Subgroups — C₃₇×#28492 #22649745

Order 9472.

1142 conjugacy classes of subgroups.

The subgroup lattice has 838 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, complemented
2	C₂×C₃₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×#468	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₇×#465	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₇×#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2540	C₂	1	1	yes	maximal, characteristic
9	C₃₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#2000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₇×#2000	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#1981	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₃₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
23	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₃₇×#497	—	2	4	no	—
34	C₃₇×#470	—	2	4	no	—
35	C₃₇×#468	—	2	4	no	—
36	C₃₇×#467	—	2	4	no	—
37	C₃₇×#465	—	2	4	no	—
38	C₃₇×#435	—	2	4	no	—
39	C₂×#107×C₃₇	C₂²	1	1	yes	characteristic
40	C₂×#106×C₃₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
43	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
44	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
45	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
46	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
47	C₂×#103×C₃₇	C₂²	1	1	yes	characteristic
48	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
49	C₂×#102×C₃₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₃₇	C₂²	1	1	yes	characteristic
52	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
53	C₃₇×#399	—	2	1	no	—
54	C₃₇×#399	—	2	1	no	—
55	C₃₇×#399	—	2	1	no	—
56	C₃₇×#392	—	2	1	no	—
57	C₃₇×#390	—	2	1	no	—
58	C₃₇×#390	—	2	1	no	—
59	C₃₇×#390	—	2	1	no	—
60	C₃₇×#384	—	2	1	no	—
61	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
63	C₃₇×#340	C₂²	1	1	yes	characteristic
64	C₃₇×#340	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₃₇	—	2	1	no	—
69	C₂²×D₄×C₃₇	—	2	1	no	—
70	C₂²×D₄×C₃₇	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂×Q₁₆×C₃₇	—	2	2	no	—
75	C₂×Q₁₆×C₃₇	—	2	2	no	—
76	C₂×Q₁₆×C₃₇	—	2	2	no	—
77	C₂×Q₁₆×C₃₇	—	2	2	no	—
78	C₂×Q₁₆×C₃₇	—	4	1	no	—
79	C₂×Q₁₆×C₃₇	—	4	1	no	—
80	C₂×SD₁₆×C₃₇	—	2	2	no	—
81	C₂×SD₁₆×C₃₇	—	2	2	no	—
82	C₂×SD₁₆×C₃₇	—	2	2	no	—
83	C₂×SD₁₆×C₃₇	—	2	2	no	—
84	C₂×SD₁₆×C₃₇	—	4	1	no	—
85	C₂×SD₁₆×C₃₇	—	4	1	no	—
86	C₂×M₁₆×C₃₇	—	2	2	no	—
87	C₂×M₁₆×C₃₇	—	2	2	no	—
88	C₂×M₁₆×C₃₇	—	2	2	no	—
89	C₂²×C₈×C₃₇	—	2	2	no	—
90	C₂²×C₈×C₃₇	—	2	2	no	—
91	C₂²×C₈×C₃₇	—	2	2	no	—
92	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₃₇	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₃₇	—	2	2	no	—
