×C₃₇	1	3	yes	complemented
412	C₂×C₂²⋊C₈	C₂²×C₃₇	1	3	yes	complemented
413	C₃₇	#60523	1	1	yes	characteristic, direct product factor, Sylow
414	H(5,𝔽₂)	—	2	4	no	—
415	H(5,𝔽₂)	—	2	4	no	—
416	C₂×#41	—	2	4	no	—
417	C₂×#41	—	2	4	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	D₄×C₃₇	1	3	yes	—
420	C₂×#41	D₄×C₃₇	1	1	yes	characteristic
421	C₂×#41	C₂³×C₃₇	1	3	yes	—
422	C₂×#41	C₂³×C₃₇	1	3	yes	—
423	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
424	C₂²×Q₈	D₄×C₃₇	1	1	yes	characteristic
425	C₂²×D₄	—	2	3	no	—
426	C₂²×D₄	—	2	3	no	—
427	C₂²×D₄	D₄×C₃₇	1	3	yes	—
428	C₂²×D₄	C₂³×C₃₇	1	3	yes	—
429	C₂³×C₄	C₂³×C₃₇	1	3	yes	—
430	#131	—	2	4	no	—
431	#131	—	2	4	no	—
432	C₂×M₁₆	C₂³×C₃₇	1	3	yes	—
433	C₂×M₁₆	C₂³×C₃₇	1	3	yes	—
434	C₂²×C₈	C₂³×C₃₇	1	3	yes	—
435	C₂²×C₈	C₂³×C₃₇	1	3	yes	—
436	#127	—	2	3	no	—
437	#124	—	2	3	no	—
438	#123	—	2	3	no	—
439	C₂²⋊Q₈	—	2	3	no	—
440	C₂²⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
441	C₂²⋊Q₈	C₂³×C₃₇	1	3	yes	—
442	#121	—	2	6	no	—
443	#121	—	2	3	no	—
444	#121	—	2	3	no	—
445	#121	—	2	3	no	—
446	#121	C₂³×C₃₇	1	3	yes	—
447	#121	C₂³×C₃₇	1	6	yes	—
448	#121	C₂³×C₃₇	1	3	yes	—
449	#120	—	2	3	no	—
450	#120	—	2	6	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	—	2	1	no	—
453	C₄×Q₈	—	2	3	no	—
454	C₄×Q₈	—	2	3	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×D₄	—	2	3	no	—
457	C₄×D₄	—	2	3	no	—
458	C₄×D₄	—	2	6	no	—
459	C₄×D₄	—	2	6	no	—
460	C₄×D₄	—	2	3	no	—
461	C₄×D₄	—	2	3	no	—
462	C₄×D₄	—	2	3	no	—
463	C₄×D₄	—	2	3	no	—
464	C₄×D₄	—	2	3	no	—
465	#117	—	2	3	no	—
466	#117	—	2	3	no	—
467	#117	—	2	3	no	—
468	#117	—	2	3	no	—
469	#117	C₂³×C₃₇	1	3	yes	—
470	#117	C₂³×C₃₇	1	1	yes	characteristic
471	#117	C₂³×C₃₇	1	3	yes	—
472	#117	C₂³×C₃₇	1	3	yes	—
473	#117	C₂³×C₃₇	1	6	yes	—
474	#117	C₂³×C₃₇	1	3	yes	—
475	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
477	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃₇	1	3	yes	—
480	C₂×C₂²⋊C₄	—	2	3	no	—
481	C₂×C₂²⋊C₄	—	2	3	no	—
482	C₂×C₂²⋊C₄	—	2	3	no	—
483	C₂×C₄²	—	2	3	no	—
484	C₂×C₄²	—	2	3	no	—
485	#107	C₂³×C₃₇	1	3	yes	—
486	#107	C₂³×C₃₇	1	6	yes	—
487	#107	C₂³×C₃₇	1	1	yes	characteristic
488	#107	C₂³×C₃₇	1	3	yes	—
489	#107	C₂³×C₃₇	1	3	yes	—
490	#106	C₂³×C₃₇	1	3	yes	—
491	#106	C₂³×C₃₇	1	6	yes	—
492	#106	C₂³×C₃₇	1	1	yes	characteristic
493	#106	C₂³×C₃₇	1	3	yes	—
494	#106	C₂³×C₃₇	1	3	yes	—
495	#103	C₂³×C₃₇	1	1	yes	characteristic
496	#103	C₂³×C₃₇	1	1	yes	characteristic
497	#103	C₂³×C₃₇	1	3	yes	—
498	#103	C₂³×C₃₇	1	3	yes	—
499	#102	C₂³×C₃₇	1	3	yes	—
500	#102	C₂³×C₃₇	1	3	yes	—
501	#102	C₂³×C₃₇	1	6	yes	—
502	#102	C₂³×C₃₇	1	6	yes	—
503	#102	C₂³×C₃₇	1	3	yes	—
504	#102	C₂³×C₃₇	1	3	yes	—
505	C₂²⋊C₈	C₂³×C₃₇	1	1	yes	characteristic
506	C₂²⋊C₈	C₂³×C₃₇	1	3	yes	—
507	C₂²⋊C₈	C₂³×C₃₇	1	3	yes	—
