Subgroups — C₃₇×#61561 #22682814

Order 9472.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3297	C₂	1	4	yes	maximal, complemented
4	C₃₇×#3296	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3282	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3280	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₃₇×#3189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#3188	C₂	1	2	yes	maximal, complemented
10	C₃₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3105	C₂	1	2	yes	maximal, complemented
12	C₃₇×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₇	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×#135×C₃₇	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₃₇	C₂²	1	2	yes	complemented
20	C₂²×D₈×C₃₇	C₂²	1	2	yes	complemented
21	C₃₇×#553	—	2	2	no	—
22	C₃₇×#553	C₂²	1	2	yes	complemented
23	C₃₇×#552	C₂²	1	2	yes	complemented
24	C₃₇×#551	—	2	2	no	—
25	C₃₇×#548	C₂²	1	2	yes	complemented
26	C₃₇×#546	—	2	2	no	—
27	C₃₇×#546	—	2	2	no	—
28	C₃₇×#546	C₂²	1	4	yes	—
29	C₃₇×#546	C₂²	1	4	yes	complemented
30	C₃₇×#546	C₂²	1	2	yes	complemented
31	C₃₇×#539	—	2	1	no	—
32	C₃₇×#538	—	2	1	no	—
33	C₃₇×#534	—	2	1	no	—
34	C₃₇×#529	C₂²	1	2	yes	complemented
35	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic, complemented
36	C₃₇×#525	C₂²	1	2	yes	complemented
37	C₂×#123×C₃₇	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₃₇	—	2	1	no	—
41	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#120×C₃₇	—	2	1	no	—
44	C₃₇×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊C₄×C₃₇	—	2	1	no	—
48	C₃₇×#495	C₂²	1	4	yes	complemented
49	C₃₇×#488	C₂²	1	4	yes	complemented
50	C₃₇×#484	C₂²	1	2	yes	complemented
51	C₃₇×#484	C₂²	1	2	yes	complemented
52	C₃₇×#483	C₂²	1	2	yes	complemented
53	C₃₇×#482	C₂²	1	4	yes	complemented
54	C₃₇×#481	C₂²	1	2	yes	complemented
55	C₃₇×#478	C₂²	1	4	yes	complemented
56	C₃₇×#467	C₂²	1	4	yes	complemented
57	C₃₇×#466	C₂²	1	4	yes	complemented
58	C₃₇×#465	C₂²	1	4	yes	complemented
59	C₃₇×#465	C₂²	1	4	yes	complemented
60	C₃₇×#464	C₂²	1	4	yes	complemented
61	C₃₇×#463	C₂²	1	4	yes	complemented
62	C₃₇×#463	C₂²	1	4	yes	complemented
63	C₃₇×#452	C₂²	1	4	yes	complemented
64	C₃₇×#451	C₂²	1	2	yes	complemented
65	C₃₇×#451	C₂²	1	2	yes	complemented
66	C₃₇×#450	C₂²	1	2	yes	complemented
67	C₃₇×#450	C₂²	1	2	yes	complemented
68	C₃₇×#450	C₂²	1	4	yes	complemented
69	C₃₇×#450	C₂²	1	2	yes	complemented
70	C₃₇×#449	C₂²	1	4	yes	complemented
71	C₃₇×#449	C₂²	1	4	yes	complemented
72	C₃₇×#448	C₂²	1	2	yes	complemented
73	C₃₇×#447	C₂²	1	2	yes	—
74	C₃₇×#447	C₂²	1	2	yes	—
75	C₃₇×#447	C₂²	1	4	yes	complemented
76	C₄×SD₁₆×C₃₇	C₂²	1	4	yes	complemented
77	C₄×D₈×C₃₇	C₂²	1	4	yes	complemented
78	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
80	C₃₇×#431	C₂²	1	2	yes	complemented
81	C₃₇×#416	C₂²	1	4	yes	complemented
82	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
83	C₂×#102×C₃₇	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
85	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊C₈×C₃₇	C₂²	1	2	yes	complemented
87	C₂⁵×C₃₇	—	2	1	no	—
88	C₂×#41×C₃₇	—	2	2	no	—
89	C₂×#41×C₃₇	—	4	4	no	—
90	C₂×#41×C₃₇	C₂³	1	4	yes	—
91	C₂×#41×C₃₇	C₂³	1	2	yes	complemented
92	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₃₇	—	2	1	no	—
95	C₂²×D₄×C₃₇	—	2	1	no	—
96	C₂²×D₄×C₃₇	—	2	1	no	—
97	C₂²×D₄×C₃₇	—	2	1	no	—
98	C₂²×D₄×C₃₇	—	2	1	no	—
99	C₂²×D₄×C₃₇	—	2	1	no	—
100	C₂²×D₄×C₃₇	—	4	4	no	—
101	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