97	C₄⋊Q₈×C₃₇	—	2	2	no	—
98	#124×C₃₇	—	2	2	no	—
99	#124×C₃₇	—	2	2	no	—
100	C₂²⋊Q₈×C₃₇	—	2	2	no	—
101	C₂²⋊Q₈×C₃₇	—	2	2	no	—
102	C₂²⋊Q₈×C₃₇	—	2	2	no	—
103	C₂²⋊Q₈×C₃₇	—	2	2	no	—
104	C₂²⋊Q₈×C₃₇	—	2	2	no	—
105	C₂²⋊Q₈×C₃₇	—	2	2	no	—
106	C₂²⋊Q₈×C₃₇	—	4	1	no	—
107	C₂²⋊Q₈×C₃₇	—	4	1	no	—
108	C₂²⋊Q₈×C₃₇	—	4	1	no	—
109	C₂²⋊Q₈×C₃₇	—	4	1	no	—
110	C₂²⋊Q₈×C₃₇	—	4	1	no	—
111	C₂²⋊Q₈×C₃₇	—	4	1	no	—
112	#121×C₃₇	—	2	2	no	—
113	#121×C₃₇	—	2	2	no	—
114	#121×C₃₇	—	4	1	no	—
115	#121×C₃₇	—	4	1	no	—
116	C₄×D₄×C₃₇	—	2	2	no	—
117	C₄×D₄×C₃₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
119	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
120	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
121	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
122	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
123	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
124	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
125	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
126	C₂×C₄⋊C₄×C₃₇	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₃₇	D₄	1	1	yes	characteristic
143	C₂×C₄²×C₃₇	—	2	1	no	—
144	C₂×C₄²×C₃₇	—	2	1	no	—
145	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
146	#107×C₃₇	D₄	1	4	yes	complemented
147	#106×C₃₇	D₄	1	4	yes	complemented
148	C₄⋊C₈×C₃₇	—	2	2	no	—
149	#103×C₃₇	—	2	2	no	—
150	#103×C₃₇	—	2	2	no	—
151	#103×C₃₇	—	2	2	no	—
152	#103×C₃₇	—	2	2	no	—
153	#103×C₃₇	—	2	2	no	—
154	#103×C₃₇	—	2	2	no	—
155	#102×C₃₇	—	2	2	no	—
156	#102×C₃₇	—	2	2	no	—
157	C₂²⋊C₈×C₃₇	—	2	2	no	—
158	C₂²⋊C₈×C₃₇	—	2	2	no	—
159	#97×C₃₇	D₄	1	4	yes	complemented
160	#95×C₃₇	—	2	1	no	—
161	#95×C₃₇	—	2	1	no	—
162	C₂⁴×C₃₇	—	2	1	no	—
163	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₃₇	C₂×D₄	1	1	yes	characteristic
165	C₂×Q₈×C₃₇	—	2	1	no	—
166	C₂×Q₈×C₃₇	—	2	1	no	—
167	C₂×Q₈×C₃₇	—	2	1	no	—
168	C₂×Q₈×C₃₇	—	2	1	no	—
169	C₂×Q₈×C₃₇	—	2	1	no	—
170	C₂×Q₈×C₃₇	—	2	1	no	—
171	C₂×Q₈×C₃₇	—	2	1	no	—
172	C₂×Q₈×C₃₇	—	2	1	no	—
173	C₂×Q₈×C₃₇	—	2	1	no	—
174	C₂×Q₈×C₃₇	—	2	1	no	—
175	C₂×Q₈×C₃₇	—	2	1	no	—
176	C₂×Q₈×C₃₇	—	2	1	no	—
177	C₂×Q₈×C₃₇	—	2	1	no	—
178	C₂×Q₈×C₃₇	—	2	1	no	—
179	C₂×Q₈×C₃₇	—	2	1	no	—
180	C₂×Q₈×C₃₇	—	2	1	no	—
181	C₂×Q₈×C₃₇	—	2	1	no	—
182	C₂×Q₈×C₃₇	—	2	1	no	—
183	C₂×D₄×C₃₇	—	2	2	no	—
184	C₂×D₄×C₃₇	—	2	2	no	—
185	C₂×D₄×C₃₇	—	2	1	no	—
186	C₂×D₄×C₃₇	—	2	1	no	—
187	C₂×D₄×C₃₇	—	2	1	no	—
188	C₂×D₄×C₃₇	—	2	1	no	—
189	C₂×D₄×C₃₇	—	2	1	no	—
190	C₂×D₄×C₃₇	—	2	1	no	—
191	C₂×D₄×C₃₇	—	4	1	no	—
192	C₂×D₄×C₃₇	—	4	2	no	—
193	C₂×D₄×C₃₇	—	4	2	no	—
