Subgroups — C₃₇×#28620 #22649873

Order 9472.

878 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₇×#489	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#2056	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2055	C₂	1	2	yes	maximal
7	C₃₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1878	C₂	1	2	yes	maximal, complemented
10	C₃₇×#1877	C₂	1	2	yes	maximal
11	C₃₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₃₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₃₇×#497	—	2	4	no	—
20	C₃₇×#489	—	2	4	no	—
21	C₂×C₄⋊C₈×C₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₃₇	C₂²	1	2	yes	—
26	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
28	C₃₇×#391	—	2	1	no	—
29	C₃₇×#391	—	2	1	no	—
30	C₃₇×#391	C₂²	1	2	yes	—
31	C₃₇×#391	C₂²	1	2	yes	—
32	C₃₇×#391	C₂²	1	1	yes	characteristic
33	C₃₇×#390	C₂²	1	1	yes	characteristic
34	C₃₇×#388	—	2	1	no	—
35	C₃₇×#388	—	2	1	no	—
36	C₃₇×#382	—	2	1	no	—
37	C₃₇×#382	—	2	1	no	—
38	C₃₇×#382	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₃₇	—	2	1	no	—
41	C₄³×C₃₇	C₂²	1	1	yes	characteristic
42	C₃₇×#340	C₂²	1	2	yes	—
43	C₃₇×#340	C₂²	1	2	yes	—
44	C₃₇×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₃₇	—	2	1	no	—
46	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
47	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₇	—	2	1	no	—
50	C₂×Q₁₆×C₃₇	—	2	4	no	—
51	C₂×Q₁₆×C₃₇	—	2	4	no	—
52	C₂×Q₁₆×C₃₇	—	4	2	no	—
53	C₂×SD₁₆×C₃₇	—	2	4	no	—
54	C₂×SD₁₆×C₃₇	—	2	4	no	—
55	C₂×SD₁₆×C₃₇	—	4	2	no	—
56	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₃₇	—	2	2	no	—
59	C₄⋊Q₈×C₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₃₇	—	2	2	no	—
61	C₄⋊Q₈×C₃₇	—	2	2	no	—
62	#124×C₃₇	—	2	2	no	—
63	#124×C₃₇	D₄	1	4	yes	—
64	C₄×Q₈×C₃₇	—	4	2	no	—
65	C₄×D₄×C₃₇	—	4	2	no	—
66	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
78	C₂×C₄²×C₃₇	—	2	1	no	—
79	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₃₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₃₇	—	2	4	no	—
87	#103×C₃₇	—	2	4	no	—
88	#103×C₃₇	—	4	2	no	—
89	#103×C₃₇	—	4	2	no	—
90	#102×C₃₇	—	2	4	no	—
91	#97×C₃₇	—	2	2	no	—
92	#97×C₃₇	—	2	2	no	—
93	#95×C₃₇	—	2	1	no	—
94	#95×C₃₇	—	2	1	no	—
95	#95×C₃₇	—	2	1	no	—
96	#95×C₃₇	—	2	1	no	—
97	#95×C₃₇	—	2	2	no	—
98	#95×C₃₇	—	2	2	no	—
99	#95×C₃₇	—	2	2	no	—
100	#95×C₃₇	—	2	2	no	—
101	C₂⁴×C₃₇	—	2	1	no	—
102	C₂×Q₈×C₃₇	—	2	1	no	—
103	C₂×Q₈×C₃₇	—	2	2	no	—
104	C₂×Q₈×C₃₇	—	2	2	no	—
105	C₂×Q₈×C₃₇	—	2	2	no	—
106	C₂×Q₈×C₃₇	—	2	2	no	—
107	C₂×Q₈×C₃₇	—	2	2	no	—
108	C₂×Q₈×C₃₇	—	2	2	no	—
109	C₂×Q₈×C₃₇	—	2	2	no	—
110	C₂×Q₈×C₃₇	—	2	2	no	—
111	C₂×Q₈×C₃₇	—	4	2	no	—
112	C₂×Q₈×C₃₇	—	4	2	no	—
113	C₂×Q₈×C₃₇	—	4	2	no	—
114	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₃₇	—	2	2	no	—