104	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₇	—	2	1	no	—
108	C₂³×C₄×C₃₇	—	2	1	no	—
109	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
111	#135×C₃₇	—	4	8	no	—
112	C₂×Q₁₆×C₃₇	C₂³	1	4	yes	complemented
113	C₂×SD₁₆×C₃₇	—	4	4	no	—
114	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	complemented
117	C₂×D₈×C₃₇	—	4	4	no	—
118	C₂×D₈×C₃₇	C₂³	1	4	yes	—
119	C₂×D₈×C₃₇	C₂³	1	4	yes	—
120	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
122	C₂²×C₈×C₃₇	C₂³	1	4	yes	complemented
123	#126×C₃₇	—	2	2	no	—
124	#126×C₃₇	—	2	2	no	—
125	#126×C₃₇	—	2	2	no	—
126	#125×C₃₇	—	2	2	no	—
127	#125×C₃₇	C₂³	1	2	yes	complemented
128	#124×C₃₇	—	2	2	no	—
129	#124×C₃₇	—	2	2	no	—
130	#124×C₃₇	C₂³	1	4	yes	—
131	#124×C₃₇	C₂³	1	2	yes	complemented
132	#123×C₃₇	—	2	2	no	—
133	#123×C₃₇	—	2	2	no	—
134	#123×C₃₇	—	2	2	no	—
135	#123×C₃₇	—	2	4	no	—
136	#123×C₃₇	—	2	4	no	—
137	#123×C₃₇	—	2	2	no	—
138	#123×C₃₇	—	2	2	no	—
139	C₂²⋊Q₈×C₃₇	—	2	1	no	—
140	C₂²⋊Q₈×C₃₇	—	2	1	no	—
141	C₂²⋊Q₈×C₃₇	—	2	1	no	—
142	C₂²⋊Q₈×C₃₇	—	2	1	no	—
143	C₂²⋊Q₈×C₃₇	—	2	2	no	—
144	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	complemented
149	#121×C₃₇	—	2	2	no	—
150	#121×C₃₇	—	2	2	no	—
151	#121×C₃₇	—	2	1	no	—
152	#121×C₃₇	—	2	1	no	—
153	#121×C₃₇	—	2	2	no	—
154	#121×C₃₇	—	2	4	no	—
155	#121×C₃₇	—	2	4	no	—
156	#121×C₃₇	—	2	2	no	—
157	#121×C₃₇	C₂³	1	2	yes	—
158	#121×C₃₇	C₂³	1	2	yes	—
159	#121×C₃₇	C₂³	1	4	yes	—
160	#121×C₃₇	C₂³	1	2	yes	complemented
161	#120×C₃₇	—	2	2	no	—
162	#120×C₃₇	—	2	4	no	—
163	#120×C₃₇	—	2	4	no	—
164	#120×C₃₇	—	2	2	no	—
165	C₄×Q₈×C₃₇	C₂³	1	2	yes	complemented
166	C₄×D₄×C₃₇	—	2	2	no	—
167	C₄×D₄×C₃₇	—	2	2	no	—
168	C₄×D₄×C₃₇	—	2	2	no	—
169	C₄×D₄×C₃₇	—	2	2	no	—
170	C₄×D₄×C₃₇	—	2	2	no	—
171	C₄×D₄×C₃₇	—	2	2	no	—
172	C₄×D₄×C₃₇	D₄	1	2	yes	—
173	C₄×D₄×C₃₇	D₄	1	2	yes	—
174	C₄×D₄×C₃₇	C₂³	1	4	yes	—
175	C₄×D₄×C₃₇	C₂³	1	2	yes	—
176	C₄×D₄×C₃₇	C₂³	1	2	yes	—
177	C₄×D₄×C₃₇	C₂³	1	2	yes	complemented
178	#117×C₃₇	—	2	2	no	—
179	#117×C₃₇	—	2	2	no	—
180	#117×C₃₇	C₂³	1	2	yes	complemented
181	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
182	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
183	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
196	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
200	#107×C₃₇	C₂³	1	4	yes	complemented
201	#106×C₃₇	C₂³	1	4	yes	complemented
202	C₄⋊C₈×C₃₇	C₂³	1	4	yes	complemented
203	#103×C₃₇	C₂³	1	4	yes	complemented
204	#103×C₃₇	C₂³	1	4	yes	complemented
205	#103×C₃₇	C₂³	1	4	yes	complemented
206	#102×C₃₇	C₂³	1	4	yes	—
207	#102×C₃₇	C₂³	1	4	yes	—
208	#102×C₃₇	C₂³	1	4	yes	—
209	#102×C₃₇	C₂³	1	4	yes	—
210	#102×C₃₇	C₂³	1	4	yes	complemented
211	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
212	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
213	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	complemented
216	C₄×C₈×C₃₇	C₂³	1	4	yes	complemented
217	C₂⁴×C₃₇	—	2	1	no	—
218	C₂⁴×C₃₇	—	2	1	no	—
219	C₂⁴×C₃₇	—	2	2	no	—
220	C₂⁴×C₃₇	—	2	2	no	—
221	C₂⁴×C₃₇	—	2	1	no	—
222	C₂⁴×C₃₇	—	4	4	no	—
223	C₂⁴×C₃₇	—	4	4	no	—
224	C₂⁴×C₃₇	—	8	2	no	—
225	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
226	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
227	#41×C₃₇	—	2	8	no	—
228	#41×C₃₇	—	4	4	no	—
229	#41×C₃₇	—	4	4	no	—
230	#41×C₃₇	—	4	8	no	—
231	C₂×Q₈×C₃₇	—	2	1	no	—
232	C₂×Q₈×C₃₇	—	2	1	no	—
233	C₂×Q₈×C₃₇	—	4	2	no	—
234	C₂×Q₈×C₃₇	—	4	2	no	—
235	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
