Subgroups — C₃₇×#29905 #22651158

Order 9472.

730 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3011	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#2889	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#2082	C₂	1	2	yes	maximal, complemented
4	C₃₇×#2080	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2049	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2047	C₂	1	2	yes	maximal, complemented
7	C₃₇×#1915	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#1909	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#1868	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#1858	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#1796	C₂	1	1	yes	maximal, characteristic
12	C₂×2₋¹⁺⁴×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×#137×C₃₇	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
15	C₃₇×#568	C₂²	1	1	yes	characteristic
16	C₃₇×#568	C₂²	1	1	yes	characteristic
17	C₃₇×#536	C₂²	1	1	yes	characteristic
18	C₃₇×#452	—	2	2	no	—
19	C₃₇×#451	—	2	2	no	—
20	C₃₇×#430	C₂²	1	2	yes	—
21	C₃₇×#424	C₂²	1	2	yes	—
22	C₃₇×#421	C₂²	1	2	yes	—
23	C₃₇×#419	C₂²	1	1	yes	characteristic
24	C₃₇×#419	C₂²	1	2	yes	—
25	C₃₇×#419	C₂²	1	2	yes	—
26	C₃₇×#416	C₂²	1	1	yes	characteristic
27	C₃₇×#413	—	2	2	no	—
28	C₃₇×#413	C₂²	1	1	yes	characteristic
29	C₃₇×#413	C₂²	1	2	yes	—
30	C₂×#101×C₃₇	—	2	2	no	—
31	C₂×#101×C₃₇	C₂²	1	2	yes	—
32	C₂×#101×C₃₇	C₂²	1	2	yes	—
33	C₃₇×#410	C₂²	1	1	yes	characteristic
34	C₃₇×#408	C₂²	1	1	yes	characteristic
35	C₃₇×#344	C₂²	1	2	yes	—
36	C₃₇×#344	C₂²	1	2	yes	—
37	C₃₇×#341	C₂²	1	2	yes	—
38	C₃₇×H(3,ℤ/4)	C₂²	1	2	yes	—
39	2₋¹⁺⁴×C₃₇	—	4	2	no	—
40	2₋¹⁺⁴×C₃₇	—	4	2	no	—
41	C₂×#41×C₃₇	—	2	1	no	—
42	C₂×#41×C₃₇	—	2	2	no	—
43	C₂×#41×C₃₇	D₄	1	2	yes	—
44	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
45	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₃₇	—	2	1	no	—
47	C₂²×Q₈×C₃₇	D₄	1	2	yes	—
48	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
50	#137×C₃₇	—	4	2	no	—
51	C₂×Q₁₆×C₃₇	—	2	2	no	—
52	C₂×Q₁₆×C₃₇	—	2	1	no	—
53	C₂×Q₁₆×C₃₇	—	4	2	no	—
54	C₂×SD₁₆×C₃₇	—	2	1	no	—
55	#131×C₃₇	—	4	2	no	—
56	#131×C₃₇	—	4	2	no	—
57	C₂×M₁₆×C₃₇	—	2	2	no	—
58	C₂×M₁₆×C₃₇	—	2	2	no	—
59	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
61	C₂×M₁₆×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₃₇	—	2	1	no	—
65	#124×C₃₇	—	2	1	no	—
66	#123×C₃₇	—	2	2	no	—
67	C₂²⋊Q₈×C₃₇	—	2	2	no	—
68	#117×C₃₇	C₂³	1	1	yes	characteristic
69	#117×C₃₇	C₂³	1	2	yes	—
70	#108×C₃₇	—	4	2	no	—
71	C₄⋊C₈×C₃₇	—	4	2	no	—
72	#104×C₃₇	—	4	2	no	—
73	#103×C₃₇	—	2	1	no	—
74	#103×C₃₇	—	2	2	no	—
75	#103×C₃₇	—	4	2	no	—
76	#103×C₃₇	—	4	2	no	—
77	#102×C₃₇	—	2	1	no	—
78	#101×C₃₇	—	2	2	no	—
79	#101×C₃₇	—	2	4	no	—
80	#101×C₃₇	—	2	1	no	—
81	#101×C₃₇	—	4	2	no	—
82	#100×C₃₇	—	2	2	no	—
83	#100×C₃₇	—	2	1	no	—
