Subgroups — C₃₇×#29910 #22651163

Order 9472.

768 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#2854	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2101	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2092	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₇×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2071	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2071	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1875	C₂	1	2	yes	maximal
10	C₃₇×#1854	C₂	1	2	yes	maximal, complemented
11	C₃₇×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#123×C₃₇	—	2	1	no	—
13	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₃₇	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#107×C₃₇	C₂²	1	2	yes	—
17	C₂×#106×C₃₇	C₂²	1	2	yes	—
18	C₂×#102×C₃₇	C₂²	1	2	yes	—
19	C₂×#102×C₃₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	—
21	C₃₇×#390	C₂²	1	1	yes	characteristic
22	C₃₇×#390	C₂²	1	1	yes	characteristic
23	C₃₇×#389	C₂²	1	1	yes	characteristic
24	C₃₇×#389	C₂²	1	1	yes	characteristic
25	C₃₇×#388	—	2	1	no	—
26	C₃₇×#388	—	2	1	no	—
27	C₃₇×#386	—	2	1	no	—
28	C₃₇×#384	C₂²	1	1	yes	characteristic
29	C₃₇×#384	C₂²	1	1	yes	characteristic
30	C₃₇×#382	C₂²	1	2	yes	—
31	C₃₇×#380	—	2	1	no	—
32	C₃₇×#380	—	2	1	no	—
33	C₃₇×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₃₇	—	2	1	no	—
36	C₃₇×#340	C₂²	1	2	yes	—
37	C₃₇×#340	C₂²	1	2	yes	—
38	C₃₇×#340	C₂²	1	2	yes	—
39	C₃₇×#340	C₂²	1	2	yes	—
40	C₃₇×#336	C₂²	1	2	yes	—
41	C₃₇×#336	C₂²	1	1	yes	characteristic
42	C₃₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₃₇	—	2	1	no	—
44	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₃₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
50	#123×C₃₇	—	4	4	no	—
51	#121×C₃₇	—	2	4	no	—
52	#117×C₃₇	—	4	2	no	—
53	#117×C₃₇	—	4	2	no	—
54	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
72	C₂×C₄²×C₃₇	—	2	4	no	—
73	C₂×C₄²×C₃₇	—	2	2	no	—
74	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
78	#107×C₃₇	—	4	2	no	—
79	#106×C₃₇	—	4	2	no	—
80	#102×C₃₇	—	4	2	no	—
81	#102×C₃₇	—	4	2	no	—
82	C₂²⋊C₈×C₃₇	—	2	4	no	—
83	#95×C₃₇	—	2	2	no	—
84	#95×C₃₇	—	2	2	no	—
85	#95×C₃₇	—	2	1	no	—
86	#95×C₃₇	—	2	1	no	—
87	#95×C₃₇	—	2	1	no	—
88	C₂⁴×C₃₇	—	2	1	no	—
89	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₃₇	—	2	2	no	—
91	C₂×D₄×C₃₇	—	2	1	no	—
92	C₂×D₄×C₃₇	—	2	1	no	—
93	C₂×D₄×C₃₇	—	2	2	no	—
94	C₂×D₄×C₃₇	—	4	2	no	—
95	C₂×D₄×C₃₇	—	4	2	no	—
96	C₂×D₄×C₃₇	—	4	2	no	—
97	C₂²×C₄×C₃₇	—	2	1	no	—
98	C₂²×C₄×C₃₇	—	2	1	no	—
99	C₂²×C₄×C₃₇	—	2	2	no	—
100	C₂²×C₄×C₃₇	—	2	2	no	—
101	C₂²×C₄×C₃₇	—	2	2	no	—
102	C₂²×C₄×C₃₇	—	2	2	no	—
103	C₂²×C₄×C₃₇	—	2	2	no	—
104	C₂²×C₄×C₃₇	—	2	2	no	—
105	C₂²×C₄×C₃₇	—	2	2	no	—
106	C₂²×C₄×C₃₇	—	2	1	no	—
107	C₂²×C₄×C₃₇	—	2	1	no	—
108	C₂²×C₄×C₃₇	—	2	1	no	—
109	C₂²×C₄×C₃₇	—	4	1	no	—
110	C₂²×C₄×C₃₇	—	4	1	no	—