237	C₂×D₄×C₃₇	—	2	4	no	—
238	C₂×D₄×C₃₇	—	2	4	no	—
239	C₂×D₄×C₃₇	—	2	4	no	—
240	C₂×D₄×C₃₇	—	2	4	no	—
241	C₂×D₄×C₃₇	—	2	2	no	—
242	C₂×D₄×C₃₇	—	2	2	no	—
243	C₂×D₄×C₃₇	—	2	4	no	—
244	C₂×D₄×C₃₇	—	2	2	no	—
245	C₂×D₄×C₃₇	—	2	4	no	—
246	C₂×D₄×C₃₇	—	2	2	no	—
247	C₂×D₄×C₃₇	—	2	1	no	—
248	C₂×D₄×C₃₇	—	2	2	no	—
249	C₂×D₄×C₃₇	—	2	2	no	—
250	C₂×D₄×C₃₇	—	2	1	no	—
251	C₂×D₄×C₃₇	—	2	1	no	—
252	C₂×D₄×C₃₇	—	4	2	no	—
253	C₂×D₄×C₃₇	—	4	2	no	—
254	C₂×D₄×C₃₇	—	4	2	no	—
255	C₂×D₄×C₃₇	—	4	2	no	—
256	C₂×D₄×C₃₇	—	4	4	no	—
257	C₂×D₄×C₃₇	—	4	4	no	—
258	C₂×D₄×C₃₇	—	4	4	no	—
259	C₂×D₄×C₃₇	—	4	4	no	—
260	C₂×D₄×C₃₇	—	4	4	no	—
261	C₂×D₄×C₃₇	—	8	2	no	—
262	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
265	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
266	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₃₇	—	2	1	no	—
268	C₂²×C₄×C₃₇	—	2	1	no	—
269	C₂²×C₄×C₃₇	—	2	1	no	—
270	C₂²×C₄×C₃₇	—	2	1	no	—
271	C₂²×C₄×C₃₇	—	2	1	no	—
272	C₂²×C₄×C₃₇	—	2	4	no	—
273	C₂²×C₄×C₃₇	—	2	4	no	—
274	C₂²×C₄×C₃₇	—	2	2	no	—
275	C₂²×C₄×C₃₇	—	2	2	no	—
276	C₂²×C₄×C₃₇	—	4	2	no	—
277	C₂²×C₄×C₃₇	—	4	2	no	—
278	C₂²×C₄×C₃₇	—	4	4	no	—
279	C₂²×C₄×C₃₇	—	8	2	no	—
280	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
291	Q₁₆×C₃₇	—	4	4	no	—
292	SD₁₆×C₃₇	—	2	8	no	—
293	SD₁₆×C₃₇	—	4	4	no	—
294	SD₁₆×C₃₇	—	4	4	no	—
295	D₈×C₃₇	—	2	8	no	—
296	D₈×C₃₇	—	4	4	no	—
297	C₂×C₈×C₃₇	—	4	2	no	—
298	C₂×C₈×C₃₇	—	4	2	no	—
299	C₂×C₈×C₃₇	—	4	4	no	—
300	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
301	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₃₇	—	2	2	no	—
303	C₄⋊C₄×C₃₇	—	2	2	no	—
304	C₄⋊C₄×C₃₇	—	2	2	no	—
305	C₄⋊C₄×C₃₇	—	2	2	no	—
306	C₄⋊C₄×C₃₇	—	2	1	no	—
307	C₄⋊C₄×C₃₇	—	2	1	no	—
308	C₄⋊C₄×C₃₇	—	2	1	no	—
309	C₄⋊C₄×C₃₇	—	2	2	no	—
310	C₄⋊C₄×C₃₇	—	2	2	no	—
311	C₄⋊C₄×C₃₇	—	2	2	no	—
312	C₄⋊C₄×C₃₇	—	2	2	no	—
313	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₃₇	—	2	2	no	—
319	C₂²⋊C₄×C₃₇	—	2	2	no	—
320	C₂²⋊C₄×C₃₇	—	2	2	no	—
321	C₂²⋊C₄×C₃₇	—	2	2	no	—
322	C₂²⋊C₄×C₃₇	—	2	2	no	—
323	C₂²⋊C₄×C₃₇	—	2	2	no	—
324	C₂²⋊C₄×C₃₇	—	2	4	no	—
325	C₂²⋊C₄×C₃₇	—	2	4	no	—
326	C₂²⋊C₄×C₃₇	—	2	2	no	—
327	C₂²⋊C₄×C₃₇	—	2	2	no	—
328	C₂²⋊C₄×C₃₇	—	2	2	no	—
329	C₂²⋊C₄×C₃₇	—	2	4	no	—
330	C₂²⋊C₄×C₃₇	—	2	4	no	—
331	C₂²⋊C₄×C₃₇	—	2	2	no	—
332	C₂²⋊C₄×C₃₇	—	2	2	no	—
333	C₂²⋊C₄×C₃₇	—	2	2	no	—
334	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
338	C₄²×C₃₇	—	2	2	no	—
339	C₄²×C₃₇	—	2	2	no	—
340	C₄²×C₃₇	C₂×D₄	1	2	yes	—
341	C₄²×C₃₇	C₂⁴	1	2	yes	—
342	C₂³×C₃₇	—	2	4	no	—
343	C₂³×C₃₇	—	2	2	no	—
344	C₂³×C₃₇	—	2	2	no	—
345	C₂³×C₃₇	—	2	2	no	—
346	C₂³×C₃₇	—	2	2	no	—
347	C₂³×C₃₇	—	4	1	no	—
348	C₂³×C₃₇	—	4	1	no	—
349	C₂³×C₃₇	—	4	1	no	—
350	C₂³×C₃₇	—	4	1	no	—
351	C₂³×C₃₇	—	4	4	no	—
352	C₂³×C₃₇	—	4	4	no	—
353	C₂³×C₃₇	—	4	2	no	—
354	C₂³×C₃₇	—	4	2	no	—
355	C₂³×C₃₇	—	4	2	no	—
356	C₂³×C₃₇	—	4	2	no	—
357	C₂³×C₃₇	—	4	4	no	—
358	C₂³×C₃₇	—	4	4	no	—
359	C₂³×C₃₇	—	4	2	no	—
360	C₂³×C₃₇	—	4	2	no	—
361	C₂³×C₃₇	—	8	2	no	—
362	C₂³×C₃₇	—	8	2	no	—
363	C₂³×C₃₇	—	8	1	no	—
364	C₂³×C₃₇	—	8	1	no	—
365	C₂³×C₃₇	—	8	16	no	—
366	C₂³×C₃₇	#135	1	4	yes	complemented
367	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
368	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
371	Q₈×C₃₇	—	2	4	no	—
372	Q₈×C₃₇	—	2	4	no	—
373	Q₈×C₃₇	—	4	2	no	—
374	Q₈×C₃₇	—	8	1	no	—
375	D₄×C₃₇	—	2	4	no	—
376	D₄×C₃₇	—	2	4	no	—
377	D₄×C₃₇	—	2	4	no	—
378	D₄×C₃₇	—	2	2	no	—
379	D₄×C₃₇	—	2	4	no	—
380	D₄×C₃₇	—	2	2	no	—