84	#99×C₃₇	—	2	2	no	—
85	C₂²⋊C₈×C₃₇	—	2	2	no	—
86	#41×C₃₇	—	2	2	no	—
87	#41×C₃₇	—	2	2	no	—
88	#41×C₃₇	—	2	2	no	—
89	#41×C₃₇	—	2	2	no	—
90	#41×C₃₇	—	4	2	no	—
91	#41×C₃₇	—	4	2	no	—
92	#41×C₃₇	—	4	8	no	—
93	#41×C₃₇	—	4	4	no	—
94	C₂×Q₈×C₃₇	—	2	2	no	—
95	C₂×Q₈×C₃₇	—	2	1	no	—
96	C₂×Q₈×C₃₇	—	2	1	no	—
97	C₂×Q₈×C₃₇	—	2	1	no	—
98	C₂×Q₈×C₃₇	—	2	2	no	—
99	C₂×Q₈×C₃₇	—	2	2	no	—
100	C₂×Q₈×C₃₇	—	2	2	no	—
101	C₂×Q₈×C₃₇	—	2	2	no	—
102	C₂×Q₈×C₃₇	—	4	2	no	—
103	C₂×Q₈×C₃₇	—	4	2	no	—
104	C₂×Q₈×C₃₇	—	4	4	no	—
105	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₃₇	#41	1	1	yes	characteristic
108	C₂×D₄×C₃₇	—	2	2	no	—
109	C₂×D₄×C₃₇	—	2	1	no	—
110	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₃₇	#41	1	2	yes	—
112	C₂×D₄×C₃₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₃₇	—	2	2	no	—
114	C₂²×C₄×C₃₇	—	2	1	no	—
115	C₂²×C₄×C₃₇	—	2	2	no	—
116	C₂²×C₄×C₃₇	—	2	1	no	—
117	C₂²×C₄×C₃₇	—	2	1	no	—
118	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₃₇	—	4	4	no	—
121	Q₁₆×C₃₇	—	4	2	no	—
122	SD₁₆×C₃₇	—	4	2	no	—
123	M₁₆×C₃₇	—	2	2	no	—
124	M₁₆×C₃₇	—	2	2	no	—
125	M₁₆×C₃₇	—	2	2	no	—
126	M₁₆×C₃₇	—	2	2	no	—
127	M₁₆×C₃₇	—	2	2	no	—
128	M₁₆×C₃₇	—	2	2	no	—
129	M₁₆×C₃₇	—	2	2	no	—
130	M₁₆×C₃₇	—	4	2	no	—
131	M₁₆×C₃₇	—	4	2	no	—
132	C₂×C₈×C₃₇	—	2	1	no	—
133	C₂×C₈×C₃₇	—	2	1	no	—
134	C₂×C₈×C₃₇	—	2	2	no	—
135	C₂×C₈×C₃₇	—	2	2	no	—
136	C₂×C₈×C₃₇	—	2	2	no	—
137	C₂×C₈×C₃₇	—	2	2	no	—
138	C₂×C₈×C₃₇	—	4	2	no	—
139	C₂×C₈×C₃₇	—	4	2	no	—
140	C₄⋊C₄×C₃₇	—	2	1	no	—
141	C₄⋊C₄×C₃₇	—	2	2	no	—
142	C₄⋊C₄×C₃₇	—	4	2	no	—
143	C₂²⋊C₄×C₃₇	—	2	2	no	—
144	C₂²⋊C₄×C₃₇	—	2	1	no	—
145	C₂²⋊C₄×C₃₇	—	4	2	no	—
146	C₄²×C₃₇	—	2	1	no	—
147	C₄²×C₃₇	—	2	2	no	—
148	C₂³×C₃₇	—	2	1	no	—
149	C₂³×C₃₇	#123	1	2	yes	—
150	C₂³×C₃₇	C₂×#41	1	1	yes	characteristic
151	Q₈×C₃₇	—	2	2	no	—
152	Q₈×C₃₇	—	2	2	no	—
153	Q₈×C₃₇	—	2	1	no	—
154	Q₈×C₃₇	—	2	2	no	—
155	Q₈×C₃₇	—	2	1	no	—
156	Q₈×C₃₇	—	4	4	no	—
157	Q₈×C₃₇	—	4	2	no	—
158	Q₈×C₃₇	—	4	1	no	—
159	Q₈×C₃₇	—	4	1	no	—
160	Q₈×C₃₇	—	4	2	no	—
161	D₄×C₃₇	—	2	4	no	—
162	D₄×C₃₇	—	2	1	no	—
163	D₄×C₃₇	—	2	1	no	—
164	D₄×C₃₇	—	2	2	no	—
165	D₄×C₃₇	—	4	4	no	—
166	D₄×C₃₇	—	4	2	no	—
167	C₂×C₄×C₃₇	—	2	2	no	—
168	C₂×C₄×C₃₇	—	2	2	no	—
169	C₂×C₄×C₃₇	—	2	1	no	—
170	C₂×C₄×C₃₇	—	2	2	no	—
171	C₂×C₄×C₃₇	—	4	4	no	—
172	C₂×C₄×C₃₇	—	4	4	no	—
173	C₂×C₄×C₃₇	—	4	2	no	—
174	C₂×C₄×C₃₇	—	4	2	no	—
175	C₂×C₄×C₃₇	—	4	1	no	—
176	C₂×C₄×C₃₇	—	4	1	no	—
177	C₂×C₄×C₃₇	—	4	2	no	—
178	C₂×C₄×C₃₇	—	4	2	no	—
179	C₂×C₄×C₃₇	#123	1	2	yes	—
180	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₃₇	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₃₇	—	4	1	no	—
185	C₈×C₃₇	—	4	2	no	—
186	C₈×C₃₇	—	4	2	no	—
187	C₈×C₃₇	—	4	1	no	—
188	C₈×C₃₇	—	4	2	no	—
189	#29905	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₃₇	—	2	2	no	—
191	C₂²×C₃₇	—	4	1	no	—
192	C₂²×C₃₇	—	4	2	no	—
