Subgroups — C₃₇×#61699 #22682952

Order 9472.

1854 conjugacy classes of subgroups.

The subgroup lattice has 868 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×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3339	C₂	1	4	yes	maximal, complemented
4	C₃₇×#3337	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3301	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3297	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3232	C₂	1	2	yes	maximal, complemented
8	C₃₇×#3188	C₂	1	2	yes	maximal, complemented
9	C₃₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3105	C₂	1	2	yes	maximal, complemented
12	C₃₇×#3091	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₇×#481	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₇×#553	—	2	2	no	—
17	C₃₇×#553	—	2	2	no	—
18	C₃₇×#553	—	2	2	no	—
19	C₃₇×#553	C₂²	1	4	yes	—
20	C₃₇×#553	C₂²	1	4	yes	complemented
21	C₃₇×#553	C₂²	1	2	yes	complemented
22	C₃₇×#552	C₂²	1	2	yes	complemented
23	C₃₇×#551	—	2	2	no	—
24	C₃₇×#548	C₂²	1	2	yes	complemented
25	C₃₇×#546	C₂²	1	2	yes	complemented
26	C₃₇×#539	—	2	1	no	—
27	C₃₇×#538	—	2	1	no	—
28	C₃₇×#534	—	2	1	no	—
29	C₃₇×#529	C₂²	1	2	yes	—
30	C₂×#126×C₃₇	—	2	1	no	—
31	C₂×#125×C₃₇	C₂²	1	1	yes	characteristic, complemented
32	C₃₇×#525	C₂²	1	2	yes	—
33	C₂×#123×C₃₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₃₇	—	2	1	no	—
36	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic, complemented
39	C₃₇×#518	—	2	1	no	—
40	C₂×C₄×D₄×C₃₇	—	2	1	no	—
41	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#117×C₃₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
45	C₃₇×#499	C₂²	1	4	yes	complemented
46	C₃₇×#488	C₂²	1	4	yes	complemented
47	C₃₇×#485	C₂²	1	4	yes	complemented
48	C₃₇×#484	C₂²	1	2	yes	complemented
49	C₃₇×#484	C₂²	1	4	yes	complemented
50	C₃₇×#484	C₂²	1	2	yes	complemented
51	C₃₇×#483	C₂²	1	2	yes	complemented
52	C₃₇×#482	C₂²	1	4	yes	complemented
53	C₃₇×#482	C₂²	1	4	yes	complemented
54	C₃₇×#481	C₂²	1	2	yes	—
55	C₃₇×#481	C₂²	1	2	yes	—
56	C₃₇×#481	C₂²	1	2	yes	complemented
57	C₃₇×#481	C₂²	1	4	yes	complemented
58	C₃₇×#480	C₂²	1	2	yes	—
59	C₃₇×#480	C₂²	1	2	yes	complemented
60	C₃₇×#479	C₂²	1	4	yes	complemented
61	C₃₇×#478	C₂²	1	4	yes	complemented
62	C₃₇×#478	C₂²	1	4	yes	complemented
63	C₃₇×#466	C₂²	1	4	yes	complemented
64	C₃₇×#466	C₂²	1	4	yes	complemented
65	C₃₇×#465	C₂²	1	4	yes	complemented
66	C₃₇×#465	C₂²	1	4	yes	complemented
67	C₃₇×#463	C₂²	1	4	yes	complemented
68	C₃₇×#450	C₂²	1	2	yes	complemented
69	C₃₇×#449	C₂²	1	4	yes	complemented
70	C₃₇×#448	C₂²	1	2	yes	complemented
71	C₃₇×#447	C₂²	1	2	yes	—
72	C₃₇×#447	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₃₇	C₂²	1	4	yes	complemented
74	C₄×D₈×C₃₇	C₂²	1	4	yes	complemented
75	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
76	C₈×D₄×C₃₇	C₂²	1	4	yes	complemented
77	C₃₇×#431	C₂²	1	2	yes	complemented
78	C₃₇×#427	C₂²	1	4	yes	complemented