194	C₂×D₄×C₃₇	—	4	2	no	—
195	C₂×D₄×C₃₇	—	4	2	no	—
196	C₂×D₄×C₃₇	—	8	1	no	—
197	C₂×D₄×C₃₇	—	8	1	no	—
198	C₂²×C₄×C₃₇	—	2	1	no	—
199	C₂²×C₄×C₃₇	—	2	1	no	—
200	C₂²×C₄×C₃₇	—	2	1	no	—
201	C₂²×C₄×C₃₇	—	2	1	no	—
202	C₂²×C₄×C₃₇	—	2	1	no	—
203	C₂²×C₄×C₃₇	—	2	1	no	—
204	C₂²×C₄×C₃₇	—	2	1	no	—
205	C₂²×C₄×C₃₇	—	2	1	no	—
206	C₂²×C₄×C₃₇	—	2	1	no	—
207	C₂²×C₄×C₃₇	—	2	1	no	—
208	C₂²×C₄×C₃₇	—	2	1	no	—
209	C₂²×C₄×C₃₇	—	2	1	no	—
210	C₂²×C₄×C₃₇	—	2	1	no	—
211	C₂²×C₄×C₃₇	—	2	1	no	—
212	C₂²×C₄×C₃₇	—	2	1	no	—
213	C₂²×C₄×C₃₇	—	2	1	no	—
214	C₂²×C₄×C₃₇	—	2	1	no	—
215	C₂²×C₄×C₃₇	—	2	1	no	—
216	C₂²×C₄×C₃₇	—	2	1	no	—
217	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₃₇	—	4	4	no	—
223	Q₁₆×C₃₇	—	4	4	no	—
224	SD₁₆×C₃₇	—	4	4	no	—
225	SD₁₆×C₃₇	—	4	4	no	—
226	M₁₆×C₃₇	—	4	4	no	—
227	C₂×C₈×C₃₇	—	2	1	no	—
228	C₂×C₈×C₃₇	—	2	1	no	—
229	C₂×C₈×C₃₇	—	2	1	no	—
230	C₂×C₈×C₃₇	—	2	1	no	—
231	C₂×C₈×C₃₇	—	2	1	no	—
232	C₂×C₈×C₃₇	—	2	1	no	—
233	C₂×C₈×C₃₇	—	2	1	no	—
234	C₂×C₈×C₃₇	—	2	1	no	—
235	C₂×C₈×C₃₇	—	4	4	no	—
236	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
238	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
239	C₂×C₈×C₃₇	C₂×D₄	1	2	yes	—
240	C₄⋊C₄×C₃₇	—	2	2	no	—
241	C₄⋊C₄×C₃₇	—	2	1	no	—
242	C₄⋊C₄×C₃₇	—	2	1	no	—
243	C₄⋊C₄×C₃₇	—	2	1	no	—
244	C₄⋊C₄×C₃₇	—	2	1	no	—
245	C₄⋊C₄×C₃₇	—	4	2	no	—
246	C₄⋊C₄×C₃₇	—	4	2	no	—
247	C₄⋊C₄×C₃₇	—	4	2	no	—
248	C₄⋊C₄×C₃₇	—	4	2	no	—
249	C₄⋊C₄×C₃₇	—	4	2	no	—
250	C₄⋊C₄×C₃₇	—	4	2	no	—
251	C₄⋊C₄×C₃₇	—	4	2	no	—
252	C₄⋊C₄×C₃₇	—	4	2	no	—
253	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₃₇	—	2	2	no	—
258	C₂²⋊C₄×C₃₇	—	2	2	no	—
259	C₂²⋊C₄×C₃₇	—	4	2	no	—
260	C₂²⋊C₄×C₃₇	—	4	2	no	—
261	C₂²⋊C₄×C₃₇	—	4	2	no	—
262	C₂²⋊C₄×C₃₇	—	4	2	no	—
263	C₂²⋊C₄×C₃₇	—	4	2	no	—
264	C₂²⋊C₄×C₃₇	—	4	2	no	—
265	C₂²⋊C₄×C₃₇	—	4	2	no	—
266	C₂²⋊C₄×C₃₇	—	4	2	no	—
267	C₂²⋊C₄×C₃₇	—	4	2	no	—
268	C₂²⋊C₄×C₃₇	—	4	2	no	—
269	C₄²×C₃₇	—	4	2	no	—
270	C₄²×C₃₇	—	8	1	no	—
271	C₄²×C₃₇	C₂×D₄	1	2	yes	—
272	C₄²×C₃₇	#41	1	2	yes	—
273	C₂³×C₃₇	—	2	1	no	—
274	C₂³×C₃₇	—	2	1	no	—
275	C₂³×C₃₇	—	2	1	no	—
276	C₂³×C₃₇	—	2	1	no	—
277	C₂³×C₃₇	—	2	1	no	—
278	C₂³×C₃₇	—	2	1	no	—
279	C₂³×C₃₇	—	2	1	no	—
280	C₂³×C₃₇	—	2	1	no	—
281	C₂³×C₃₇	—	2	1	no	—
282	C₂³×C₃₇	—	2	1	no	—
283	C₂³×C₃₇	—	2	1	no	—
284	C₂³×C₃₇	—	2	1	no	—
285	C₂³×C₃₇	—	2	1	no	—
286	C₂³×C₃₇	—	4	1	no	—
287	C₂³×C₃₇	—	4	1	no	—
288	C₂³×C₃₇	—	4	1	no	—
289	C₂³×C₃₇	—	4	1	no	—
290	C₂³×C₃₇	—	4	1	no	—
291	C₂³×C₃₇	—	4	1	no	—
292	C₂³×C₃₇	—	4	1	no	—
293	C₂³×C₃₇	#137	1	2	yes	—
294	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₃₇	—	4	1	no	—
296	Q₈×C₃₇	—	4	1	no	—