116	C₂×D₄×C₃₇	—	2	1	no	—
117	C₂×D₄×C₃₇	—	2	2	no	—
118	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	—	2	1	no	—
120	C₂²×C₄×C₃₇	—	2	1	no	—
121	C₂²×C₄×C₃₇	—	2	2	no	—
122	C₂²×C₄×C₃₇	—	2	2	no	—
123	C₂²×C₄×C₃₇	—	2	1	no	—
124	C₂²×C₄×C₃₇	—	4	2	no	—
125	C₂²×C₄×C₃₇	—	4	2	no	—
126	C₂²×C₄×C₃₇	—	4	2	no	—
127	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₃₇	—	4	8	no	—
135	SD₁₆×C₃₇	—	4	8	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	2	2	no	—
139	C₂×C₈×C₃₇	—	2	2	no	—
140	C₂×C₈×C₃₇	—	2	2	no	—
141	C₂×C₈×C₃₇	#41	1	4	yes	—
142	C₄⋊C₄×C₃₇	—	2	2	no	—
143	C₄⋊C₄×C₃₇	—	2	2	no	—
144	C₄⋊C₄×C₃₇	—	2	2	no	—
145	C₄⋊C₄×C₃₇	—	2	2	no	—
146	C₄⋊C₄×C₃₇	—	4	2	no	—
147	C₄⋊C₄×C₃₇	—	4	2	no	—
148	C₄⋊C₄×C₃₇	—	4	2	no	—
149	C₄⋊C₄×C₃₇	—	4	2	no	—
150	C₂²⋊C₄×C₃₇	—	2	4	no	—
151	C₂²⋊C₄×C₃₇	—	2	4	no	—
152	C₂²⋊C₄×C₃₇	—	4	2	no	—
153	C₂²⋊C₄×C₃₇	—	4	2	no	—
154	C₂²⋊C₄×C₃₇	—	4	2	no	—
155	C₄²×C₃₇	—	2	2	no	—
156	C₄²×C₃₇	—	2	2	no	—
157	C₄²×C₃₇	—	2	2	no	—
158	C₄²×C₃₇	—	2	2	no	—
159	C₄²×C₃₇	—	4	1	no	—
160	C₄²×C₃₇	—	4	1	no	—
161	C₄²×C₃₇	—	4	2	no	—
162	C₄²×C₃₇	C₂×D₄	1	2	yes	—
163	C₄²×C₃₇	#41	1	2	yes	—
164	C₂³×C₃₇	—	2	2	no	—
165	C₂³×C₃₇	—	4	1	no	—
166	C₂³×C₃₇	—	4	1	no	—
167	C₂³×C₃₇	—	4	1	no	—
168	C₂³×C₃₇	—	4	1	no	—
169	C₂³×C₃₇	—	4	1	no	—
170	C₂³×C₃₇	—	4	1	no	—
171	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₃₇	—	2	4	no	—
173	Q₈×C₃₇	—	4	2	no	—
174	Q₈×C₃₇	—	4	2	no	—
175	Q₈×C₃₇	—	4	2	no	—
176	Q₈×C₃₇	—	4	2	no	—
177	Q₈×C₃₇	—	4	2	no	—
178	Q₈×C₃₇	—	8	4	no	—
179	D₄×C₃₇	—	2	4	no	—
180	D₄×C₃₇	—	4	2	no	—
181	C₂×C₄×C₃₇	—	2	1	no	—
182	C₂×C₄×C₃₇	—	2	1	no	—
183	C₂×C₄×C₃₇	—	2	1	no	—
184	C₂×C₄×C₃₇	—	2	1	no	—
185	C₂×C₄×C₃₇	—	2	1	no	—
186	C₂×C₄×C₃₇	—	2	1	no	—
187	C₂×C₄×C₃₇	—	2	1	no	—
188	C₂×C₄×C₃₇	—	2	1	no	—
189	C₂×C₄×C₃₇	—	2	2	no	—
190	C₂×C₄×C₃₇	—	2	1	no	—
191	C₂×C₄×C₃₇	—	2	1	no	—
192	C₂×C₄×C₃₇	—	2	1	no	—
193	C₂×C₄×C₃₇	—	2	1	no	—
194	C₂×C₄×C₃₇	—	2	1	no	—
195	C₂×C₄×C₃₇	—	2	1	no	—
196	C₂×C₄×C₃₇	—	4	1	no	—
197	C₂×C₄×C₃₇	—	4	1	no	—
198	C₂×C₄×C₃₇	—	4	2	no	—
199	C₂×C₄×C₃₇	—	4	2	no	—
200	C₂×C₄×C₃₇	—	4	2	no	—
201	C₂×C₄×C₃₇	—	4	1	no	—
202	C₂×C₄×C₃₇	—	4	1	no	—
203	C₂×C₄×C₃₇	—	4	2	no	—
204	C₂×C₄×C₃₇	—	4	1	no	—
205	C₂×C₄×C₃₇	—	4	1	no	—
206	C₂×C₄×C₃₇	—	4	1	no	—
207	C₂×C₄×C₃₇	—	4	1	no	—
208	C₂×C₄×C₃₇	—	4	2	no	—
209	C₂×C₄×C₃₇	—	4	2	no	—
210	C₂×C₄×C₃₇	—	8	4	no	—
211	C₂×C₄×C₃₇	#121	1	2	yes	—
212	C₂×C₄×C₃₇	#121	1	2	yes	—
213	C₂×C₄×C₃₇	#137	1	2	yes	—
214	C₂×C₄×C₃₇	#137	1	2	yes	—
215	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₃₇	C₂×#41	1	2	yes	—
217	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₃₇	—	2	4	no	—
220	C₈×C₃₇	—	4	2	no	—
221	#28620	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₃₇	—	4	2	no	—
223	C₂²×C₃₇	—	4	2	no	—
224	C₂²×C₃₇	—	4	2	no	—
225	C₂²×C₃₇	—	8	1	no	—