508	C₂²⋊C₈	C₂³×C₃₇	1	3	yes	—
509	C₂²⋊C₈	C₂³×C₃₇	1	6	yes	—
510	C₂⁴	—	2	3	no	—
511	C₂⁴	C₂×D₄×C₃₇	1	3	yes	—
512	#41	—	2	4	no	—
513	#41	—	2	12	no	—
514	#41	—	2	6	no	—
515	#41	—	2	6	no	—
516	#41	—	2	6	no	—
517	#41	—	2	6	no	—
518	#41	—	4	4	no	—
519	#41	#41×C₃₇	1	4	yes	—
520	#41	#41×C₃₇	1	4	yes	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	C₂×D₄×C₃₇	1	3	yes	—
523	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
524	C₂×Q₈	C₂⁴×C₃₇	1	1	yes	characteristic
525	C₂×D₄	—	2	12	no	—
526	C₂×D₄	—	2	3	no	—
527	C₂×D₄	—	2	3	no	—
528	C₂×D₄	—	2	3	no	—
529	C₂×D₄	—	2	6	no	—
530	C₂×D₄	—	2	3	no	—
531	C₂×D₄	—	2	6	no	—
532	C₂×D₄	—	2	6	no	—
533	C₂×D₄	—	4	12	no	—
534	C₂×D₄	—	8	6	no	—
535	C₂×D₄	C₂×D₄×C₃₇	1	6	yes	—
536	C₂×D₄	C₂×D₄×C₃₇	1	3	yes	—
537	C₂×D₄	C₂×D₄×C₃₇	1	3	yes	—
538	C₂×D₄	C₂⁴×C₃₇	1	3	yes	—
539	C₂²×C₄	—	2	6	no	—
540	C₂²×C₄	—	2	6	no	—
541	C₂²×C₄	—	2	3	no	—
542	C₂²×C₄	—	2	3	no	—
543	C₂²×C₄	—	2	3	no	—
544	C₂²×C₄	—	2	3	no	—
545	C₂²×C₄	—	2	3	no	—
546	C₂²×C₄	—	2	3	no	—
547	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
548	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
549	C₂²×C₄	C₂×D₄×C₃₇	1	3	yes	—
550	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
551	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃₇	1	3	yes	—
553	M₁₆	—	2	6	no	—
554	M₁₆	—	2	6	no	—
555	C₂×C₈	—	2	6	no	—
556	C₂×C₈	—	2	6	no	—
557	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
558	C₂×C₈	C₂⁴×C₃₇	1	3	yes	—
559	C₂×C₈	C₂⁴×C₃₇	1	3	yes	—
560	C₂×C₈	C₂⁴×C₃₇	1	1	yes	characteristic
561	C₄⋊C₄	—	2	3	no	—
562	C₄⋊C₄	—	2	3	no	—
563	C₄⋊C₄	—	2	3	no	—
564	C₄⋊C₄	—	2	3	no	—
565	C₄⋊C₄	—	2	3	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	3	no	—
568	C₄⋊C₄	C₂⁴×C₃₇	1	3	yes	—
569	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
570	C₄⋊C₄	C₂⁴×C₃₇	1	3	yes	—
571	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
572	C₄⋊C₄	C₂⁴×C₃₇	1	3	yes	—
573	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
574	C₂²⋊C₄	—	2	3	no	—
575	C₂²⋊C₄	—	2	1	no	—
576	C₂²⋊C₄	—	2	6	no	—
577	C₂²⋊C₄	—	2	3	no	—
578	C₂²⋊C₄	—	2	3	no	—
579	C₂²⋊C₄	—	2	3	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	2	3	no	—
582	C₂²⋊C₄	—	2	3	no	—
583	C₂²⋊C₄	—	2	6	no	—
584	C₂²⋊C₄	—	2	3	no	—
585	C₄²	—	2	3	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	6	no	—
588	C₄²	—	2	3	no	—
589	C₄²	—	2	3	no	—
590	C₄²	—	2	3	no	—
591	C₂³	—	2	6	no	—
592	C₂³	—	2	3	no	—
593	C₂³	—	4	3	no	—
594	C₂³	—	4	3	no	—
595	C₂³	—	4	6	no	—
596	C₂³	—	8	3	no	—
597	C₂³	—	8	3	no	—
598	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
599	C₂³	C₂²×D₄×C₃₇	1	3	yes	—
600	C₂³	C₂²×D₄×C₃₇	1	3	yes	—
601	Q₈	—	2	6	no	—
602	Q₈	—	2	1	no	—
603	Q₈	—	2	1	no	—
604	Q₈	#123×C₃₇	1	4	yes	—
605	D₄	—	2	12	no	—
606	D₄	—	2	6	no	—