193	C₂²×C₃₇	—	4	1	no	—
194	C₂²×C₃₇	—	8	1	no	—
195	C₂²×C₃₇	C₂×#123	1	1	yes	characteristic
196	C₂²×C₃₇	#538	1	2	yes	—
197	C₄×C₃₇	—	2	2	no	—
198	C₄×C₃₇	—	4	2	no	—
199	C₄×C₃₇	—	4	1	no	—
200	C₄×C₃₇	—	8	1	no	—
201	C₄×C₃₇	—	8	2	no	—
202	C₄×C₃₇	—	8	1	no	—
203	C₄×C₃₇	#534	1	1	yes	characteristic
204	C₄×C₃₇	#534	1	1	yes	characteristic
205	C₄×C₃₇	#538	1	2	yes	—
206	#3011	C₂×C₃₇	1	1	yes	characteristic
207	#2889	C₂×C₃₇	1	1	yes	characteristic
208	#2082	C₂×C₃₇	1	2	yes	complemented
209	#2080	C₂×C₃₇	1	2	yes	complemented
210	#2049	C₂×C₃₇	1	2	yes	complemented
211	#2047	C₂×C₃₇	1	2	yes	complemented
212	#1915	C₂×C₃₇	1	1	yes	characteristic, complemented
213	#1909	C₂×C₃₇	1	1	yes	characteristic, complemented
214	#1868	C₂×C₃₇	1	1	yes	characteristic, complemented
215	#1858	C₂×C₃₇	1	1	yes	characteristic, complemented
216	#1796	C₂×C₃₇	1	1	yes	characteristic
217	C₂×C₃₇	—	2	1	no	—
218	C₂×C₃₇	—	2	2	no	—
219	C₂×C₃₇	—	4	2	no	—
220	C₂×C₃₇	—	8	1	no	—
221	C₂×C₃₇	#2622	1	1	yes	characteristic
222	C₂×2₋¹⁺⁴	C₂²×C₃₇	1	1	yes	characteristic
223	C₂×#137	C₂²×C₃₇	1	1	yes	characteristic
224	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
225	#568	C₂²×C₃₇	1	1	yes	characteristic
226	#568	C₂²×C₃₇	1	1	yes	characteristic
227	#536	C₂²×C₃₇	1	1	yes	characteristic
228	#452	—	2	2	no	—
229	#451	—	2	2	no	—
230	#430	C₂²×C₃₇	1	2	yes	—
231	#424	C₂²×C₃₇	1	2	yes	—
232	#421	C₂²×C₃₇	1	2	yes	—
233	#419	C₂²×C₃₇	1	1	yes	characteristic
234	#419	C₂²×C₃₇	1	2	yes	—
235	#419	C₂²×C₃₇	1	2	yes	—
236	#416	C₂²×C₃₇	1	1	yes	characteristic
237	#413	—	2	2	no	—
238	#413	C₂²×C₃₇	1	2	yes	—
239	#413	C₂²×C₃₇	1	1	yes	characteristic
240	C₂×#101	—	2	2	no	—
241	C₂×#101	C₂²×C₃₇	1	2	yes	—
242	C₂×#101	C₂²×C₃₇	1	2	yes	—
243	#410	C₂²×C₃₇	1	1	yes	characteristic
244	#408	C₂²×C₃₇	1	1	yes	characteristic
245	#344	C₂²×C₃₇	1	2	yes	—
246	#344	C₂²×C₃₇	1	2	yes	—
247	#341	C₂²×C₃₇	1	2	yes	—
248	H(3,ℤ/4)	C₂²×C₃₇	1	2	yes	—
249	C₃₇	#29905	1	1	yes	characteristic, direct product factor, Sylow
250	2₋¹⁺⁴	—	4	2	no	—
251	2₋¹⁺⁴	—	4	2	no	—
252	C₂×#41	—	2	1	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	D₄×C₃₇	1	2	yes	—
255	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
256	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	D₄×C₃₇	1	2	yes	—
259	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
260	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
261	#137	—	4	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×Q₁₆	—	4	2	no	—
265	C₂×SD₁₆	—	2	1	no	—
266	#131	—	4	2	no	—
267	#131	—	4	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
271	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
272	C₂×M₁₆	C₂³×C₃₇	1	1	yes	characteristic
273	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
274	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	1	no	—
276	#124	—	2	1	no	—