79	C₂×#107×C₃₇	C₂²	1	2	yes	complemented
80	C₂×#106×C₃₇	C₂²	1	2	yes	complemented
81	C₃₇×#416	C₂²	1	4	yes	complemented
82	C₂×#103×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	C₂×#41×C₃₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₇	—	2	1	no	—
90	C₂²×D₄×C₃₇	—	2	1	no	—
91	C₂²×D₄×C₃₇	—	2	1	no	—
92	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₇	—	2	1	no	—
96	C₂³×C₄×C₃₇	—	2	1	no	—
97	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
99	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
100	C₂×D₈×C₃₇	C₂³	1	4	yes	—
101	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
104	#126×C₃₇	—	2	4	no	—
105	#126×C₃₇	—	2	4	no	—
106	#126×C₃₇	—	2	2	no	—
107	#126×C₃₇	—	2	2	no	—
108	#126×C₃₇	—	2	2	no	—
109	#125×C₃₇	—	2	2	no	—
110	#125×C₃₇	—	2	2	no	—
111	#125×C₃₇	C₂³	1	4	yes	—
112	#125×C₃₇	C₂³	1	2	yes	—
113	#124×C₃₇	—	2	2	no	—
114	#124×C₃₇	C₂³	1	2	yes	—
115	#123×C₃₇	—	2	2	no	—
116	#123×C₃₇	—	2	2	no	—
117	#123×C₃₇	—	2	2	no	—
118	#123×C₃₇	—	2	2	no	—
119	#123×C₃₇	—	2	4	no	—
120	#123×C₃₇	—	2	4	no	—
121	#123×C₃₇	—	2	2	no	—
122	C₂²⋊Q₈×C₃₇	—	2	1	no	—
123	C₂²⋊Q₈×C₃₇	—	2	1	no	—
124	C₂²⋊Q₈×C₃₇	—	2	2	no	—
125	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
126	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
127	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
128	#121×C₃₇	—	2	4	no	—
129	#121×C₃₇	—	2	4	no	—
130	#121×C₃₇	—	2	2	no	—
131	#121×C₃₇	—	2	2	no	—
132	#121×C₃₇	—	2	1	no	—
133	#121×C₃₇	—	2	1	no	—
134	#121×C₃₇	—	2	1	no	—
135	#121×C₃₇	—	2	1	no	—
136	#121×C₃₇	—	2	2	no	—
137	#121×C₃₇	—	2	2	no	—
138	#121×C₃₇	C₂³	1	2	yes	—
139	#121×C₃₇	C₂³	1	2	yes	—
140	#121×C₃₇	C₂³	1	2	yes	—
141	#121×C₃₇	C₂³	1	2	yes	—
142	#121×C₃₇	C₂³	1	4	yes	—
143	#121×C₃₇	C₂³	1	2	yes	—
144	#120×C₃₇	—	2	2	no	—
145	#120×C₃₇	—	2	2	no	—
146	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
147	C₄×D₄×C₃₇	—	2	2	no	—
148	C₄×D₄×C₃₇	—	2	2	no	—
149	C₄×D₄×C₃₇	—	2	2	no	—
150	C₄×D₄×C₃₇	—	2	2	no	—
151	C₄×D₄×C₃₇	—	2	4	no	—
152	C₄×D₄×C₃₇	—	2	4	no	—
153	C₄×D₄×C₃₇	—	2	2	no	—
154	C₄×D₄×C₃₇	—	2	2	no	—
155	C₄×D₄×C₃₇	D₄	1	2	yes	—
156	C₄×D₄×C₃₇	D₄	1	2	yes	—
157	C₄×D₄×C₃₇	C₂³	1	2	yes	—
158	C₄×D₄×C₃₇	C₂³	1	4	yes	—
159	C₄×D₄×C₃₇	C₂³	1	2	yes	—
160	C₄×D₄×C₃₇	C₂³	1	2	yes	—
161	#117×C₃₇	—	2	2	no	—
162	#117×C₃₇	—	2	2	no	—
163	#117×C₃₇	—	2	2	no	—
164	#117×C₃₇	C₂³	1	2	yes	—
165	#117×C₃₇	C₂³	1	4	yes	—
166	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
167	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₃₇	—	2	1	no	—
190	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
191	#107×C₃₇	C₂³	1	4	yes	—
192	#107×C₃₇	C₂³	1	4	yes	—
193	#107×C₃₇	C₂³	1	4	yes	—
194	#106×C₃₇	C₂³	1	4	yes	—
195	#106×C₃₇	C₂³	1	4	yes	—
196	#106×C₃₇	C₂³	1	4	yes	—
197	C₄⋊C₈×C₃₇	C₂³	1	4	yes	—
198	#103×C₃₇	C₂³	1	4	yes	—
199	#103×C₃₇	C₂³	1	4	yes	—
200	#103×C₃₇	C₂³	1	4	yes	—
201	#102×C₃₇	C₂³	1	4	yes	—
202	#102×C₃₇	C₂³	1	4	yes	—