381	D₄×C₃₇	—	2	2	no	—
382	D₄×C₃₇	—	4	4	no	—
383	D₄×C₃₇	—	4	4	no	—
384	D₄×C₃₇	—	4	2	no	—
385	D₄×C₃₇	—	4	8	no	—
386	D₄×C₃₇	—	4	4	no	—
387	D₄×C₃₇	—	4	4	no	—
388	D₄×C₃₇	—	8	1	no	—
389	D₄×C₃₇	—	8	2	no	—
390	D₄×C₃₇	—	8	4	no	—
391	D₄×C₃₇	—	8	2	no	—
392	D₄×C₃₇	H(5,𝔽₂)	1	4	yes	—
393	C₂×C₄×C₃₇	—	2	2	no	—
394	C₂×C₄×C₃₇	—	2	2	no	—
395	C₂×C₄×C₃₇	—	2	2	no	—
396	C₂×C₄×C₃₇	—	2	4	no	—
397	C₂×C₄×C₃₇	—	2	2	no	—
398	C₂×C₄×C₃₇	—	2	2	no	—
399	C₂×C₄×C₃₇	—	2	2	no	—
400	C₂×C₄×C₃₇	—	2	2	no	—
401	C₂×C₄×C₃₇	—	2	2	no	—
402	C₂×C₄×C₃₇	—	2	2	no	—
403	C₂×C₄×C₃₇	—	4	1	no	—
404	C₂×C₄×C₃₇	—	4	1	no	—
405	C₂×C₄×C₃₇	—	4	1	no	—
406	C₂×C₄×C₃₇	—	4	1	no	—
407	C₂×C₄×C₃₇	—	4	2	no	—
408	C₂×C₄×C₃₇	—	4	1	no	—
409	C₂×C₄×C₃₇	—	4	8	no	—
410	C₂×C₄×C₃₇	—	4	2	no	—
411	C₂×C₄×C₃₇	—	4	2	no	—
412	C₂×C₄×C₃₇	—	4	2	no	—
413	C₂×C₄×C₃₇	—	8	2	no	—
414	C₂×C₄×C₃₇	—	8	4	no	—
415	C₂×C₄×C₃₇	—	8	2	no	—
416	C₂×C₄×C₃₇	—	8	1	no	—
417	C₂×C₄×C₃₇	—	8	1	no	—
418	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
425	C₈×C₃₇	—	2	4	no	—
426	C₈×C₃₇	—	2	4	no	—
427	#61561	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂²×C₃₇	—	2	1	no	—
429	C₂²×C₃₇	—	2	1	no	—
430	C₂²×C₃₇	—	2	1	no	—
431	C₂²×C₃₇	—	2	1	no	—
432	C₂²×C₃₇	—	2	1	no	—
433	C₂²×C₃₇	—	2	1	no	—
434	C₂²×C₃₇	—	2	2	no	—
435	C₂²×C₃₇	—	2	2	no	—
436	C₂²×C₃₇	—	2	4	no	—
437	C₂²×C₃₇	—	2	2	no	—
438	C₂²×C₃₇	—	4	4	no	—
439	C₂²×C₃₇	—	4	8	no	—
440	C₂²×C₃₇	—	4	2	no	—
441	C₂²×C₃₇	—	4	2	no	—
442	C₂²×C₃₇	—	4	2	no	—
443	C₂²×C₃₇	—	4	2	no	—
444	C₂²×C₃₇	—	4	2	no	—
445	C₂²×C₃₇	—	4	2	no	—
446	C₂²×C₃₇	—	4	2	no	—
447	C₂²×C₃₇	—	4	2	no	—
448	C₂²×C₃₇	—	8	2	no	—
449	C₂²×C₃₇	—	8	8	no	—
450	C₂²×C₃₇	—	8	8	no	—
451	C₂²×C₃₇	—	8	4	no	—
452	C₂²×C₃₇	—	16	2	no	—
453	C₂²×C₃₇	C₂×#135	1	2	yes	—
454	C₂²×C₃₇	C₂×#135	1	2	yes	—
455	C₂²×C₃₇	C₂×#135	1	2	yes	—
456	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₃₇	—	2	2	no	—
458	C₄×C₃₇	—	2	2	no	—
459	C₄×C₃₇	—	2	1	no	—
460	C₄×C₃₇	—	2	1	no	—
461	C₄×C₃₇	—	2	1	no	—
462	C₄×C₃₇	—	2	2	no	—
463	C₄×C₃₇	—	4	2	no	—
464	C₄×C₃₇	—	4	2	no	—
465	C₄×C₃₇	—	4	2	no	—
466	C₄×C₃₇	—	4	2	no	—
467	C₄×C₃₇	—	4	2	no	—
468	C₄×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
469	#3505	C₂×C₃₇	1	1	yes	characteristic, complemented
470	C₂×#546	C₂×C₃₇	1	1	yes	characteristic, complemented
471	#3297	C₂×C₃₇	1	4	yes	complemented
472	#3296	C₂×C₃₇	1	4	yes	complemented
473	#3282	C₂×C₃₇	1	4	yes	complemented
474	#3280	C₂×C₃₇	1	4	yes	complemented
475	#3211	C₂×C₃₇	1	2	yes	complemented
476	#3189	C₂×C₃₇	1	1	yes	characteristic, complemented
477	#3188	C₂×C₃₇	1	2	yes	complemented
478	#3187	C₂×C₃₇	1	1	yes	characteristic, complemented
479	#3105	C₂×C₃₇	1	2	yes	complemented
480	#3002	C₂×C₃₇	1	2	yes	complemented
481	C₂×#450	C₂×C₃₇	1	1	yes	characteristic, complemented
482	C₂×#447	C₂×C₃₇	1	1	yes	characteristic, complemented
483	#2972	C₂×C₃₇	1	1	yes	characteristic, complemented
484	C₂×C₃₇	—	2	2	no	—
485	C₂×C₃₇	—	2	2	no	—
486	C₂×C₃₇	—	2	2	no	—
487	C₂×C₃₇	—	4	2	no	—
488	C₂×C₃₇	—	4	4	no	—
489	C₂×C₃₇	—	8	2	no	—
490	C₂×C₃₇	—	8	2	no	—
491	C₂×C₃₇	#3484	1	1	yes	characteristic
492	C₂×C₃₇	C₂²×#135	1	1	yes	characteristic
493	C₂×C₃₇	#3585	1	1	yes	characteristic
494	C₂²×#41	C₂²×C₃₇	1	1	yes	characteristic, complemented
495	C₂³×D₄	C₂²×C₃₇	1	1	yes	characteristic
496	C₂×#135	C₂²×C₃₇	1	4	yes	complemented
497	C₂²×SD₁₆	C₂²×C₃₇	1	2	yes	complemented
498	C₂²×D₈	C₂²×C₃₇	1	2	yes	complemented
499	#553	—	2	2	no	—
500	#553	C₂²×C₃₇	1	2	yes	complemented
501	#552	C₂²×C₃₇	1	2	yes	complemented