277	#123	—	2	2	no	—
278	C₂²⋊Q₈	—	2	2	no	—
279	#117	C₂³×C₃₇	1	1	yes	characteristic
280	#117	C₂³×C₃₇	1	2	yes	—
281	#108	—	4	2	no	—
282	C₄⋊C₈	—	4	2	no	—
283	#104	—	4	2	no	—
284	#103	—	2	1	no	—
285	#103	—	2	2	no	—
286	#103	—	4	2	no	—
287	#103	—	4	2	no	—
288	#102	—	2	1	no	—
289	#101	—	2	2	no	—
290	#101	—	2	4	no	—
291	#101	—	2	1	no	—
292	#101	—	4	2	no	—
293	#100	—	2	2	no	—
294	#100	—	2	1	no	—
295	#99	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	4	2	no	—
302	#41	—	4	2	no	—
303	#41	—	4	8	no	—
304	#41	—	4	4	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
317	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
318	C₂×Q₈	#41×C₃₇	1	1	yes	characteristic
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
322	C₂×D₄	#41×C₃₇	1	2	yes	—
323	C₂×D₄	#41×C₃₇	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
331	Q₁₆	—	4	4	no	—
332	Q₁₆	—	4	2	no	—
333	SD₁₆	—	4	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	2	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	4	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	#123×C₃₇	1	2	yes	—
361	C₂³	C₂×#41×C₃₇	1	1	yes	characteristic
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	1	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#123×C₃₇	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
393	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
394	C₂×C₄	H(5,𝔽₂)×C₃₇	1	2	yes	—
395	C₈	—	4	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₂×#123×C₃₇	1	1	yes	characteristic
406	C₂²	C₃₇×#538	1	2	yes	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	1	no	—
413	C₄	C₃₇×#534	1	1	yes	characteristic
414	C₄	C₃₇×#534	1	1	yes	characteristic
415	C₄	C₃₇×#538	1	2	yes	—
416	C₂	—	2	1	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	2	no	—
419	C₂	—	8	1	no	—
420	C₂	C₃₇×#2622	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₇	#2622
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₂×2₋¹⁺⁴×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₇×#2082	C₂	semidirect
4. C₃₇×#2080	C₂	semidirect
5. C₃₇×#2049	C₂	semidirect
6. C₃₇×#2047	C₂	semidirect
7. C₃₇×#1915	C₂	semidirect
8. C₃₇×#1909	C₂	semidirect
9. C₃₇×#1868	C₂	semidirect
10. C₃₇×#1858	C₂	semidirect
189. #29905	C₃₇	direct (N × H)
208. #2082	C₂×C₃₇	semidirect
209. #2080	C₂×C₃₇	semidirect
210. #2049	C₂×C₃₇	semidirect
211. #2047	C₂×C₃₇	semidirect
212. #1915	C₂×C₃₇	semidirect
213. #1909	C₂×C₃₇	semidirect
214. #1868	C₂×C₃₇	semidirect
215. #1858	C₂×C₃₇	semidirect
249. C₃₇	#29905	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×#3011	2
C₃₇×#2889	2
C₃₇×#2082	2
C₃₇×#2080	2
C₃₇×#2049	2
C₃₇×#2047	2
C₃₇×#1915	2
C₃₇×#1909	2
C₃₇×#1868	2
C₃₇×#1858	2
C₃₇×#1796	2
#29905	37

Subgroups — C37×#29905 #22651158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#29905 #22651158