203	#102×C₃₇	C₂³	1	4	yes	—
204	#102×C₃₇	C₂³	1	4	yes	—
205	#102×C₃₇	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
209	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
211	C₄×C₈×C₃₇	C₂³	1	4	yes	—
212	C₂⁴×C₃₇	—	2	1	no	—
213	C₂⁴×C₃₇	—	2	1	no	—
214	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
216	#41×C₃₇	—	4	4	no	—
217	C₂×Q₈×C₃₇	—	2	1	no	—
218	C₂×Q₈×C₃₇	—	4	2	no	—
219	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
220	C₂×D₄×C₃₇	—	2	4	no	—
221	C₂×D₄×C₃₇	—	2	2	no	—
222	C₂×D₄×C₃₇	—	2	2	no	—
223	C₂×D₄×C₃₇	—	2	2	no	—
224	C₂×D₄×C₃₇	—	2	2	no	—
225	C₂×D₄×C₃₇	—	2	2	no	—
226	C₂×D₄×C₃₇	—	2	2	no	—
227	C₂×D₄×C₃₇	—	2	4	no	—
228	C₂×D₄×C₃₇	—	2	1	no	—
229	C₂×D₄×C₃₇	—	2	1	no	—
230	C₂×D₄×C₃₇	—	4	2	no	—
231	C₂×D₄×C₃₇	—	4	2	no	—
232	C₂×D₄×C₃₇	—	4	4	no	—
233	C₂×D₄×C₃₇	—	4	4	no	—
234	C₂×D₄×C₃₇	—	8	2	no	—
235	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₇	—	2	1	no	—
240	C₂²×C₄×C₃₇	—	2	1	no	—
241	C₂²×C₄×C₃₇	—	2	1	no	—
242	C₂²×C₄×C₃₇	—	2	1	no	—
243	C₂²×C₄×C₃₇	—	2	1	no	—
244	C₂²×C₄×C₃₇	—	2	1	no	—
245	C₂²×C₄×C₃₇	—	2	2	no	—
246	C₂²×C₄×C₃₇	—	2	2	no	—
247	C₂²×C₄×C₃₇	—	2	2	no	—
248	C₂²×C₄×C₃₇	—	2	2	no	—
249	C₂²×C₄×C₃₇	—	2	4	no	—
250	C₂²×C₄×C₃₇	—	4	2	no	—
251	C₂²×C₄×C₃₇	—	4	2	no	—
252	C₂²×C₄×C₃₇	—	8	2	no	—
253	C₂²×C₄×C₃₇	—	8	2	no	—
254	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
265	SD₁₆×C₃₇	—	4	4	no	—
266	D₈×C₃₇	—	4	4	no	—
267	C₂×C₈×C₃₇	—	4	2	no	—
268	C₂×C₈×C₃₇	—	4	4	no	—
269	C₂×C₈×C₃₇	—	4	2	no	—
270	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
271	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₃₇	—	2	1	no	—
273	C₄⋊C₄×C₃₇	—	2	1	no	—
274	C₄⋊C₄×C₃₇	—	2	2	no	—
275	C₄⋊C₄×C₃₇	—	2	2	no	—
276	C₄⋊C₄×C₃₇	—	2	2	no	—
277	C₄⋊C₄×C₃₇	—	2	4	no	—
278	C₄⋊C₄×C₃₇	—	2	4	no	—
279	C₄⋊C₄×C₃₇	—	2	2	no	—
280	C₄⋊C₄×C₃₇	—	2	1	no	—
281	C₄⋊C₄×C₃₇	—	2	1	no	—
282	C₄⋊C₄×C₃₇	—	2	1	no	—
283	C₄⋊C₄×C₃₇	—	2	2	no	—
284	C₄⋊C₄×C₃₇	—	2	2	no	—
285	C₄⋊C₄×C₃₇	—	2	2	no	—
286	C₄⋊C₄×C₃₇	—	2	2	no	—
287	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
288	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
294	C₂²⋊C₄×C₃₇	—	2	2	no	—
295	C₂²⋊C₄×C₃₇	—	2	4	no	—
296	C₂²⋊C₄×C₃₇	—	2	2	no	—
297	C₂²⋊C₄×C₃₇	—	2	2	no	—
298	C₂²⋊C₄×C₃₇	—	2	2	no	—
299	C₂²⋊C₄×C₃₇	—	2	2	no	—
300	C₂²⋊C₄×C₃₇	—	2	4	no	—
301	C₂²⋊C₄×C₃₇	—	2	2	no	—
302	C₂²⋊C₄×C₃₇	—	2	2	no	—
303	C₂²⋊C₄×C₃₇	—	2	4	no	—
304	C₂²⋊C₄×C₃₇	—	2	2	no	—
305	C₂²⋊C₄×C₃₇	—	2	2	no	—
306	C₂²⋊C₄×C₃₇	—	2	2	no	—
307	C₂²⋊C₄×C₃₇	—	2	2	no	—
308	C₂²⋊C₄×C₃₇	—	2	2	no	—
309	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
312	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
313	C₄²×C₃₇	—	2	4	no	—
314	C₄²×C₃₇	—	2	2	no	—
315	C₄²×C₃₇	—	2	2	no	—
316	C₄²×C₃₇	C₂×D₄	1	2	yes	—
317	C₄²×C₃₇	C₂⁴	1	2	yes	—
318	C₂³×C₃₇	—	2	2	no	—
319	C₂³×C₃₇	—	2	2	no	—
320	C₂³×C₃₇	—	2	2	no	—
321	C₂³×C₃₇	—	4	1	no	—
322	C₂³×C₃₇	—	4	1	no	—
323	C₂³×C₃₇	—	4	1	no	—
324	C₂³×C₃₇	—	4	1	no	—