502	#551	—	2	2	no	—
503	#548	C₂²×C₃₇	1	2	yes	complemented
504	#546	—	2	2	no	—
505	#546	—	2	2	no	—
506	#546	C₂²×C₃₇	1	4	yes	—
507	#546	C₂²×C₃₇	1	4	yes	complemented
508	#546	C₂²×C₃₇	1	2	yes	complemented
509	#539	—	2	1	no	—
510	#538	—	2	1	no	—
511	#534	—	2	1	no	—
512	#529	C₂²×C₃₇	1	2	yes	complemented
513	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic, complemented
514	#525	C₂²×C₃₇	1	2	yes	complemented
515	C₂×#123	—	2	1	no	—
516	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
517	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
518	C₂×#121	—	2	1	no	—
519	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
520	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic, complemented
521	C₂×#120	—	2	1	no	—
522	#518	—	2	1	no	—
523	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic, complemented
525	C₂²×C₂²⋊C₄	—	2	1	no	—
526	#495	C₂²×C₃₇	1	4	yes	complemented
527	#488	C₂²×C₃₇	1	4	yes	complemented
528	#484	C₂²×C₃₇	1	2	yes	complemented
529	#484	C₂²×C₃₇	1	2	yes	complemented
530	#483	C₂²×C₃₇	1	2	yes	complemented
531	#482	C₂²×C₃₇	1	4	yes	complemented
532	#481	C₂²×C₃₇	1	2	yes	complemented
533	#478	C₂²×C₃₇	1	4	yes	complemented
534	#467	C₂²×C₃₇	1	4	yes	complemented
535	#466	C₂²×C₃₇	1	4	yes	complemented
536	#465	C₂²×C₃₇	1	4	yes	complemented
537	#465	C₂²×C₃₇	1	4	yes	complemented
538	#464	C₂²×C₃₇	1	4	yes	complemented
539	#463	C₂²×C₃₇	1	4	yes	complemented
540	#463	C₂²×C₃₇	1	4	yes	complemented
541	#452	C₂²×C₃₇	1	4	yes	complemented
542	#451	C₂²×C₃₇	1	2	yes	complemented
543	#451	C₂²×C₃₇	1	2	yes	complemented
544	#450	C₂²×C₃₇	1	2	yes	complemented
545	#450	C₂²×C₃₇	1	2	yes	complemented
546	#450	C₂²×C₃₇	1	4	yes	complemented
547	#450	C₂²×C₃₇	1	2	yes	complemented
548	#449	C₂²×C₃₇	1	4	yes	complemented
549	#449	C₂²×C₃₇	1	4	yes	complemented
550	#448	C₂²×C₃₇	1	2	yes	complemented
551	#447	C₂²×C₃₇	1	2	yes	—
552	#447	C₂²×C₃₇	1	2	yes	—
553	#447	C₂²×C₃₇	1	4	yes	complemented
554	C₄×SD₁₆	C₂²×C₃₇	1	4	yes	complemented
555	C₄×D₈	C₂²×C₃₇	1	4	yes	complemented
556	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
557	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
558	#431	C₂²×C₃₇	1	2	yes	complemented
559	#416	C₂²×C₃₇	1	4	yes	complemented
560	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
561	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
562	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
563	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
564	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	complemented
565	C₃₇	#61561	1	1	yes	characteristic, direct product factor, Sylow
566	C₂⁵	—	2	1	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	4	4	no	—
569	C₂×#41	C₂³×C₃₇	1	4	yes	—
570	C₂×#41	C₂³×C₃₇	1	2	yes	complemented
571	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	—	4	4	no	—
580	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
583	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
584	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
586	C₂³×C₄	—	2	1	no	—
587	C₂³×C₄	—	2	1	no	—
588	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
590	#135	—	4	8	no	—
591	C₂×Q₁₆	C₂³×C₃₇	1	4	yes	complemented
592	C₂×SD₁₆	—	4	4	no	—
593	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
595	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	complemented
596	C₂×D₈	—	4	4	no	—
597	C₂×D₈	C₂³×C₃₇	1	4	yes	—
598	C₂×D₈	C₂³×C₃₇	1	4	yes	—
599	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