111	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₇	#41	1	4	yes	—
117	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₃₇	—	2	2	no	—
119	C₂×C₈×C₃₇	—	2	2	no	—
120	C₂×C₈×C₃₇	—	2	2	no	—
121	C₂×C₈×C₃₇	—	2	2	no	—
122	C₂×C₈×C₃₇	—	2	2	no	—
123	C₂×C₈×C₃₇	—	2	2	no	—
124	C₄⋊C₄×C₃₇	—	2	2	no	—
125	C₄⋊C₄×C₃₇	—	2	2	no	—
126	C₄⋊C₄×C₃₇	—	2	2	no	—
127	C₄⋊C₄×C₃₇	—	2	1	no	—
128	C₄⋊C₄×C₃₇	—	2	2	no	—
129	C₄⋊C₄×C₃₇	—	2	1	no	—
130	C₄⋊C₄×C₃₇	—	2	2	no	—
131	C₄⋊C₄×C₃₇	—	2	2	no	—
132	C₄⋊C₄×C₃₇	—	4	2	no	—
133	C₄⋊C₄×C₃₇	—	4	2	no	—
134	C₄⋊C₄×C₃₇	—	4	2	no	—
135	C₄⋊C₄×C₃₇	—	4	2	no	—
136	C₄⋊C₄×C₃₇	—	4	2	no	—
137	C₄⋊C₄×C₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₃₇	—	4	2	no	—
139	C₂²⋊C₄×C₃₇	—	4	2	no	—
140	C₂²⋊C₄×C₃₇	—	4	4	no	—
141	C₂²⋊C₄×C₃₇	—	4	2	no	—
142	C₂²⋊C₄×C₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₃₇	—	4	2	no	—
144	C₂²⋊C₄×C₃₇	—	4	2	no	—
145	C₄²×C₃₇	—	2	2	no	—
146	C₄²×C₃₇	—	2	2	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₄²×C₃₇	—	2	2	no	—
149	C₄²×C₃₇	—	4	4	no	—
150	C₂³×C₃₇	—	2	1	no	—
151	C₂³×C₃₇	—	2	1	no	—
152	C₂³×C₃₇	—	2	1	no	—
153	C₂³×C₃₇	—	2	1	no	—
154	C₂³×C₃₇	—	2	1	no	—
155	C₂³×C₃₇	—	2	1	no	—
156	C₂³×C₃₇	—	4	1	no	—
157	C₂³×C₃₇	—	4	1	no	—
158	C₂³×C₃₇	—	4	1	no	—
159	C₂³×C₃₇	—	4	1	no	—
160	C₂³×C₃₇	—	4	1	no	—
161	C₂³×C₃₇	—	4	1	no	—
162	C₂³×C₃₇	—	4	1	no	—
163	C₂³×C₃₇	#123	1	2	yes	—
164	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
165	D₄×C₃₇	—	4	2	no	—
166	D₄×C₃₇	—	4	2	no	—
167	D₄×C₃₇	—	8	4	no	—
168	C₂×C₄×C₃₇	—	2	1	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	1	no	—
171	C₂×C₄×C₃₇	—	2	1	no	—
172	C₂×C₄×C₃₇	—	2	1	no	—
173	C₂×C₄×C₃₇	—	2	1	no	—
174	C₂×C₄×C₃₇	—	2	4	no	—
175	C₂×C₄×C₃₇	—	2	4	no	—
176	C₂×C₄×C₃₇	—	2	1	no	—
177	C₂×C₄×C₃₇	—	2	1	no	—
178	C₂×C₄×C₃₇	—	2	1	no	—
179	C₂×C₄×C₃₇	—	2	1	no	—
180	C₂×C₄×C₃₇	—	2	1	no	—
181	C₂×C₄×C₃₇	—	2	1	no	—
182	C₂×C₄×C₃₇	—	4	4	no	—
183	C₂×C₄×C₃₇	—	4	4	no	—
184	C₂×C₄×C₃₇	—	4	1	no	—
185	C₂×C₄×C₃₇	—	4	2	no	—
186	C₂×C₄×C₃₇	—	4	2	no	—
187	C₂×C₄×C₃₇	—	4	1	no	—
188	C₂×C₄×C₃₇	—	4	1	no	—
189	C₂×C₄×C₃₇	—	4	1	no	—
190	C₂×C₄×C₃₇	—	4	2	no	—
191	C₂×C₄×C₃₇	—	4	1	no	—
192	C₂×C₄×C₃₇	—	4	1	no	—
193	C₂×C₄×C₃₇	—	4	1	no	—
194	C₂×C₄×C₃₇	—	4	2	no	—
195	C₂×C₄×C₃₇	—	4	1	no	—
196	C₂×C₄×C₃₇	—	4	2	no	—
197	C₂×C₄×C₃₇	—	4	2	no	—
198	C₂×C₄×C₃₇	—	4	1	no	—
199	C₂×C₄×C₃₇	#123	1	2	yes	—
200	C₂×C₄×C₃₇	#135	1	2	yes	—
201	C₂×C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	—
202	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
203	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₃₇	2₋¹⁺⁴	1	2	yes	—
206	C₈×C₃₇	—	4	2	no	—
207	C₈×C₃₇	—	4	2	no	—
208	#29910	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₃₇	—	2	2	no	—
210	C₂²×C₃₇	—	2	2	no	—
211	C₂²×C₃₇	—	2	2	no	—
212	C₂²×C₃₇	—	4	1	no	—
213	C₂²×C₃₇	—	4	1	no	—
214	C₂²×C₃₇	—	4	1	no	—
215	C₂²×C₃₇	—	4	1	no	—
216	C₂²×C₃₇	—	8	1	no	—
217	C₂²×C₃₇	—	8	1	no	—
218	C₂²×C₃₇	—	8	1	no	—