325	C₂³×C₃₇	—	4	2	no	—
326	C₂³×C₃₇	—	4	2	no	—
327	C₂³×C₃₇	—	4	2	no	—
328	C₂³×C₃₇	—	4	2	no	—
329	C₂³×C₃₇	—	8	1	no	—
330	C₂³×C₃₇	—	8	1	no	—
331	C₂³×C₃₇	#135	1	4	yes	—
332	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
333	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₃₇	—	2	4	no	—
337	Q₈×C₃₇	—	8	1	no	—
338	D₄×C₃₇	—	2	4	no	—
339	D₄×C₃₇	—	2	4	no	—
340	D₄×C₃₇	—	2	4	no	—
341	D₄×C₃₇	—	2	4	no	—
342	D₄×C₃₇	—	4	2	no	—
343	D₄×C₃₇	—	4	4	no	—
344	D₄×C₃₇	—	4	4	no	—
345	D₄×C₃₇	—	4	4	no	—
346	D₄×C₃₇	—	4	4	no	—
347	D₄×C₃₇	—	8	1	no	—
348	D₄×C₃₇	—	8	2	no	—
349	D₄×C₃₇	—	8	4	no	—
350	D₄×C₃₇	—	8	2	no	—
351	C₂×C₄×C₃₇	—	2	2	no	—
352	C₂×C₄×C₃₇	—	2	2	no	—
353	C₂×C₄×C₃₇	—	2	2	no	—
354	C₂×C₄×C₃₇	—	2	4	no	—
355	C₂×C₄×C₃₇	—	2	2	no	—
356	C₂×C₄×C₃₇	—	2	2	no	—
357	C₂×C₄×C₃₇	—	2	2	no	—
358	C₂×C₄×C₃₇	—	2	2	no	—
359	C₂×C₄×C₃₇	—	2	2	no	—
360	C₂×C₄×C₃₇	—	2	2	no	—
361	C₂×C₄×C₃₇	—	2	2	no	—
362	C₂×C₄×C₃₇	—	4	2	no	—
363	C₂×C₄×C₃₇	—	4	1	no	—
364	C₂×C₄×C₃₇	—	4	1	no	—
365	C₂×C₄×C₃₇	—	4	1	no	—
366	C₂×C₄×C₃₇	—	4	1	no	—
367	C₂×C₄×C₃₇	—	4	1	no	—
368	C₂×C₄×C₃₇	—	4	2	no	—
369	C₂×C₄×C₃₇	—	4	2	no	—
370	C₂×C₄×C₃₇	—	4	2	no	—
371	C₂×C₄×C₃₇	—	4	2	no	—
372	C₂×C₄×C₃₇	—	8	2	no	—
373	C₂×C₄×C₃₇	—	8	4	no	—
374	C₂×C₄×C₃₇	—	8	2	no	—
375	C₂×C₄×C₃₇	—	8	1	no	—
376	C₂×C₄×C₃₇	—	8	2	no	—
377	C₂×C₄×C₃₇	—	8	2	no	—
378	C₂×C₄×C₃₇	—	8	1	no	—
379	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
386	C₈×C₃₇	—	2	4	no	—
387	C₈×C₃₇	—	2	4	no	—
388	#61699	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂²×C₃₇	—	2	1	no	—
390	C₂²×C₃₇	—	2	1	no	—
391	C₂²×C₃₇	—	2	1	no	—
392	C₂²×C₃₇	—	2	1	no	—
393	C₂²×C₃₇	—	2	1	no	—
394	C₂²×C₃₇	—	2	1	no	—
395	C₂²×C₃₇	—	2	2	no	—
396	C₂²×C₃₇	—	2	2	no	—
397	C₂²×C₃₇	—	2	2	no	—
398	C₂²×C₃₇	—	4	4	no	—
399	C₂²×C₃₇	—	4	2	no	—
400	C₂²×C₃₇	—	4	2	no	—
401	C₂²×C₃₇	—	4	2	no	—
402	C₂²×C₃₇	—	4	2	no	—
403	C₂²×C₃₇	—	4	2	no	—
404	C₂²×C₃₇	—	4	2	no	—
405	C₂²×C₃₇	—	8	2	no	—
406	C₂²×C₃₇	—	8	4	no	—
407	C₂²×C₃₇	—	16	2	no	—
408	C₂²×C₃₇	C₂×#135	1	2	yes	—
409	C₂²×C₃₇	C₂×#135	1	2	yes	—
410	C₂²×C₃₇	C₂×#135	1	2	yes	—
411	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₃₇	—	2	2	no	—
413	C₄×C₃₇	—	2	1	no	—
414	C₄×C₃₇	—	2	2	no	—
415	C₄×C₃₇	—	2	1	no	—
416	C₄×C₃₇	—	2	1	no	—
417	C₄×C₃₇	—	2	2	no	—
418	C₄×C₃₇	—	4	2	no	—
419	C₄×C₃₇	—	4	2	no	—
420	C₄×C₃₇	—	4	2	no	—
421	C₄×C₃₇	—	4	2	no	—
422	C₄×C₃₇	—	4	2	no	—
423	C₄×C₃₇	—	4	2	no	—
424	C₄×C₃₇	#585	1	2	yes	—
425	#3505	C₂×C₃₇	1	1	yes	characteristic, complemented
426	C₂×#553	C₂×C₃₇	1	1	yes	characteristic, complemented
427	#3339	C₂×C₃₇	1	4	yes	complemented
428	#3337	C₂×C₃₇	1	4	yes	complemented
429	#3301	C₂×C₃₇	1	4	yes	complemented
430	#3297	C₂×C₃₇	1	4	yes	complemented
431	#3232	C₂×C₃₇	1	2	yes	complemented
432	#3188	C₂×C₃₇	1	2	yes	complemented
433	#3187	C₂×C₃₇	1	1	yes	characteristic, complemented
434	#3186	C₂×C₃₇	1	1	yes	characteristic, complemented
435	#3105	C₂×C₃₇	1	2	yes	complemented