600	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
601	C₂²×C₈	C₂³×C₃₇	1	4	yes	complemented
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	C₂³×C₃₇	1	2	yes	complemented
607	#124	—	2	2	no	—
608	#124	—	2	2	no	—
609	#124	C₂³×C₃₇	1	4	yes	—
610	#124	C₂³×C₃₇	1	2	yes	complemented
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	4	no	—
615	#123	—	2	4	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	1	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
627	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	complemented
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	2	no	—
633	#121	—	2	4	no	—
634	#121	—	2	4	no	—
635	#121	—	2	2	no	—
636	#121	C₂³×C₃₇	1	2	yes	—
637	#121	C₂³×C₃₇	1	2	yes	—
638	#121	C₂³×C₃₇	1	4	yes	—
639	#121	C₂³×C₃₇	1	2	yes	complemented
640	#120	—	2	2	no	—
641	#120	—	2	4	no	—
642	#120	—	2	4	no	—
643	#120	—	2	2	no	—
644	C₄×Q₈	C₂³×C₃₇	1	2	yes	complemented
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	D₄×C₃₇	1	2	yes	—
652	C₄×D₄	D₄×C₃₇	1	2	yes	—
653	C₄×D₄	C₂³×C₃₇	1	4	yes	—
654	C₄×D₄	C₂³×C₃₇	1	2	yes	—
655	C₄×D₄	C₂³×C₃₇	1	2	yes	—
656	C₄×D₄	C₂³×C₃₇	1	2	yes	complemented
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	C₂³×C₃₇	1	2	yes	complemented
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	4	no	—
674	C₂×C₂²⋊C₄	—	2	4	no	—
675	C₂×C₂²⋊C₄	—	2	2	no	—
676	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
679	#107	C₂³×C₃₇	1	4	yes	complemented
680	#106	C₂³×C₃₇	1	4	yes	complemented
681	C₄⋊C₈	C₂³×C₃₇	1	4	yes	complemented
682	#103	C₂³×C₃₇	1	4	yes	complemented
683	#103	C₂³×C₃₇	1	4	yes	complemented
684	#103	C₂³×C₃₇	1	4	yes	complemented
685	#102	C₂³×C₃₇	1	4	yes	—
686	#102	C₂³×C₃₇	1	4	yes	—
687	#102	C₂³×C₃₇	1	4	yes	—
688	#102	C₂³×C₃₇	1	4	yes	—
689	#102	C₂³×C₃₇	1	4	yes	complemented
690	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
693	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	complemented
695	C₄×C₈	C₂³×C₃₇	1	4	yes	complemented
696	C₂⁴	—	2	1	no	—
697	C₂⁴	—	2	1	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	2	no	—
700	C₂⁴	—	2	1	no	—
701	C₂⁴	—	4	4	no	—
702	C₂⁴	—	4	4	no	—
703	C₂⁴	—	8	2	no	—
704	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
705	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
706	#41	—	2	8	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	8	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	8	2	no	—
741	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
743	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
744	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
745	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	4	no	—
758	C₂²×C₄	—	8	2	no	—
759	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
765	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
770	Q₁₆	—	4	4	no	—
771	SD₁₆	—	2	8	no	—
772	SD₁₆	—	4	4	no	—
773	SD₁₆	—	4	4	no	—
774	D₈	—	2	8	no	—
775	D₈	—	4	4	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	—	4	2	no	—
778	C₂×C₈	—	4	4	no	—
779	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
780	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
816	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	C₂×D₄×C₃₇	1	2	yes	—
820	C₄²	C₂⁴×C₃₇	1	2	yes	—
821	C₂³	—	2	4	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	1	no	—
843	C₂³	—	8	1	no	—
844	C₂³	—	8	16	no	—
845	C₂³	#135×C₃₇	1	4	yes	complemented
846	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