226	C₂²×C₃₇	—	8	1	no	—
227	C₂²×C₃₇	—	8	1	no	—
228	C₂²×C₃₇	—	8	1	no	—
229	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
230	C₂²×C₃₇	#532	1	1	yes	characteristic
231	C₂²×C₃₇	#535	1	1	yes	characteristic
232	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
233	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
234	C₂²×C₃₇	#575	1	1	yes	characteristic
235	C₂²×C₃₇	#575	1	1	yes	characteristic
236	C₄×C₃₇	—	2	2	no	—
237	C₄×C₃₇	—	2	2	no	—
238	C₄×C₃₇	—	2	2	no	—
239	C₄×C₃₇	—	2	2	no	—
240	C₄×C₃₇	—	4	1	no	—
241	C₄×C₃₇	—	4	1	no	—
242	C₄×C₃₇	—	4	2	no	—
243	C₄×C₃₇	—	8	1	no	—
244	C₄×C₃₇	—	8	1	no	—
245	C₄×C₃₇	—	8	2	no	—
246	C₄×C₃₇	—	8	2	no	—
247	C₄×C₃₇	#546	1	2	yes	—
248	C₄×C₃₇	#559	1	2	yes	—
249	C₂×#497	C₂×C₃₇	1	1	yes	characteristic
250	C₂×#489	C₂×C₃₇	1	1	yes	characteristic
251	#2862	C₂×C₃₇	1	1	yes	characteristic, complemented
252	C₄×#124	C₂×C₃₇	1	1	yes	characteristic
253	#2056	C₂×C₃₇	1	2	yes	complemented
254	#2055	C₂×C₃₇	1	2	yes	—
255	#1993	C₂×C₃₇	1	1	yes	characteristic, complemented
256	#1960	C₂×C₃₇	1	1	yes	characteristic, complemented
257	#1878	C₂×C₃₇	1	2	yes	complemented
258	#1877	C₂×C₃₇	1	2	yes	—
259	#1767	C₂×C₃₇	1	1	yes	characteristic, complemented
260	C₂×C₃₇	—	8	2	no	—
261	C₂×C₃₇	#2544	1	1	yes	characteristic
262	C₂×C₃₇	#3039	1	1	yes	characteristic
263	C₂×C₃₇	#3040	1	1	yes	characteristic
264	C₂×C₃₇	#3172	1	1	yes	characteristic
265	C₂×C₃₇	#3181	1	1	yes	characteristic
266	C₂×C₃₇	#3215	1	1	yes	characteristic
267	C₂×C₃₇	#3216	1	1	yes	characteristic
268	C₂²×Q₁₆	C₂²×C₃₇	1	2	yes	—
269	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
272	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
275	#497	—	2	4	no	—
276	#489	—	2	4	no	—
277	C₂×C₄⋊C₈	C₂²×C₃₇	1	2	yes	—
278	C₂×#103	C₂²×C₃₇	1	2	yes	—
279	C₂×#103	C₂²×C₃₇	1	2	yes	—
280	C₂×#103	C₂²×C₃₇	1	2	yes	—
281	C₂×#102	C₂²×C₃₇	1	2	yes	—
282	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
283	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
284	#391	—	2	1	no	—
285	#391	—	2	1	no	—
286	#391	C₂²×C₃₇	1	2	yes	—
287	#391	C₂²×C₃₇	1	1	yes	characteristic
288	#391	C₂²×C₃₇	1	2	yes	—
289	#390	C₂²×C₃₇	1	1	yes	characteristic
290	#388	—	2	1	no	—
291	#388	—	2	1	no	—
292	#382	—	2	1	no	—
293	#382	—	2	1	no	—
294	#382	C₂²×C₃₇	1	1	yes	characteristic
295	C₄×C₂²⋊C₄	—	2	1	no	—
296	C₄×C₂²⋊C₄	—	2	1	no	—
297	C₄³	C₂²×C₃₇	1	1	yes	characteristic
298	#340	C₂²×C₃₇	1	2	yes	—
299	#340	C₂²×C₃₇	1	2	yes	—
300	#336	C₂²×C₃₇	1	2	yes	—
301	C₃₇	#28620	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
304	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂×Q₁₆	—	2	4	no	—
308	C₂×Q₁₆	—	2	4	no	—
309	C₂×Q₁₆	—	4	2	no	—
310	C₂×SD₁₆	—	2	4	no	—
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×SD₁₆	—	4	2	no	—