436	#3091	C₂×C₃₇	1	2	yes	complemented
437	C₂×#484	C₂×C₃₇	1	1	yes	characteristic, complemented
438	C₂×#481	C₂×C₃₇	1	1	yes	characteristic, complemented
439	#2972	C₂×C₃₇	1	1	yes	characteristic, complemented
440	C₂×C₃₇	—	2	2	no	—
441	C₂×C₃₇	—	2	2	no	—
442	C₂×C₃₇	—	2	2	no	—
443	C₂×C₃₇	—	4	2	no	—
444	C₂×C₃₇	—	8	2	no	—
445	C₂×C₃₇	—	8	2	no	—
446	C₂×C₃₇	#3485	1	1	yes	characteristic
447	C₂×C₃₇	C₂²×#135	1	1	yes	characteristic
448	C₂×C₃₇	#3585	1	1	yes	characteristic
449	#553	—	2	2	no	—
450	#553	—	2	2	no	—
451	#553	—	2	2	no	—
452	#553	C₂²×C₃₇	1	4	yes	—
453	#553	C₂²×C₃₇	1	2	yes	complemented
454	#553	C₂²×C₃₇	1	4	yes	complemented
455	#552	C₂²×C₃₇	1	2	yes	complemented
456	#551	—	2	2	no	—
457	#548	C₂²×C₃₇	1	2	yes	complemented
458	#546	C₂²×C₃₇	1	2	yes	complemented
459	#539	—	2	1	no	—
460	#538	—	2	1	no	—
461	#534	—	2	1	no	—
462	#529	C₂²×C₃₇	1	2	yes	—
463	C₂×#126	—	2	1	no	—
464	C₂×#125	C₂²×C₃₇	1	1	yes	characteristic, complemented
465	#525	C₂²×C₃₇	1	2	yes	—
466	C₂×#123	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
468	C₂×#121	—	2	1	no	—
469	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
470	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
471	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic, complemented
472	#518	—	2	1	no	—
473	C₂×C₄×D₄	—	2	1	no	—
474	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic, complemented
476	C₂×#117	C₂²×C₃₇	1	1	yes	characteristic, complemented
477	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
478	#499	C₂²×C₃₇	1	4	yes	complemented
479	#488	C₂²×C₃₇	1	4	yes	complemented
480	#485	C₂²×C₃₇	1	4	yes	complemented
481	#484	C₂²×C₃₇	1	4	yes	complemented
482	#484	C₂²×C₃₇	1	2	yes	complemented
483	#484	C₂²×C₃₇	1	2	yes	complemented
484	#483	C₂²×C₃₇	1	2	yes	complemented
485	#482	C₂²×C₃₇	1	4	yes	complemented
486	#482	C₂²×C₃₇	1	4	yes	complemented
487	#481	C₂²×C₃₇	1	2	yes	—
488	#481	C₂²×C₃₇	1	2	yes	—
489	#481	C₂²×C₃₇	1	2	yes	complemented
490	#481	C₂²×C₃₇	1	4	yes	complemented
491	#480	C₂²×C₃₇	1	2	yes	—
492	#480	C₂²×C₃₇	1	2	yes	complemented
493	#479	C₂²×C₃₇	1	4	yes	complemented
494	#478	C₂²×C₃₇	1	4	yes	complemented
495	#478	C₂²×C₃₇	1	4	yes	complemented
496	#466	C₂²×C₃₇	1	4	yes	complemented
497	#466	C₂²×C₃₇	1	4	yes	complemented
498	#465	C₂²×C₃₇	1	4	yes	complemented
499	#465	C₂²×C₃₇	1	4	yes	complemented
500	#463	C₂²×C₃₇	1	4	yes	complemented
501	#450	C₂²×C₃₇	1	2	yes	complemented
502	#449	C₂²×C₃₇	1	4	yes	complemented
503	#448	C₂²×C₃₇	1	2	yes	complemented
504	#447	C₂²×C₃₇	1	2	yes	—
505	#447	C₂²×C₃₇	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₃₇	1	4	yes	complemented
507	C₄×D₈	C₂²×C₃₇	1	4	yes	complemented
508	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
509	C₈×D₄	C₂²×C₃₇	1	4	yes	complemented
510	#431	C₂²×C₃₇	1	2	yes	complemented
511	#427	C₂²×C₃₇	1	4	yes	complemented
512	C₂×#107	C₂²×C₃₇	1	2	yes	complemented