297	Q₈×C₃₇	—	4	1	no	—
298	Q₈×C₃₇	—	4	1	no	—
299	Q₈×C₃₇	—	4	1	no	—
300	Q₈×C₃₇	—	4	1	no	—
301	Q₈×C₃₇	—	4	1	no	—
302	Q₈×C₃₇	—	4	1	no	—
303	Q₈×C₃₇	—	4	1	no	—
304	Q₈×C₃₇	—	4	1	no	—
305	Q₈×C₃₇	—	4	1	no	—
306	Q₈×C₃₇	—	4	1	no	—
307	D₄×C₃₇	—	4	4	no	—
308	D₄×C₃₇	—	4	1	no	—
309	D₄×C₃₇	—	4	1	no	—
310	D₄×C₃₇	—	4	1	no	—
311	D₄×C₃₇	—	4	1	no	—
312	D₄×C₃₇	—	8	4	no	—
313	D₄×C₃₇	—	8	4	no	—
314	C₂×C₄×C₃₇	—	2	1	no	—
315	C₂×C₄×C₃₇	—	2	1	no	—
316	C₂×C₄×C₃₇	—	2	1	no	—
317	C₂×C₄×C₃₇	—	2	1	no	—
318	C₂×C₄×C₃₇	—	2	1	no	—
319	C₂×C₄×C₃₇	—	2	1	no	—
320	C₂×C₄×C₃₇	—	2	2	no	—
321	C₂×C₄×C₃₇	—	2	2	no	—
322	C₂×C₄×C₃₇	—	2	2	no	—
323	C₂×C₄×C₃₇	—	2	2	no	—
324	C₂×C₄×C₃₇	—	2	1	no	—
325	C₂×C₄×C₃₇	—	2	1	no	—
326	C₂×C₄×C₃₇	—	2	1	no	—
327	C₂×C₄×C₃₇	—	2	1	no	—
328	C₂×C₄×C₃₇	—	4	1	no	—
329	C₂×C₄×C₃₇	—	4	1	no	—
330	C₂×C₄×C₃₇	—	4	1	no	—
331	C₂×C₄×C₃₇	—	4	1	no	—
332	C₂×C₄×C₃₇	—	4	1	no	—
333	C₂×C₄×C₃₇	—	4	1	no	—
334	C₂×C₄×C₃₇	—	4	1	no	—
335	C₂×C₄×C₃₇	—	4	1	no	—
336	C₂×C₄×C₃₇	—	4	1	no	—
337	C₂×C₄×C₃₇	—	4	1	no	—
338	C₂×C₄×C₃₇	—	4	1	no	—
339	C₂×C₄×C₃₇	—	4	1	no	—
340	C₂×C₄×C₃₇	—	4	1	no	—
341	C₂×C₄×C₃₇	—	4	1	no	—
342	C₂×C₄×C₃₇	—	4	1	no	—
343	C₂×C₄×C₃₇	—	4	1	no	—
344	C₂×C₄×C₃₇	—	4	1	no	—
345	C₂×C₄×C₃₇	—	4	1	no	—
346	C₂×C₄×C₃₇	—	4	1	no	—
347	C₂×C₄×C₃₇	—	4	1	no	—
348	C₂×C₄×C₃₇	—	4	1	no	—
349	C₂×C₄×C₃₇	—	4	1	no	—
350	C₂×C₄×C₃₇	—	4	1	no	—
351	C₂×C₄×C₃₇	—	4	1	no	—
352	C₂×C₄×C₃₇	—	4	1	no	—
353	C₂×C₄×C₃₇	#121	1	2	yes	—
354	C₂×C₄×C₃₇	#121	1	2	yes	—
355	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₇	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
361	C₈×C₃₇	—	2	2	no	—
362	C₈×C₃₇	—	4	1	no	—
363	C₈×C₃₇	—	4	1	no	—
364	C₈×C₃₇	#127	1	4	yes	—
365	#28492	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂²×C₃₇	—	2	2	no	—
367	C₂²×C₃₇	—	2	2	no	—
368	C₂²×C₃₇	—	2	2	no	—
369	C₂²×C₃₇	—	4	1	no	—
370	C₂²×C₃₇	—	4	1	no	—
371	C₂²×C₃₇	—	4	1	no	—
372	C₂²×C₃₇	—	4	1	no	—
373	C₂²×C₃₇	—	4	1	no	—
374	C₂²×C₃₇	—	4	1	no	—
375	C₂²×C₃₇	—	4	1	no	—
376	C₂²×C₃₇	—	4	1	no	—
377	C₂²×C₃₇	—	4	1	no	—
378	C₂²×C₃₇	—	4	1	no	—
379	C₂²×C₃₇	—	4	1	no	—
380	C₂²×C₃₇	—	8	1	no	—
381	C₂²×C₃₇	—	8	1	no	—
382	C₂²×C₃₇	—	8	1	no	—
383	C₂²×C₃₇	—	8	1	no	—
384	C₂²×C₃₇	—	8	1	no	—
385	C₂²×C₃₇	—	8	1	no	—
386	C₂²×C₃₇	—	8	1	no	—
387	C₂²×C₃₇	C₂×#121	1	1	yes	characteristic
388	C₂²×C₃₇	D₄²	1	1	yes	characteristic
389	C₂²×C₃₇	D₄²	1	1	yes	characteristic
390	C₂²×C₃₇	C₂×#137	1	1	yes	characteristic
391	C₂²×C₃₇	#575	1	1	yes	characteristic
392	C₂²×C₃₇	#577	1	1	yes	characteristic
393	C₂²×C₃₇	#578	1	1	yes	characteristic
394	C₄×C₃₇	—	2	2	no	—
395	C₄×C₃₇	—	2	2	no	—
396	C₄×C₃₇	—	4	2	no	—