219	C₂²×C₃₇	—	8	1	no	—
220	C₂²×C₃₇	—	8	1	no	—
221	C₂²×C₃₇	—	8	1	no	—
222	C₂²×C₃₇	—	8	1	no	—
223	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
224	C₂²×C₃₇	#535	1	1	yes	characteristic
225	C₂²×C₃₇	#536	1	1	yes	characteristic
226	C₂²×C₃₇	C₂×#135	1	1	yes	characteristic
227	C₂²×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂²×C₃₇	#575	1	1	yes	characteristic
229	C₂²×C₃₇	#575	1	1	yes	characteristic
230	C₄×C₃₇	—	2	2	no	—
231	C₄×C₃₇	—	2	2	no	—
232	C₄×C₃₇	—	2	2	no	—
233	C₄×C₃₇	—	4	1	no	—
234	C₄×C₃₇	—	4	1	no	—
235	C₄×C₃₇	—	8	1	no	—
236	C₄×C₃₇	—	8	2	no	—
237	C₄×C₃₇	—	8	2	no	—
238	C₄×C₃₇	—	8	1	no	—
239	C₄×C₃₇	—	8	1	no	—
240	C₄×C₃₇	#539	1	2	yes	—
241	C₄×C₃₇	#539	1	2	yes	—
242	#2854	C₂×C₃₇	1	1	yes	characteristic
243	#2285	C₂×C₃₇	1	1	yes	characteristic, complemented
244	#2101	C₂×C₃₇	1	2	yes	complemented
245	#2092	C₂×C₃₇	1	2	yes	complemented
246	#2084	C₂×C₃₇	1	1	yes	characteristic, complemented
247	#2083	C₂×C₃₇	1	1	yes	characteristic, complemented
248	#2071	C₂×C₃₇	1	1	yes	characteristic, complemented
249	#2071	C₂×C₃₇	1	1	yes	characteristic, complemented
250	#1875	C₂×C₃₇	1	2	yes	—
251	#1854	C₂×C₃₇	1	2	yes	complemented
252	#1817	C₂×C₃₇	1	1	yes	characteristic, complemented
253	C₂×C₃₇	—	4	2	no	—
254	C₂×C₃₇	—	16	1	no	—
255	C₂×C₃₇	#2623	1	1	yes	characteristic
256	C₂×C₃₇	#3091	1	1	yes	characteristic
257	C₂×C₃₇	#3094	1	1	yes	characteristic
258	C₂×C₃₇	#3212	1	1	yes	characteristic
259	C₂×C₃₇	#3214	1	1	yes	characteristic
260	C₂×C₃₇	#3228	1	1	yes	characteristic
261	C₂×C₃₇	#3240	1	1	yes	characteristic
262	C₂×#123	—	2	1	no	—
263	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
264	C₂×#117	C₂²×C₃₇	1	2	yes	—
265	C₂²×C₄²	C₂²×C₃₇	1	1	yes	characteristic
266	C₂×#107	C₂²×C₃₇	1	2	yes	—
267	C₂×#106	C₂²×C₃₇	1	2	yes	—
268	C₂×#102	C₂²×C₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₃₇	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	—
271	#390	C₂²×C₃₇	1	1	yes	characteristic
272	#390	C₂²×C₃₇	1	1	yes	characteristic
273	#389	C₂²×C₃₇	1	1	yes	characteristic
274	#389	C₂²×C₃₇	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#388	—	2	1	no	—
277	#386	—	2	1	no	—
278	#384	C₂²×C₃₇	1	1	yes	characteristic
279	#384	C₂²×C₃₇	1	1	yes	characteristic
280	#382	C₂²×C₃₇	1	2	yes	—
281	#380	—	2	1	no	—
282	#380	—	2	1	no	—
283	#380	C₂²×C₃₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	—	2	1	no	—
285	C₄×C₄⋊C₄	—	2	1	no	—
286	#340	C₂²×C₃₇	1	2	yes	—
287	#340	C₂²×C₃₇	1	2	yes	—
288	#340	C₂²×C₃₇	1	2	yes	—
289	#340	C₂²×C₃₇	1	2	yes	—
290	#336	C₂²×C₃₇	1	1	yes	characteristic
291	#336	C₂²×C₃₇	1	1	yes	characteristic
292	#336	C₂²×C₃₇	1	2	yes	—
293	C₃₇	#29910	1	1	yes	characteristic, direct product factor, Sylow
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
296	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₃₇	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