313	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
314	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	#124	—	2	2	no	—
320	#124	D₄×C₃₇	1	4	yes	—
321	C₄×Q₈	—	4	2	no	—
322	C₄×D₄	—	4	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₃₇	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
343	C₄⋊C₈	—	2	4	no	—
344	#103	—	2	4	no	—
345	#103	—	4	2	no	—
346	#103	—	4	2	no	—
347	#102	—	2	4	no	—
348	#97	—	2	2	no	—
349	#97	—	2	2	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	C₂⁴	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
391	Q₁₆	—	4	8	no	—
392	SD₁₆	—	4	8	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	#41×C₃₇	1	4	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	4	2	no	—
419	C₄²	C₂×D₄×C₃₇	1	2	yes	—
420	C₄²	#41×C₃₇	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	8	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	4	no	—
468	C₂×C₄	#121×C₃₇	1	2	yes	—
469	C₂×C₄	#121×C₃₇	1	2	yes	—
470	C₂×C₄	#137×C₃₇	1	2	yes	—
471	C₂×C₄	#137×C₃₇	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₃₇	1	2	yes	—
474	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
476	C₈	—	2	4	no	—
477	C₈	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
486	C₂²	C₃₇×#532	1	1	yes	characteristic
487	C₂²	C₃₇×#535	1	1	yes	characteristic
488	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
489	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
490	C₂²	C₃₇×#575	1	1	yes	characteristic
491	C₂²	C₃₇×#575	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	1	no	—
501	C₄	—	8	2	no	—
502	C₄	—	8	2	no	—
503	C₄	C₃₇×#546	1	2	yes	—
504	C₄	C₃₇×#559	1	2	yes	—
505	C₂	—	8	2	no	—
506	C₂	C₃₇×#2544	1	1	yes	characteristic
507	C₂	C₃₇×#3039	1	1	yes	characteristic
508	C₂	C₃₇×#3040	1	1	yes	characteristic
509	C₂	C₃₇×#3172	1	1	yes	characteristic
510	C₂	C₃₇×#3181	1	1	yes	characteristic
511	C₂	C₃₇×#3215	1	1	yes	characteristic
512	C₂	C₃₇×#3216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₄³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2862	C₂	semidirect
5. C₃₇×#2056	C₂	semidirect
7. C₃₇×#1993	C₂	semidirect
8. C₃₇×#1960	C₂	semidirect
9. C₃₇×#1878	C₂	semidirect
11. C₃₇×#1767	C₂	semidirect
221. #28620	C₃₇	direct (N × H)
251. #2862	C₂×C₃₇	semidirect
253. #2056	C₂×C₃₇	semidirect
255. #1993	C₂×C₃₇	semidirect
256. #1960	C₂×C₃₇	semidirect
257. #1878	C₂×C₃₇	semidirect
259. #1767	C₂×C₃₇	semidirect
301. C₃₇	#28620	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×#497	2
C₂×C₃₇×#489	2
C₃₇×#2862	2
C₄×#124×C₃₇	2
C₃₇×#2056	2
C₃₇×#2055	2
C₃₇×#1993	2
C₃₇×#1960	2
C₃₇×#1878	2
C₃₇×#1877	2
C₃₇×#1767	2
#28620	37

Subgroups — C37×#28620 #22649873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28620 #22649873