Subgroups — C₂×C₃₇×#2377 #22655593

Order 9472.

3302 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2377	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₇×#390	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₇×#388	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₇×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₇×#386	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₇×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₇×#385	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₇×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₃₇	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₃₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×#121×C₃₇	C₄	1	16	yes	complemented
16	C₂×#121×C₃₇	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₃₇	C₂²	1	2	yes	—
28	C₃₇×#390	C₂²	1	16	yes	complemented
29	C₃₇×#388	C₂²	1	16	yes	complemented
30	C₃₇×#387	C₂²	1	16	yes	complemented
31	C₃₇×#386	C₂²	1	16	yes	complemented
32	C₃₇×#386	C₂²	1	16	yes	complemented
33	C₃₇×#385	C₂²	1	16	yes	complemented
34	C₃₇×#381	C₂²	1	8	yes	complemented
35	C₃₇×#380	C₂²	1	8	yes	complemented
36	C₂×#95×C₃₇	C₂²	1	2	yes	—
37	C₂×#95×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#95×C₃₇	C₂²	1	2	yes	—
39	C₂×#95×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#95×C₃₇	C₂²	1	2	yes	—
41	C₂×#95×C₃₇	C₂²	1	2	yes	—
42	C₂⁵×C₃₇	C₂³	1	1	yes	characteristic
43	C₂⁵×C₃₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₃₇	—	4	4	no	—
45	C₂²×D₄×C₃₇	—	4	4	no	—
46	C₂²×D₄×C₃₇	—	4	4	no	—
47	C₂²×D₄×C₃₇	C₂×C₄	1	8	yes	—
48	C₂²×D₄×C₃₇	C₂×C₄	1	16	yes	complemented
49	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
50	C₂²×D₄×C₃₇	C₂³	1	8	yes	—
51	C₂³×C₄×C₃₇	—	4	4	no	—
52	C₂³×C₄×C₃₇	—	4	4	no	—
53	C₂³×C₄×C₃₇	—	4	4	no	—
54	C₂³×C₄×C₃₇	—	4	4	no	—
55	C₂³×C₄×C₃₇	C₂×C₄	1	8	yes	complemented
56	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₃₇	C₂³	1	8	yes	—
64	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
65	#121×C₃₇	C₂×C₄	1	64	yes	complemented
66	C₂×C₄⋊C₄×C₃₇	—	4	4	no	—
67	C₂×C₄⋊C₄×C₃₇	—	4	4	no	—
68	C₂×C₄⋊C₄×C₃₇	C₂×C₄	1	8	yes	complemented
69	C₂×C₄⋊C₄×C₃₇	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₃₇	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₃₇	—	4	2	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	4	4	no	—
75	C₂×C₂²⋊C₄×C₃₇	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	4	4	no	—
77	C₂×C₂²⋊C₄×C₃₇	—	4	2	no	—
78	C₂×C₂²⋊C₄×C₃₇	C₂×C₄	1	16	yes	complemented
79	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
84	C₂×C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
86	C₂×C₄²×C₃₇	—	4	4	no	—