607	D₄	—	2	3	no	—
608	D₄	—	2	3	no	—
609	D₄	—	4	6	no	—
610	D₄	—	4	6	no	—
611	D₄	—	4	6	no	—
612	D₄	—	8	6	no	—
613	D₄	—	8	3	no	—
614	D₄	#123×C₃₇	1	12	yes	—
615	C₂×C₄	—	2	6	no	—
616	C₂×C₄	—	2	6	no	—
617	C₂×C₄	—	2	6	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	3	no	—
621	C₂×C₄	—	2	3	no	—
622	C₂×C₄	—	2	3	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	3	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	3	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	4	6	no	—
630	C₂×C₄	—	8	3	no	—
631	C₂×C₄	—	8	3	no	—
632	C₂×C₄	—	8	3	no	—
633	C₂×C₄	—	8	3	no	—
634	C₂×C₄	—	8	3	no	—
635	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
637	C₂×C₄	C₂²×D₄×C₃₇	1	3	yes	—
638	C₂×C₄	C₂×#41×C₃₇	1	6	yes	—
639	C₂×C₄	C₂×#41×C₃₇	1	6	yes	—
640	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
641	C₈	—	2	1	no	—
642	C₈	—	2	1	no	—
643	C₈	—	2	3	no	—
644	C₈	—	2	3	no	—
645	C₂²	—	2	3	no	—
646	C₂²	—	2	3	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	3	no	—
649	C₂²	—	2	3	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	3	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	4	3	no	—
654	C₂²	—	4	3	no	—
655	C₂²	—	4	3	no	—
656	C₂²	—	8	6	no	—
657	C₂²	—	16	6	no	—
658	C₂²	C₂×#123×C₃₇	1	6	yes	—
659	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
660	C₄	—	2	1	no	—
661	C₄	—	2	3	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	3	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	3	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	3	no	—
669	C₄	C₂×#123×C₃₇	1	6	yes	—
670	C₄	C₂²×#41×C₃₇	1	1	yes	characteristic
671	C₄	C₂²×#41×C₃₇	1	1	yes	characteristic
672	C₂	—	2	6	no	—
673	C₂	—	4	1	no	—
674	C₂	—	4	3	no	—
675	C₂	—	8	3	no	—
676	C₂	C₂²×#123×C₃₇	1	1	yes	characteristic
677	C₂	C₃₇×#3584	1	1	yes	characteristic
678	C₂	C₃₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₇
prime radical	C₃₇×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#3428	C₂	semidirect
3. C₃₇×#3099	C₂	semidirect
4. C₃₇×#3098	C₂	semidirect
5. C₃₇×#3096	C₂	semidirect
6. C₃₇×#3096	C₂	semidirect
7. C₃₇×#3094	C₂	semidirect
8. C₃₇×#3093	C₂	semidirect
9. C₃₇×#3091	C₂	semidirect
10. C₂×C₃₇×#482	C₂	semidirect
11. C₃₇×#2913	C₂	semidirect
12. C₃₇×#2912	C₂	semidirect
13. C₃₇×#2897	C₂	semidirect
14. C₃₇×#2897	C₂	semidirect
15. C₃₇×#2880	C₂	semidirect
31. C₃₇×#520	C₂²	semidirect
32. C₃₇×#520	C₂²	semidirect
37. C₂×#117×C₃₇	C₂²	semidirect
38. C₂×#117×C₃₇	C₂²	semidirect
39. C₃₇×#485	C₂²	semidirect
40. C₃₇×#485	C₂²	semidirect
41. C₃₇×#485	C₂²	semidirect
42. C₃₇×#484	C₂²	semidirect
43. C₃₇×#483	C₂²	semidirect
44. C₃₇×#482	C₂²	semidirect
45. C₃₇×#482	C₂²	semidirect
46. C₃₇×#482	C₂²	semidirect
47. C₃₇×#482	C₂²	semidirect
48. C₃₇×#482	C₂²	semidirect
49. C₃₇×#482	C₂²	semidirect