397	C₄×C₃₇	—	4	2	no	—
398	C₄×C₃₇	—	4	2	no	—
399	C₄×C₃₇	—	4	2	no	—
400	C₄×C₃₇	—	4	1	no	—
401	C₄×C₃₇	—	4	1	no	—
402	C₄×C₃₇	—	8	1	no	—
403	C₄×C₃₇	—	8	1	no	—
404	C₄×C₃₇	—	8	1	no	—
405	C₄×C₃₇	C₂×#127	1	1	yes	characteristic
406	C₄×C₃₇	#535	1	1	yes	characteristic
407	C₄×C₃₇	#550	1	1	yes	characteristic
408	C₄×C₃₇	#550	1	1	yes	characteristic
409	C₂×#497	C₂×C₃₇	1	1	yes	characteristic, complemented
410	C₂×#470	C₂×C₃₇	1	1	yes	characteristic, complemented
411	C₂×#468	C₂×C₃₇	1	1	yes	characteristic, complemented
412	C₂×#467	C₂×C₃₇	1	1	yes	characteristic, complemented
413	C₂×#465	C₂×C₃₇	1	1	yes	characteristic, complemented
414	C₂×#435	C₂×C₃₇	1	1	yes	characteristic, complemented
415	#2542	C₂×C₃₇	1	1	yes	characteristic, complemented
416	#2540	C₂×C₃₇	1	1	yes	characteristic
417	#2001	C₂×C₃₇	1	1	yes	characteristic, complemented
418	#2001	C₂×C₃₇	1	1	yes	characteristic, complemented
419	#2000	C₂×C₃₇	1	1	yes	characteristic, complemented
420	#2000	C₂×C₃₇	1	1	yes	characteristic, complemented
421	#1983	C₂×C₃₇	1	1	yes	characteristic, complemented
422	#1981	C₂×C₃₇	1	1	yes	characteristic, complemented
423	#1776	C₂×C₃₇	1	1	yes	characteristic, complemented
424	C₂×C₃₇	—	4	2	no	—
425	C₂×C₃₇	—	8	1	no	—
426	C₂×C₃₇	—	16	1	no	—
427	C₂×C₃₇	#2541	1	1	yes	characteristic
428	C₂×C₃₇	#3056	1	1	yes	characteristic
429	C₂×C₃₇	#3063	1	1	yes	characteristic
430	C₂×C₃₇	#3266	1	1	yes	characteristic
431	C₂×C₃₇	#3267	1	1	yes	characteristic
432	C₂×C₃₇	#3269	1	1	yes	characteristic
433	C₂×C₃₇	#3270	1	1	yes	characteristic
434	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
435	C₂²×Q₁₆	C₂²×C₃₇	1	1	yes	characteristic
436	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
437	C₂²×SD₁₆	C₂²×C₃₇	1	1	yes	characteristic
438	C₂²×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
439	C₂³×C₈	C₂²×C₃₇	1	1	yes	characteristic
440	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
441	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
442	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
444	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
445	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
446	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
447	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
448	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
449	C₂×#121	C₂²×C₃₇	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
451	#497	—	2	4	no	—
452	#470	—	2	4	no	—
453	#468	—	2	4	no	—
454	#467	—	2	4	no	—
455	#465	—	2	4	no	—
456	#435	—	2	4	no	—
457	C₂×#107	C₂²×C₃₇	1	1	yes	characteristic