87	C₂×C₄²×C₃₇	C₂³	1	8	yes	—
88	#95×C₃₇	C₂³	1	8	yes	—
89	#95×C₃₇	C₂³	1	4	yes	—
90	#95×C₃₇	C₂³	1	8	yes	—
91	#95×C₃₇	C₂³	1	4	yes	—
92	#95×C₃₇	C₂³	1	8	yes	—
93	#95×C₃₇	C₂³	1	8	yes	—
94	C₂⁴×C₃₇	—	2	2	no	—
95	C₂⁴×C₃₇	—	2	4	no	—
96	C₂⁴×C₃₇	—	2	4	no	—
97	C₂⁴×C₃₇	—	2	4	no	—
98	C₂⁴×C₃₇	—	2	4	no	—
99	C₂⁴×C₃₇	—	2	4	no	—
100	C₂⁴×C₃₇	—	2	4	no	—
101	C₂⁴×C₃₇	—	2	4	no	—
102	C₂⁴×C₃₇	—	2	2	no	—
103	C₂⁴×C₃₇	—	2	4	no	—
104	C₂⁴×C₃₇	C₂²×C₄	1	8	yes	—
105	C₂⁴×C₃₇	C₂²×C₄	1	4	yes	—
106	C₂⁴×C₃₇	C₂⁴	1	2	yes	—
107	C₂⁴×C₃₇	C₂⁴	1	4	yes	—
108	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
109	C₂×D₄×C₃₇	—	4	16	no	—
110	C₂×D₄×C₃₇	—	4	32	no	—
111	C₂×D₄×C₃₇	—	4	8	no	—
112	C₂×D₄×C₃₇	—	4	8	no	—
113	C₂×D₄×C₃₇	—	4	8	no	—
114	C₂×D₄×C₃₇	C₂²×C₄	1	16	yes	—
115	C₂×D₄×C₃₇	C₂²×C₄	1	32	yes	complemented
116	C₂²×C₄×C₃₇	—	2	4	no	—
117	C₂²×C₄×C₃₇	—	2	4	no	—
118	C₂²×C₄×C₃₇	—	2	4	no	—
119	C₂²×C₄×C₃₇	—	2	4	no	—
120	C₂²×C₄×C₃₇	—	2	4	no	—
121	C₂²×C₄×C₃₇	—	2	4	no	—
122	C₂²×C₄×C₃₇	—	2	4	no	—
123	C₂²×C₄×C₃₇	—	2	4	no	—
124	C₂²×C₄×C₃₇	—	2	4	no	—
125	C₂²×C₄×C₃₇	—	2	4	no	—
126	C₂²×C₄×C₃₇	—	2	4	no	—
127	C₂²×C₄×C₃₇	—	2	4	no	—
128	C₂²×C₄×C₃₇	—	2	4	no	—
129	C₂²×C₄×C₃₇	—	2	4	no	—
130	C₂²×C₄×C₃₇	—	2	4	no	—
131	C₂²×C₄×C₃₇	—	2	4	no	—
132	C₂²×C₄×C₃₇	—	4	16	no	—
133	C₂²×C₄×C₃₇	—	4	8	no	—
134	C₂²×C₄×C₃₇	—	4	8	no	—
135	C₂²×C₄×C₃₇	—	4	8	no	—
136	C₂²×C₄×C₃₇	—	4	8	no	—
137	C₂²×C₄×C₃₇	—	4	32	no	—
138	C₂²×C₄×C₃₇	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₃₇	C₂²×C₄	1	8	yes	—
140	C₂²×C₄×C₃₇	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₃₇	C₂²×C₄	1	16	yes	complemented
142	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
149	C₄⋊C₄×C₃₇	—	4	8	no	—
150	C₄⋊C₄×C₃₇	—	4	8	no	—
151	C₄⋊C₄×C₃₇	C₂²×C₄	1	16	yes	complemented
152	C₂²⋊C₄×C₃₇	—	4	8	no	—
153	C₂²⋊C₄×C₃₇	—	4	4	no	—
154	C₂²⋊C₄×C₃₇	—	4	8	no	—
155	C₂²⋊C₄×C₃₇	—	4	8	no	—
156	C₂²⋊C₄×C₃₇	—	4	8	no	—
157	C₂²⋊C₄×C₃₇	—	4	4	no	—
158	C₂²⋊C₄×C₃₇	C₂²×C₄	1	32	yes	complemented
159	C₄²×C₃₇	—	4	8	no	—
160	C₂³×C₃₇	—	2	8	no	—
161	C₂³×C₃₇	—	2	8	no	—
162	C₂³×C₃₇	—	2	16	no	—
163	C₂³×C₃₇	—	2	16	no	—
164	C₂³×C₃₇	—	2	8	no	—
165	C₂³×C₃₇	—	2	16	no	—
166	C₂³×C₃₇	—	2	2	no	—
167	C₂³×C₃₇	—	2	4	no	—
168	C₂³×C₃₇	—	2	4	no	—
169	C₂³×C₃₇	—	2	4	no	—
170	C₂³×C₃₇	—	2	4	no	—
171	C₂³×C₃₇	—	2	4	no	—
172	C₂³×C₃₇	—	2	4	no	—
173	C₂³×C₃₇	—	2	4	no	—
174	C₂³×C₃₇	—	2	2	no	—
175	C₂³×C₃₇	—	2	4	no	—
176	C₂³×C₃₇	—	4	8	no	—
177	C₂³×C₃₇	—	4	8	no	—
178	C₂³×C₃₇	—	4	8	no	—
179	C₂³×C₃₇	—	4	8	no	—
180	C₂³×C₃₇	—	4	8	no	—
181	C₂³×C₃₇	—	4	8	no	—
182	C₂³×C₃₇	C₂³×C₄	1	8	yes	—
183	C₂³×C₃₇	C₂³×C₄	1	4	yes	—
184	C₂³×C₃₇	C₂³×C₄	1	2	yes	—
185	C₂³×C₃₇	H(5,𝔽₂)	1	4	yes	—
186	C₂³×C₃₇	H(5,𝔽₂)	1	4	yes	—