513	C₂×#106	C₂²×C₃₇	1	2	yes	complemented
514	#416	C₂²×C₃₇	1	4	yes	complemented
515	C₂×#103	C₂²×C₃₇	1	2	yes	complemented
516	C₂×#102	C₂²×C₃₇	1	2	yes	complemented
517	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
518	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
519	C₂×C₂²⋊C₈	C₂²×C₃₇	1	2	yes	complemented
520	C₃₇	#61699	1	1	yes	characteristic, direct product factor, Sylow
521	C₂×#41	C₂³×C₃₇	1	2	yes	—
522	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
533	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
534	C₂×D₈	C₂³×C₃₇	1	4	yes	—
535	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
536	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
537	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	C₂³×C₃₇	1	4	yes	—
546	#125	C₂³×C₃₇	1	2	yes	—
547	#124	—	2	2	no	—
548	#124	C₂³×C₃₇	1	2	yes	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	#123	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
560	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
561	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
562	#121	—	2	4	no	—
563	#121	—	2	4	no	—
564	#121	—	2	2	no	—
565	#121	—	2	2	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	C₂³×C₃₇	1	2	yes	—
573	#121	C₂³×C₃₇	1	2	yes	—
574	#121	C₂³×C₃₇	1	2	yes	—
575	#121	C₂³×C₃₇	1	2	yes	—
576	#121	C₂³×C₃₇	1	4	yes	—
577	#121	C₂³×C₃₇	1	2	yes	—
578	#120	—	2	2	no	—
579	#120	—	2	2	no	—
580	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	D₄×C₃₇	1	2	yes	—
590	C₄×D₄	D₄×C₃₇	1	2	yes	—
591	C₄×D₄	C₂³×C₃₇	1	4	yes	—
592	C₄×D₄	C₂³×C₃₇	1	2	yes	—
593	C₄×D₄	C₂³×C₃₇	1	2	yes	—
594	C₄×D₄	C₂³×C₃₇	1	2	yes	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	C₂³×C₃₇	1	4	yes	—
599	#117	C₂³×C₃₇	1	2	yes	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	2	no	—
621	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
623	C₂×C₄²	—	2	1	no	—
624	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
625	#107	C₂³×C₃₇	1	4	yes	—
626	#107	C₂³×C₃₇	1	4	yes	—
627	#107	C₂³×C₃₇	1	4	yes	—
628	#106	C₂³×C₃₇	1	4	yes	—
629	#106	C₂³×C₃₇	1	4	yes	—
630	#106	C₂³×C₃₇	1	4	yes	—
631	C₄⋊C₈	C₂³×C₃₇	1	4	yes	—
632	#103	C₂³×C₃₇	1	4	yes	—
633	#103	C₂³×C₃₇	1	4	yes	—
634	#103	C₂³×C₃₇	1	4	yes	—
635	#102	C₂³×C₃₇	1	4	yes	—
636	#102	C₂³×C₃₇	1	4	yes	—
637	#102	C₂³×C₃₇	1	4	yes	—
638	#102	C₂³×C₃₇	1	4	yes	—
639	#102	C₂³×C₃₇	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
641	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
643	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
644	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
645	C₄×C₈	C₂³×C₃₇	1	4	yes	—
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	1	no	—
648	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
649	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
650	#41	—	4	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	8	2	no	—
669	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