458	C₂×#106	C₂²×C₃₇	1	1	yes	characteristic
459	C₂×C₄⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
460	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
461	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
462	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
463	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
464	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
465	C₂×#103	C₂²×C₃₇	1	1	yes	characteristic
466	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
467	C₂×#102	C₂²×C₃₇	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₃₇	1	1	yes	characteristic
470	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
471	#399	—	2	1	no	—
472	#399	—	2	1	no	—
473	#399	—	2	1	no	—
474	#392	—	2	1	no	—
475	#390	—	2	1	no	—
476	#390	—	2	1	no	—
477	#390	—	2	1	no	—
478	#384	—	2	1	no	—
479	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
481	#340	C₂²×C₃₇	1	1	yes	characteristic
482	#340	C₂²×C₃₇	1	1	yes	characteristic
483	C₃₇	#28492	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	D₄×C₃₇	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
493	C₂×Q₁₆	—	2	2	no	—
494	C₂×Q₁₆	—	2	2	no	—
495	C₂×Q₁₆	—	2	2	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×Q₁₆	—	4	1	no	—
498	C₂×Q₁₆	—	4	1	no	—
499	C₂×SD₁₆	—	2	2	no	—
500	C₂×SD₁₆	—	2	2	no	—
501	C₂×SD₁₆	—	2	2	no	—
502	C₂×SD₁₆	—	2	2	no	—
503	C₂×SD₁₆	—	4	1	no	—
504	C₂×SD₁₆	—	4	1	no	—
505	C₂×M₁₆	—	2	2	no	—
506	C₂×M₁₆	—	2	2	no	—
507	C₂×M₁₆	—	2	2	no	—
508	C₂²×C₈	—	2	2	no	—
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₃₇	1	1	yes	characteristic
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	4	1	no	—
526	C₂²⋊Q₈	—	4	1	no	—
527	C₂²⋊Q₈	—	4	1	no	—
528	C₂²⋊Q₈	—	4	1	no	—
529	C₂²⋊Q₈	—	4	1	no	—
530	C₂²⋊Q₈	—	4	1	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	4	1	no	—
534	#121	—	4	1	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	D₄×C₃₇	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	D₄×C₃₇	1	1	yes	characteristic
562	C₂×C₄²	—	2	1	no	—
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
565	#107	D₄×C₃₇	1	4	yes	complemented
566	#106	D₄×C₃₇	1	4	yes	complemented
567	C₄⋊C₈	—	2	2	no	—
568	#103	—	2	2	no	—
569	#103	—	2	2	no	—
570	#103	—	2	2	no	—
571	#103	—	2	2	no	—
572	#103	—	2	2	no	—
573	#103	—	2	2	no	—
574	#102	—	2	2	no	—
575	#102	—	2	2	no	—
576	C₂²⋊C₈	—	2	2	no	—
577	C₂²⋊C₈	—	2	2	no	—
578	#97	D₄×C₃₇	1	4	yes	complemented
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
583	C₂⁴	C₂×D₄×C₃₇	1	1	yes	characteristic
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	8	1	no	—