187	C₂³×C₃₇	H(5,𝔽₂)	1	2	yes	—
188	C₂³×C₃₇	2₋¹⁺⁴	1	2	yes	—
189	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
190	D₄×C₃₇	—	4	16	no	—
191	D₄×C₃₇	—	4	32	no	—
192	C₂×C₄×C₃₇	—	2	8	no	—
193	C₂×C₄×C₃₇	—	2	8	no	—
194	C₂×C₄×C₃₇	—	2	16	no	—
195	C₂×C₄×C₃₇	—	2	4	no	—
196	C₂×C₄×C₃₇	—	2	4	no	—
197	C₂×C₄×C₃₇	—	2	4	no	—
198	C₂×C₄×C₃₇	—	2	4	no	—
199	C₂×C₄×C₃₇	—	2	4	no	—
200	C₂×C₄×C₃₇	—	2	4	no	—
201	C₂×C₄×C₃₇	—	2	4	no	—
202	C₂×C₄×C₃₇	—	2	4	no	—
203	C₂×C₄×C₃₇	—	2	4	no	—
204	C₂×C₄×C₃₇	—	2	4	no	—
205	C₂×C₄×C₃₇	—	2	4	no	—
206	C₂×C₄×C₃₇	—	2	4	no	—
207	C₂×C₄×C₃₇	—	2	4	no	—
208	C₂×C₄×C₃₇	—	2	4	no	—
209	C₂×C₄×C₃₇	—	2	4	no	—
210	C₂×C₄×C₃₇	—	2	4	no	—
211	C₂×C₄×C₃₇	—	4	16	no	—
212	C₂×C₄×C₃₇	—	4	32	no	—
213	C₂×C₄×C₃₇	—	4	8	no	—
214	C₂×C₄×C₃₇	—	4	8	no	—
215	C₂×C₄×C₃₇	—	4	8	no	—
216	C₂×C₄×C₃₇	—	4	8	no	—
217	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₃₇	C₂³×C₄	1	8	yes	—
219	C₂×C₄×C₃₇	C₂³×C₄	1	4	yes	—
220	C₂×#2377	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₃₇	—	2	4	no	—
222	C₂²×C₃₇	—	2	4	no	—
223	C₂²×C₃₇	—	2	8	no	—
224	C₂²×C₃₇	—	2	8	no	—
225	C₂²×C₃₇	—	2	4	no	—
226	C₂²×C₃₇	—	2	8	no	—
227	C₂²×C₃₇	—	4	16	no	—
228	C₂²×C₃₇	—	4	32	no	—
229	C₂²×C₃₇	—	4	4	no	—
230	C₂²×C₃₇	—	4	4	no	—
231	C₂²×C₃₇	—	4	4	no	—
232	C₂²×C₃₇	—	4	4	no	—
233	C₂²×C₃₇	—	4	4	no	—
234	C₂²×C₃₇	—	4	4	no	—
235	C₂²×C₃₇	#518	1	4	yes	—
236	C₂²×C₃₇	#518	1	4	yes	—
237	C₂²×C₃₇	#520	1	4	yes	—
238	C₂²×C₃₇	#560	1	8	yes	—
239	C₂²×C₃₇	#562	1	8	yes	—
240	C₂²×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
241	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
242	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
243	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂²×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
245	C₄×C₃₇	—	2	4	no	—
246	C₄×C₃₇	—	2	4	no	—
247	C₄×C₃₇	—	2	8	no	—
248	C₄×C₃₇	—	4	4	no	—
249	C₄×C₃₇	—	4	4	no	—
250	C₄×C₃₇	—	4	4	no	—
251	C₄×C₃₇	—	4	4	no	—
252	C₂²×#121	C₂×C₃₇	1	1	yes	characteristic
253	#2377	C₂×C₃₇	1	16	yes	direct product factor
254	C₂×#390	C₂×C₃₇	1	2	yes	complemented
255	C₂×#388	C₂×C₃₇	1	2	yes	complemented
256	C₂×#387	C₂×C₃₇	1	2	yes	complemented
257	C₂×#386	C₂×C₃₇	1	2	yes	complemented
258	C₂×#386	C₂×C₃₇	1	2	yes	complemented
259	C₂×#385	C₂×C₃₇	1	2	yes	complemented
260	C₂×#381	C₂×C₃₇	1	1	yes	characteristic, complemented
261	C₂×#380	C₂×C₃₇	1	1	yes	characteristic, complemented
262	C₂×C₃₇	—	4	4	no	—
263	C₂×C₃₇	—	4	8	no	—
264	C₂×C₃₇	#2377	1	8	yes	direct product factor
265	C₂×C₃₇	C₂×#518	1	1	yes	characteristic
266	C₂×C₃₇	C₂×#518	1	1	yes	characteristic
267	C₂×C₃₇	C₂×#520	1	1	yes	characteristic
268	C₂×C₃₇	C₂×#560	1	2	yes	—
269	C₂×C₃₇	C₂×#562	1	2	yes	—