847	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
848	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
849	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
850	Q₈	—	2	4	no	—
851	Q₈	—	2	4	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	8	1	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	2	4	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	8	1	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	H(5,𝔽₂)×C₃₇	1	4	yes	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	8	4	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	—	8	1	no	—
897	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
904	C₈	—	2	4	no	—
905	C₈	—	2	4	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	8	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	2	no	—
927	C₂²	—	8	8	no	—
928	C₂²	—	8	8	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	16	2	no	—
931	C₂²	C₂×#135×C₃₇	1	2	yes	—
932	C₂²	C₂×#135×C₃₇	1	2	yes	—
933	C₂²	C₂×#135×C₃₇	1	2	yes	—
934	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
947	C₂	—	2	2	no	—
948	C₂	—	2	2	no	—
949	C₂	—	2	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	8	2	no	—
953	C₂	—	8	2	no	—
954	C₂	C₃₇×#3484	1	1	yes	characteristic
955	C₂	C₂²×#135×C₃₇	1	1	yes	characteristic
956	C₂	C₃₇×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3505	C₂	semidirect
2. C₂×C₃₇×#546	C₂	semidirect
3. C₃₇×#3297	C₂	semidirect
4. C₃₇×#3296	C₂	semidirect
5. C₃₇×#3282	C₂	semidirect
6. C₃₇×#3280	C₂	semidirect
7. C₃₇×#3211	C₂	semidirect
8. C₃₇×#3189	C₂	semidirect
9. C₃₇×#3188	C₂	semidirect
10. C₃₇×#3187	C₂	semidirect
11. C₃₇×#3105	C₂	semidirect
12. C₃₇×#3002	C₂	semidirect
13. C₂×C₃₇×#450	C₂	semidirect
14. C₂×C₃₇×#447	C₂	semidirect
15. C₃₇×#2972	C₂	semidirect
16. C₂²×#41×C₃₇	C₂²	semidirect
18. C₂×#135×C₃₇	C₂²	semidirect
19. C₂²×SD₁₆×C₃₇	C₂²	semidirect
20. C₂²×D₈×C₃₇	C₂²	semidirect
22. C₃₇×#553	C₂²	semidirect
23. C₃₇×#552	C₂²	semidirect
25. C₃₇×#548	C₂²	semidirect
29. C₃₇×#546	C₂²	semidirect
30. C₃₇×#546	C₂²	semidirect
34. C₃₇×#529	C₂²	semidirect
35. C₂×#124×C₃₇	C₂²	semidirect
36. C₃₇×#525	C₂²	semidirect
42. C₂×#121×C₃₇	C₂²	semidirect
46. C₂×C₄×D₄×C₃₇	C₂²	semidirect
48. C₃₇×#495	C₂²	semidirect
49. C₃₇×#488	C₂²	semidirect
50. C₃₇×#484	C₂²	semidirect
51. C₃₇×#484	C₂²	semidirect
52. C₃₇×#483	C₂²	semidirect
53. C₃₇×#482	C₂²	semidirect
54. C₃₇×#481	C₂²	semidirect
55. C₃₇×#478	C₂²	semidirect
56. C₃₇×#467	C₂²	semidirect
57. C₃₇×#466	C₂²	semidirect
58. C₃₇×#465	C₂²	semidirect
59. C₃₇×#465	C₂²	semidirect
60. C₃₇×#464	C₂²	semidirect
61. C₃₇×#463	C₂²	semidirect
62. C₃₇×#463	C₂²	semidirect
63. C₃₇×#452	C₂²	semidirect
64. C₃₇×#451	C₂²	semidirect
65. C₃₇×#451	C₂²	semidirect
66. C₃₇×#450	C₂²	semidirect
67. C₃₇×#450	C₂²	semidirect
68. C₃₇×#450	C₂²	semidirect
69. C₃₇×#450	C₂²	semidirect
70. C₃₇×#449	C₂²	semidirect
71. C₃₇×#449	C₂²	semidirect
72. C₃₇×#448	C₂²	semidirect
75. C₃₇×#447	C₂²	semidirect
76. C₄×SD₁₆×C₃₇	C₂²	semidirect
77. C₄×D₈×C₃₇	C₂²	semidirect
78. C₈×D₄×C₃₇	C₂²	semidirect
79. C₈×D₄×C₃₇	C₂²	semidirect
80. C₃₇×#431	C₂²	semidirect
81. C₃₇×#416	C₂²	semidirect
82. C₂×#102×C₃₇	C₂²	semidirect
83. C₂×#102×C₃₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
91. C₂×#41×C₃₇	C₂³	semidirect
112. C₂×Q₁₆×C₃₇	C₂³	semidirect
116. C₂×SD₁₆×C₃₇	C₂³	semidirect
122. C₂²×C₈×C₃₇	C₂³	semidirect
127. #125×C₃₇	C₂³	semidirect
131. #124×C₃₇	C₂³	semidirect
148. C₂²⋊Q₈×C₃₇	C₂³	semidirect