671	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
672	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	8	2	no	—
687	C₂²×C₄	—	8	2	no	—
688	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
699	SD₁₆	—	4	4	no	—
700	D₈	—	4	4	no	—
701	C₂×C₈	—	4	2	no	—
702	C₂×C₈	—	4	4	no	—
703	C₂×C₈	—	4	2	no	—
704	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
705	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
746	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	C₂×D₄×C₃₇	1	2	yes	—
751	C₄²	C₂⁴×C₃₇	1	2	yes	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	#135×C₃₇	1	4	yes	—
766	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
767	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
768	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
769	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	8	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	2	4	no	—
774	D₄	—	2	4	no	—
775	D₄	—	2	4	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	4	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	—	8	1	no	—
813	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
819	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
820	C₈	—	2	4	no	—
821	C₈	—	2	4	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	4	no	—
840	C₂²	—	16	2	no	—
841	C₂²	C₂×#135×C₃₇	1	2	yes	—
842	C₂²	C₂×#135×C₃₇	1	2	yes	—
843	C₂²	C₂×#135×C₃₇	1	2	yes	—
844	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
845	C₄	—	2	1	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	C₃₇×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	2	no	—
861	C₂	—	4	2	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₃₇×#3485	1	1	yes	characteristic
865	C₂	C₂²×#135×C₃₇	1	1	yes	characteristic
866	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×#553	C₂	semidirect
3. C₃₇×#3339	C₂	semidirect
4. C₃₇×#3337	C₂	semidirect
5. C₃₇×#3301	C₂	semidirect
6. C₃₇×#3297	C₂	semidirect
7. C₃₇×#3232	C₂	semidirect
8. C₃₇×#3188	C₂	semidirect
9. C₃₇×#3187	C₂	semidirect
10. C₃₇×#3186	C₂	semidirect
11. C₃₇×#3105	C₂	semidirect
12. C₃₇×#3091	C₂	semidirect
13. C₂×C₃₇×#484	C₂	semidirect
14. C₂×C₃₇×#481	C₂	semidirect
15. C₃₇×#2972	C₂	semidirect
20. C₃₇×#553	C₂²	semidirect
21. C₃₇×#553	C₂²	semidirect
22. C₃₇×#552	C₂²	semidirect
24. C₃₇×#548	C₂²	semidirect
25. C₃₇×#546	C₂²	semidirect
31. C₂×#125×C₃₇	C₂²	semidirect
38. C₂×#121×C₃₇	C₂²	semidirect
42. C₂×C₄×D₄×C₃₇	C₂²	semidirect
43. C₂×#117×C₃₇	C₂²	semidirect
45. C₃₇×#499	C₂²	semidirect
46. C₃₇×#488	C₂²	semidirect
47. C₃₇×#485	C₂²	semidirect
48. C₃₇×#484	C₂²	semidirect
49. C₃₇×#484	C₂²	semidirect
50. C₃₇×#484	C₂²	semidirect
51. C₃₇×#483	C₂²	semidirect
52. C₃₇×#482	C₂²	semidirect
53. C₃₇×#482	C₂²	semidirect
56. C₃₇×#481	C₂²	semidirect
57. C₃₇×#481	C₂²	semidirect
59. C₃₇×#480	C₂²	semidirect
60. C₃₇×#479	C₂²	semidirect
61. C₃₇×#478	C₂²	semidirect