270	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
271	C₂³×D₄	C₂²×C₃₇	1	2	yes	—
272	C₂⁴×C₄	C₂²×C₃₇	1	2	yes	—
273	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×#121	C₄×C₃₇	1	16	yes	complemented
275	C₂×#121	C₂²×C₃₇	1	8	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
284	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
286	C₂²×C₄²	C₂²×C₃₇	1	2	yes	—
287	#390	C₂²×C₃₇	1	16	yes	complemented
288	#388	C₂²×C₃₇	1	16	yes	complemented
289	#387	C₂²×C₃₇	1	16	yes	complemented
290	#386	C₂²×C₃₇	1	16	yes	complemented
291	#386	C₂²×C₃₇	1	16	yes	complemented
292	#385	C₂²×C₃₇	1	16	yes	complemented
293	#381	C₂²×C₃₇	1	8	yes	complemented
294	#380	C₂²×C₃₇	1	8	yes	complemented
295	C₂×#95	C₂²×C₃₇	1	2	yes	—
296	C₂×#95	C₂²×C₃₇	1	1	yes	characteristic
297	C₂×#95	C₂²×C₃₇	1	2	yes	—
298	C₂×#95	C₂²×C₃₇	1	1	yes	characteristic
299	C₂×#95	C₂²×C₃₇	1	2	yes	—
300	C₂×#95	C₂²×C₃₇	1	2	yes	—
301	C₃₇	C₂×#2377	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁵	C₂³×C₃₇	1	1	yes	characteristic
303	C₂⁵	C₂³×C₃₇	1	2	yes	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	—	4	4	no	—
306	C₂²×D₄	—	4	4	no	—
307	C₂²×D₄	C₂×C₄×C₃₇	1	8	yes	—
308	C₂²×D₄	C₂×C₄×C₃₇	1	16	yes	complemented
309	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
310	C₂²×D₄	C₂³×C₃₇	1	8	yes	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	—	4	4	no	—
313	C₂³×C₄	—	4	4	no	—
314	C₂³×C₄	—	4	4	no	—
315	C₂³×C₄	C₂×C₄×C₃₇	1	8	yes	complemented
316	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
317	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
318	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
319	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
320	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
322	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₃₇	1	8	yes	—
324	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
325	#121	C₂×C₄×C₃₇	1	64	yes	complemented
326	C₂×C₄⋊C₄	—	4	4	no	—
327	C₂×C₄⋊C₄	—	4	4	no	—
328	C₂×C₄⋊C₄	C₂×C₄×C₃₇	1	8	yes	complemented
329	C₂×C₄⋊C₄	C₂³×C₃₇	1	8	yes	—
330	C₂×C₄⋊C₄	C₂³×C₃₇	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
332	C₂×C₂²⋊C₄	—	4	4	no	—
333	C₂×C₂²⋊C₄	—	4	2	no	—
334	C₂×C₂²⋊C₄	—	4	4	no	—
335	C₂×C₂²⋊C₄	—	4	4	no	—
336	C₂×C₂²⋊C₄	—	4	4	no	—
337	C₂×C₂²⋊C₄	—	4	2	no	—
338	C₂×C₂²⋊C₄	C₂×C₄×C₃₇	1	16	yes	complemented
339	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₃₇	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₃₇	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₃₇	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₃₇	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₃₇	1	8	yes	—