160. #121×C₃₇	C₂³	semidirect
165. C₄×Q₈×C₃₇	C₂³	semidirect
177. C₄×D₄×C₃₇	C₂³	semidirect
180. #117×C₃₇	C₂³	semidirect
200. #107×C₃₇	C₂³	semidirect
201. #106×C₃₇	C₂³	semidirect
202. C₄⋊C₈×C₃₇	C₂³	semidirect
203. #103×C₃₇	C₂³	semidirect
204. #103×C₃₇	C₂³	semidirect
205. #103×C₃₇	C₂³	semidirect
210. #102×C₃₇	C₂³	semidirect
215. C₂²⋊C₈×C₃₇	C₂³	semidirect
216. C₄×C₈×C₃₇	C₂³	semidirect
366. C₂³×C₃₇	#135	semidirect
427. #61561	C₃₇	direct (N × H)
469. #3505	C₂×C₃₇	semidirect
470. C₂×#546	C₂×C₃₇	semidirect
471. #3297	C₂×C₃₇	semidirect
472. #3296	C₂×C₃₇	semidirect
473. #3282	C₂×C₃₇	semidirect
474. #3280	C₂×C₃₇	semidirect
475. #3211	C₂×C₃₇	semidirect
476. #3189	C₂×C₃₇	semidirect
477. #3188	C₂×C₃₇	semidirect
478. #3187	C₂×C₃₇	semidirect
479. #3105	C₂×C₃₇	semidirect
480. #3002	C₂×C₃₇	semidirect
481. C₂×#450	C₂×C₃₇	semidirect
482. C₂×#447	C₂×C₃₇	semidirect
483. #2972	C₂×C₃₇	semidirect
494. C₂²×#41	C₂²×C₃₇	semidirect
496. C₂×#135	C₂²×C₃₇	semidirect
497. C₂²×SD₁₆	C₂²×C₃₇	semidirect
498. C₂²×D₈	C₂²×C₃₇	semidirect
500. #553	C₂²×C₃₇	semidirect
501. #552	C₂²×C₃₇	semidirect
503. #548	C₂²×C₃₇	semidirect
507. #546	C₂²×C₃₇	semidirect
508. #546	C₂²×C₃₇	semidirect
512. #529	C₂²×C₃₇	semidirect
513. C₂×#124	C₂²×C₃₇	semidirect
514. #525	C₂²×C₃₇	semidirect
520. C₂×#121	C₂²×C₃₇	semidirect
524. C₂×C₄×D₄	C₂²×C₃₇	semidirect
526. #495	C₂²×C₃₇	semidirect
527. #488	C₂²×C₃₇	semidirect
528. #484	C₂²×C₃₇	semidirect
529. #484	C₂²×C₃₇	semidirect
530. #483	C₂²×C₃₇	semidirect
531. #482	C₂²×C₃₇	semidirect
532. #481	C₂²×C₃₇	semidirect
533. #478	C₂²×C₃₇	semidirect
534. #467	C₂²×C₃₇	semidirect
535. #466	C₂²×C₃₇	semidirect
536. #465	C₂²×C₃₇	semidirect
537. #465	C₂²×C₃₇	semidirect
538. #464	C₂²×C₃₇	semidirect
539. #463	C₂²×C₃₇	semidirect
540. #463	C₂²×C₃₇	semidirect
541. #452	C₂²×C₃₇	semidirect
542. #451	C₂²×C₃₇	semidirect
543. #451	C₂²×C₃₇	semidirect
544. #450	C₂²×C₃₇	semidirect
545. #450	C₂²×C₃₇	semidirect
546. #450	C₂²×C₃₇	semidirect
547. #450	C₂²×C₃₇	semidirect
548. #449	C₂²×C₃₇	semidirect
549. #449	C₂²×C₃₇	semidirect
550. #448	C₂²×C₃₇	semidirect
553. #447	C₂²×C₃₇	semidirect
554. C₄×SD₁₆	C₂²×C₃₇	semidirect
555. C₄×D₈	C₂²×C₃₇	semidirect
556. C₈×D₄	C₂²×C₃₇	semidirect
557. C₈×D₄	C₂²×C₃₇	semidirect
558. #431	C₂²×C₃₇	semidirect
559. #416	C₂²×C₃₇	semidirect
560. C₂×#102	C₂²×C₃₇	semidirect
561. C₂×#102	C₂²×C₃₇	semidirect
564. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
565. C₃₇	#61561	direct (N × H)
570. C₂×#41	C₂³×C₃₇	semidirect
591. C₂×Q₁₆	C₂³×C₃₇	semidirect
595. C₂×SD₁₆	C₂³×C₃₇	semidirect
601. C₂²×C₈	C₂³×C₃₇	semidirect
606. #125	C₂³×C₃₇	semidirect
610. #124	C₂³×C₃₇	semidirect
627. C₂²⋊Q₈	C₂³×C₃₇	semidirect
639. #121	C₂³×C₃₇	semidirect
644. C₄×Q₈	C₂³×C₃₇	semidirect
656. C₄×D₄	C₂³×C₃₇	semidirect
659. #117	C₂³×C₃₇	semidirect
679. #107	C₂³×C₃₇	semidirect
680. #106	C₂³×C₃₇	semidirect
681. C₄⋊C₈	C₂³×C₃₇	semidirect
682. #103	C₂³×C₃₇	semidirect
683. #103	C₂³×C₃₇	semidirect
684. #103	C₂³×C₃₇	semidirect
689. #102	C₂³×C₃₇	semidirect
694. C₂²⋊C₈	C₂³×C₃₇	semidirect
695. C₄×C₈	C₂³×C₃₇	semidirect
845. C₂³	#135×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3505	2
C₂×C₃₇×#546	2
C₃₇×#3297	2
C₃₇×#3296	2
C₃₇×#3282	2
C₃₇×#3280	2
C₃₇×#3211	2
C₃₇×#3189	2
C₃₇×#3188	2
C₃₇×#3187	2
C₃₇×#3105	2
C₃₇×#3002	2
C₂×C₃₇×#450	2
C₂×C₃₇×#447	2
C₃₇×#2972	2
#61561	37

Subgroups — C37×#61561 #22682814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61561 #22682814