62. C₃₇×#478	C₂²	semidirect
63. C₃₇×#466	C₂²	semidirect
64. C₃₇×#466	C₂²	semidirect
65. C₃₇×#465	C₂²	semidirect
66. C₃₇×#465	C₂²	semidirect
67. C₃₇×#463	C₂²	semidirect
68. C₃₇×#450	C₂²	semidirect
69. C₃₇×#449	C₂²	semidirect
70. C₃₇×#448	C₂²	semidirect
72. C₃₇×#447	C₂²	semidirect
73. C₄×SD₁₆×C₃₇	C₂²	semidirect
74. C₄×D₈×C₃₇	C₂²	semidirect
75. C₈×D₄×C₃₇	C₂²	semidirect
76. C₈×D₄×C₃₇	C₂²	semidirect
77. C₃₇×#431	C₂²	semidirect
78. C₃₇×#427	C₂²	semidirect
79. C₂×#107×C₃₇	C₂²	semidirect
80. C₂×#106×C₃₇	C₂²	semidirect
81. C₃₇×#416	C₂²	semidirect
82. C₂×#103×C₃₇	C₂²	semidirect
83. C₂×#102×C₃₇	C₂²	semidirect
86. C₂×C₂²⋊C₈×C₃₇	C₂²	semidirect
388. #61699	C₃₇	direct (N × H)
425. #3505	C₂×C₃₇	semidirect
426. C₂×#553	C₂×C₃₇	semidirect
427. #3339	C₂×C₃₇	semidirect
428. #3337	C₂×C₃₇	semidirect
429. #3301	C₂×C₃₇	semidirect
430. #3297	C₂×C₃₇	semidirect
431. #3232	C₂×C₃₇	semidirect
432. #3188	C₂×C₃₇	semidirect
433. #3187	C₂×C₃₇	semidirect
434. #3186	C₂×C₃₇	semidirect
435. #3105	C₂×C₃₇	semidirect
436. #3091	C₂×C₃₇	semidirect
437. C₂×#484	C₂×C₃₇	semidirect
438. C₂×#481	C₂×C₃₇	semidirect
439. #2972	C₂×C₃₇	semidirect
453. #553	C₂²×C₃₇	semidirect
454. #553	C₂²×C₃₇	semidirect
455. #552	C₂²×C₃₇	semidirect
457. #548	C₂²×C₃₇	semidirect
458. #546	C₂²×C₃₇	semidirect
464. C₂×#125	C₂²×C₃₇	semidirect
471. C₂×#121	C₂²×C₃₇	semidirect
475. C₂×C₄×D₄	C₂²×C₃₇	semidirect
476. C₂×#117	C₂²×C₃₇	semidirect
478. #499	C₂²×C₃₇	semidirect
479. #488	C₂²×C₃₇	semidirect
480. #485	C₂²×C₃₇	semidirect
481. #484	C₂²×C₃₇	semidirect
482. #484	C₂²×C₃₇	semidirect
483. #484	C₂²×C₃₇	semidirect
484. #483	C₂²×C₃₇	semidirect
485. #482	C₂²×C₃₇	semidirect
486. #482	C₂²×C₃₇	semidirect
489. #481	C₂²×C₃₇	semidirect
490. #481	C₂²×C₃₇	semidirect
492. #480	C₂²×C₃₇	semidirect
493. #479	C₂²×C₃₇	semidirect
494. #478	C₂²×C₃₇	semidirect
495. #478	C₂²×C₃₇	semidirect
496. #466	C₂²×C₃₇	semidirect
497. #466	C₂²×C₃₇	semidirect
498. #465	C₂²×C₃₇	semidirect
499. #465	C₂²×C₃₇	semidirect
500. #463	C₂²×C₃₇	semidirect
501. #450	C₂²×C₃₇	semidirect
502. #449	C₂²×C₃₇	semidirect
503. #448	C₂²×C₃₇	semidirect
505. #447	C₂²×C₃₇	semidirect
506. C₄×SD₁₆	C₂²×C₃₇	semidirect
507. C₄×D₈	C₂²×C₃₇	semidirect
508. C₈×D₄	C₂²×C₃₇	semidirect
509. C₈×D₄	C₂²×C₃₇	semidirect
510. #431	C₂²×C₃₇	semidirect
511. #427	C₂²×C₃₇	semidirect
512. C₂×#107	C₂²×C₃₇	semidirect
513. C₂×#106	C₂²×C₃₇	semidirect
514. #416	C₂²×C₃₇	semidirect
515. C₂×#103	C₂²×C₃₇	semidirect
516. C₂×#102	C₂²×C₃₇	semidirect
519. C₂×C₂²⋊C₈	C₂²×C₃₇	semidirect
520. C₃₇	#61699	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×#3505	2
C₂×C₃₇×#553	2
C₃₇×#3339	2
C₃₇×#3337	2
C₃₇×#3301	2
C₃₇×#3297	2
C₃₇×#3232	2
C₃₇×#3188	2
C₃₇×#3187	2
C₃₇×#3186	2
C₃₇×#3105	2
C₃₇×#3091	2
C₂×C₃₇×#484	2
C₂×C₃₇×#481	2
C₃₇×#2972	2
#61699	37

Subgroups — C37×#61699 #22682952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61699 #22682952