346	C₂×C₄²	—	4	4	no	—
347	C₂×C₄²	C₂³×C₃₇	1	8	yes	—
348	#95	C₂³×C₃₇	1	8	yes	—
349	#95	C₂³×C₃₇	1	4	yes	—
350	#95	C₂³×C₃₇	1	8	yes	—
351	#95	C₂³×C₃₇	1	4	yes	—
352	#95	C₂³×C₃₇	1	8	yes	—
353	#95	C₂³×C₃₇	1	8	yes	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	4	no	—
364	C₂⁴	C₂²×C₄×C₃₇	1	8	yes	—
365	C₂⁴	C₂²×C₄×C₃₇	1	4	yes	—
366	C₂⁴	C₂⁴×C₃₇	1	2	yes	—
367	C₂⁴	C₂⁴×C₃₇	1	4	yes	—
368	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
369	C₂×D₄	—	4	16	no	—
370	C₂×D₄	—	4	32	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	C₂²×C₄×C₃₇	1	16	yes	—
375	C₂×D₄	C₂²×C₄×C₃₇	1	32	yes	complemented
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	4	16	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	—	4	8	no	—
395	C₂²×C₄	—	4	8	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	32	no	—
398	C₂²×C₄	C₂²×C₄×C₃₇	1	4	yes	—
399	C₂²×C₄	C₂²×C₄×C₃₇	1	8	yes	—
400	C₂²×C₄	C₂²×C₄×C₃₇	1	4	yes	—
401	C₂²×C₄	C₂²×C₄×C₃₇	1	16	yes	complemented
402	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
409	C₄⋊C₄	—	4	8	no	—
410	C₄⋊C₄	—	4	8	no	—
411	C₄⋊C₄	C₂²×C₄×C₃₇	1	16	yes	complemented
412	C₂²⋊C₄	—	4	8	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	8	no	—
415	C₂²⋊C₄	—	4	8	no	—
416	C₂²⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	C₂²×C₄×C₃₇	1	32	yes	complemented
419	C₄²	—	4	8	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	16	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	16	no	—
435	C₂³	—	2	16	no	—
436	C₂³	—	4	8	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	8	no	—
442	C₂³	C₂³×C₄×C₃₇	1	8	yes	—
443	C₂³	C₂³×C₄×C₃₇	1	4	yes	—
444	C₂³	C₂³×C₄×C₃₇	1	2	yes	—
445	C₂³	H(5,𝔽₂)×C₃₇	1	2	yes	—
446	C₂³	H(5,𝔽₂)×C₃₇	1	4	yes	—
447	C₂³	H(5,𝔽₂)×C₃₇	1	4	yes	—
448	C₂³	2₋¹⁺⁴×C₃₇	1	2	yes	—
449	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
450	D₄	—	4	16	no	—
451	D₄	—	4	32	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	16	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	—	4	32	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
478	C₂×C₄	C₂³×C₄×C₃₇	1	8	yes	—
479	C₂×C₄	C₂³×C₄×C₃₇	1	4	yes	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	8	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	32	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	C₃₇×#518	1	4	yes	—
495	C₂²	C₃₇×#518	1	4	yes	—
496	C₂²	C₃₇×#520	1	4	yes	—
497	C₂²	C₃₇×#560	1	8	yes	—
498	C₂²	C₃₇×#562	1	8	yes	—
499	C₂²	C₂⁴×C₄×C₃₇	1	1	yes	characteristic
500	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
501	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
502	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