300	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
301	#123	—	4	4	no	—
302	#121	—	2	4	no	—
303	#117	—	4	2	no	—
304	#117	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	—	2	4	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
329	#107	—	4	2	no	—
330	#106	—	4	2	no	—
331	#102	—	4	2	no	—
332	#102	—	4	2	no	—
333	C₂²⋊C₈	—	2	4	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
367	C₂²×C₄	#41×C₃₇	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	4	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	#123×C₃₇	1	2	yes	—
415	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	4	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	#123×C₃₇	1	2	yes	—
451	C₂×C₄	#135×C₃₇	1	2	yes	—
452	C₂×C₄	AGL(1,ℤ/8)×C₃₇	1	2	yes	—
453	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
454	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
455	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
456	C₂×C₄	2₋¹⁺⁴×C₃₇	1	2	yes	—
457	C₈	—	4	2	no	—
458	C₈	—	4	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	—	8	1	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
474	C₂²	C₃₇×#535	1	1	yes	characteristic
475	C₂²	C₃₇×#536	1	1	yes	characteristic
476	C₂²	C₂×#135×C₃₇	1	1	yes	characteristic
477	C₂²	C₂×AGL(1,ℤ/8)×C₃₇	1	1	yes	characteristic
478	C₂²	C₃₇×#575	1	1	yes	characteristic
479	C₂²	C₃₇×#575	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	8	2	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₄	C₃₇×#539	1	2	yes	—
491	C₄	C₃₇×#539	1	2	yes	—
492	C₂	—	4	2	no	—
493	C₂	—	16	1	no	—
494	C₂	C₃₇×#2623	1	1	yes	characteristic
495	C₂	C₃₇×#3091	1	1	yes	characteristic
496	C₂	C₃₇×#3094	1	1	yes	characteristic
497	C₂	C₃₇×#3212	1	1	yes	characteristic
498	C₂	C₃₇×#3214	1	1	yes	characteristic
499	C₂	C₃₇×#3228	1	1	yes	characteristic
500	C₂	C₃₇×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×#121×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄²×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2285	C₂	semidirect
3. C₃₇×#2101	C₂	semidirect
4. C₃₇×#2092	C₂	semidirect
5. C₃₇×#2084	C₂	semidirect
6. C₃₇×#2083	C₂	semidirect
7. C₃₇×#2071	C₂	semidirect
8. C₃₇×#2071	C₂	semidirect
10. C₃₇×#1854	C₂	semidirect
11. C₃₇×#1817	C₂	semidirect
208. #29910	C₃₇	direct (N × H)
243. #2285	C₂×C₃₇	semidirect
244. #2101	C₂×C₃₇	semidirect
245. #2092	C₂×C₃₇	semidirect
246. #2084	C₂×C₃₇	semidirect
247. #2083	C₂×C₃₇	semidirect
248. #2071	C₂×C₃₇	semidirect
249. #2071	C₂×C₃₇	semidirect
251. #1854	C₂×C₃₇	semidirect
252. #1817	C₂×C₃₇	semidirect
293. C₃₇	#29910	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×#2854	2
C₃₇×#2285	2
C₃₇×#2101	2
C₃₇×#2092	2
C₃₇×#2084	2
C₃₇×#2083	2
C₃₇×#2071	2
C₃₇×#1875	2
C₃₇×#1854	2
C₃₇×#1817	2
#29910	37

Subgroups — C37×#29910 #22651163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29910 #22651163