50. C₃₇×#481	C₂²	semidirect
51. C₃₇×#481	C₂²	semidirect
52. C₃₇×#480	C₂²	semidirect
53. C₃₇×#480	C₂²	semidirect
54. C₃₇×#428	C₂²	semidirect
55. C₃₇×#428	C₂²	semidirect
56. C₃₇×#428	C₂²	semidirect
57. C₃₇×#428	C₂²	semidirect
58. C₃₇×#427	C₂²	semidirect
59. C₃₇×#427	C₂²	semidirect
60. C₂×#107×C₃₇	C₂²	semidirect
61. C₂×#106×C₃₇	C₂²	semidirect
62. C₃₇×#418	C₂²	semidirect
63. C₃₇×#418	C₂²	semidirect
64. C₃₇×#417	C₂²	semidirect
65. C₃₇×#417	C₂²	semidirect
66. C₃₇×#416	C₂²	semidirect
67. C₃₇×#416	C₂²	semidirect
68. C₂×#102×C₃₇	C₂²	semidirect
69. C₂×#102×C₃₇	C₂²	semidirect
70. C₃₇×#408	C₂²	semidirect
71. C₃₇×#408	C₂²	semidirect
72. C₃₇×#407	C₂²	semidirect
73. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
305. #60523	C₃₇	direct (N × H)
334. #3428	C₂×C₃₇	semidirect
335. #3099	C₂×C₃₇	semidirect
336. #3098	C₂×C₃₇	semidirect
337. #3096	C₂×C₃₇	semidirect
338. #3096	C₂×C₃₇	semidirect
339. #3094	C₂×C₃₇	semidirect
340. #3093	C₂×C₃₇	semidirect
341. #3091	C₂×C₃₇	semidirect
342. C₂×#482	C₂×C₃₇	semidirect
343. #2913	C₂×C₃₇	semidirect
344. #2912	C₂×C₃₇	semidirect
345. #2897	C₂×C₃₇	semidirect
346. #2897	C₂×C₃₇	semidirect
347. #2880	C₂×C₃₇	semidirect
370. #520	C₂²×C₃₇	semidirect
371. #520	C₂²×C₃₇	semidirect
376. C₂×#117	C₂²×C₃₇	semidirect
377. C₂×#117	C₂²×C₃₇	semidirect
378. #485	C₂²×C₃₇	semidirect
379. #485	C₂²×C₃₇	semidirect
380. #485	C₂²×C₃₇	semidirect
381. #484	C₂²×C₃₇	semidirect
382. #483	C₂²×C₃₇	semidirect
383. #482	C₂²×C₃₇	semidirect
384. #482	C₂²×C₃₇	semidirect
385. #482	C₂²×C₃₇	semidirect
386. #482	C₂²×C₃₇	semidirect
387. #482	C₂²×C₃₇	semidirect
388. #482	C₂²×C₃₇	semidirect
389. #481	C₂²×C₃₇	semidirect
390. #481	C₂²×C₃₇	semidirect
391. #480	C₂²×C₃₇	semidirect
392. #480	C₂²×C₃₇	semidirect
393. #428	C₂²×C₃₇	semidirect
394. #428	C₂²×C₃₇	semidirect
395. #428	C₂²×C₃₇	semidirect
396. #428	C₂²×C₃₇	semidirect
397. #427	C₂²×C₃₇	semidirect
398. #427	C₂²×C₃₇	semidirect
399. C₂×#107	C₂²×C₃₇	semidirect
400. C₂×#106	C₂²×C₃₇	semidirect
401. #418	C₂²×C₃₇	semidirect
402. #418	C₂²×C₃₇	semidirect
403. #417	C₂²×C₃₇	semidirect
404. #417	C₂²×C₃₇	semidirect
405. #416	C₂²×C₃₇	semidirect
406. #416	C₂²×C₃₇	semidirect
407. C₂×#102	C₂²×C₃₇	semidirect
408. C₂×#102	C₂²×C₃₇	semidirect
409. #408	C₂²×C₃₇	semidirect
410. #408	C₂²×C₃₇	semidirect
411. #407	C₂²×C₃₇	semidirect
412. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
413. C₃₇	#60523	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₇×#3488	2
C₃₇×#3428	2
C₃₇×#3099	2
C₃₇×#3098	2
C₃₇×#3096	2
C₃₇×#3094	2
C₃₇×#3093	2
C₃₇×#3091	2
C₂×C₃₇×#482	2
C₃₇×#2913	2
C₃₇×#2912	2
C₃₇×#2897	2
C₃₇×#2880	2
#60523	37

Subgroups — C37×#60523 #22681776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60523 #22681776