503	C₂²	C₂×2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	8	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₂	—	4	4	no	—
512	C₂	—	4	8	no	—
513	C₂	C₃₇×#2377	1	8	yes	direct product factor
514	C₂	C₂×C₃₇×#518	1	1	yes	characteristic
515	C₂	C₂×C₃₇×#518	1	1	yes	characteristic
516	C₂	C₂×C₃₇×#520	1	1	yes	characteristic
517	C₂	C₂×C₃₇×#560	1	2	yes	—
518	C₂	C₂×C₃₇×#562	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₇
Frattini, cosocle	C₂³	C₂⁵×C₃₇
prime radical	C₂²×#121×C₃₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₇×#2377	C₂	direct (N × H)
3. C₂×C₃₇×#390	C₂	semidirect
4. C₂×C₃₇×#388	C₂	semidirect
5. C₂×C₃₇×#387	C₂	semidirect
6. C₂×C₃₇×#386	C₂	semidirect
7. C₂×C₃₇×#386	C₂	semidirect
8. C₂×C₃₇×#385	C₂	semidirect
9. C₂×C₃₇×#381	C₂	semidirect
10. C₂×C₃₇×#380	C₂	semidirect
15. C₂×#121×C₃₇	C₄	semidirect
28. C₃₇×#390	C₂²	semidirect
29. C₃₇×#388	C₂²	semidirect
30. C₃₇×#387	C₂²	semidirect
31. C₃₇×#386	C₂²	semidirect
32. C₃₇×#386	C₂²	semidirect
33. C₃₇×#385	C₂²	semidirect
34. C₃₇×#381	C₂²	semidirect
35. C₃₇×#380	C₂²	semidirect
48. C₂²×D₄×C₃₇	C₂×C₄	semidirect
55. C₂³×C₄×C₃₇	C₂×C₄	semidirect
65. #121×C₃₇	C₂×C₄	semidirect
68. C₂×C₄⋊C₄×C₃₇	C₂×C₄	semidirect
78. C₂×C₂²⋊C₄×C₃₇	C₂×C₄	semidirect
115. C₂×D₄×C₃₇	C₂²×C₄	semidirect
141. C₂²×C₄×C₃₇	C₂²×C₄	semidirect
151. C₄⋊C₄×C₃₇	C₂²×C₄	semidirect
158. C₂²⋊C₄×C₃₇	C₂²×C₄	semidirect
220. C₂×#2377	C₃₇	direct (N × H)
253. #2377	C₂×C₃₇	direct (N × H)
254. C₂×#390	C₂×C₃₇	semidirect
255. C₂×#388	C₂×C₃₇	semidirect
256. C₂×#387	C₂×C₃₇	semidirect
257. C₂×#386	C₂×C₃₇	semidirect
258. C₂×#386	C₂×C₃₇	semidirect
259. C₂×#385	C₂×C₃₇	semidirect
260. C₂×#381	C₂×C₃₇	semidirect
261. C₂×#380	C₂×C₃₇	semidirect
264. C₂×C₃₇	#2377	direct (N × H)
274. C₂×#121	C₄×C₃₇	semidirect
287. #390	C₂²×C₃₇	semidirect
288. #388	C₂²×C₃₇	semidirect
289. #387	C₂²×C₃₇	semidirect
290. #386	C₂²×C₃₇	semidirect
291. #386	C₂²×C₃₇	semidirect
292. #385	C₂²×C₃₇	semidirect
293. #381	C₂²×C₃₇	semidirect
294. #380	C₂²×C₃₇	semidirect
301. C₃₇	C₂×#2377	direct (N × H)
308. C₂²×D₄	C₂×C₄×C₃₇	semidirect
315. C₂³×C₄	C₂×C₄×C₃₇	semidirect
325. #121	C₂×C₄×C₃₇	semidirect
328. C₂×C₄⋊C₄	C₂×C₄×C₃₇	semidirect
338. C₂×C₂²⋊C₄	C₂×C₄×C₃₇	semidirect
375. C₂×D₄	C₂²×C₄×C₃₇	semidirect
401. C₂²×C₄	C₂²×C₄×C₃₇	semidirect
411. C₄⋊C₄	C₂²×C₄×C₃₇	semidirect
418. C₂²⋊C₄	C₂²×C₄×C₃₇	semidirect
513. C₂	C₃₇×#2377	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₃₇	2
C₃₇×#2377	2
C₂×C₃₇×#390	2
C₂×C₃₇×#388	2
C₂×C₃₇×#387	2
C₂×C₃₇×#386	2
C₂×C₃₇×#385	2
C₂×C₃₇×#381	2
C₂×C₃₇×#380	2
C₂×#2377	37

Subgroups — C2×C37×#2377 #22655593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇×#2377 #22655593