616	C₂×D₄	—	8	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
641	Q₁₆	—	4	4	no	—
642	Q₁₆	—	4	4	no	—
643	SD₁₆	—	4	4	no	—
644	SD₁₆	—	4	4	no	—
645	M₁₆	—	4	4	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	4	4	no	—
655	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
656	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
657	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
658	C₂×C₈	C₂×D₄×C₃₇	1	2	yes	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
673	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	4	2	no	—
687	C₂²⋊C₄	—	4	2	no	—
688	C₄²	—	4	2	no	—
689	C₄²	—	8	1	no	—
690	C₄²	C₂×D₄×C₃₇	1	2	yes	—
691	C₄²	#41×C₃₇	1	2	yes	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	#137×C₃₇	1	2	yes	—
713	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
714	Q₈	—	4	1	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	1	no	—
717	Q₈	—	4	1	no	—
718	Q₈	—	4	1	no	—
719	Q₈	—	4	1	no	—
720	Q₈	—	4	1	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	Q₈	—	4	1	no	—
724	Q₈	—	4	1	no	—
725	Q₈	—	4	1	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	#121×C₃₇	1	2	yes	—
773	C₂×C₄	#121×C₃₇	1	2	yes	—
774	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
777	C₂×C₄	C₂×#41×C₃₇	1	1	yes	characteristic
778	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
779	C₂×C₄	H(5,𝔽₂)×C₃₇	1	1	yes	characteristic
780	C₈	—	2	2	no	—
781	C₈	—	4	1	no	—
782	C₈	—	4	1	no	—
783	C₈	#127×C₃₇	1	4	yes	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	C₂×#121×C₃₇	1	1	yes	characteristic
806	C₂²	D₄²×C₃₇	1	1	yes	characteristic
807	C₂²	D₄²×C₃₇	1	1	yes	characteristic
808	C₂²	C₂×#137×C₃₇	1	1	yes	characteristic
809	C₂²	C₃₇×#575	1	1	yes	characteristic
810	C₂²	C₃₇×#577	1	1	yes	characteristic
811	C₂²	C₃₇×#578	1	1	yes	characteristic
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	8	1	no	—
821	C₄	—	8	1	no	—
822	C₄	—	8	1	no	—
823	C₄	C₂×#127×C₃₇	1	1	yes	characteristic
824	C₄	C₃₇×#535	1	1	yes	characteristic
825	C₄	C₃₇×#550	1	1	yes	characteristic
826	C₄	C₃₇×#550	1	1	yes	characteristic
827	C₂	—	4	2	no	—
828	C₂	—	8	1	no	—
829	C₂	—	16	1	no	—
830	C₂	C₃₇×#2541	1	1	yes	characteristic
831	C₂	C₃₇×#3056	1	1	yes	characteristic
832	C₂	C₃₇×#3063	1	1	yes	characteristic
833	C₂	C₃₇×#3266	1	1	yes	characteristic
834	C₂	C₃₇×#3267	1	1	yes	characteristic
835	C₂	C₃₇×#3269	1	1	yes	characteristic
836	C₂	C₃₇×#3270	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#2540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄×D₄×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#497	C₂	semidirect
2. C₂×C₃₇×#470	C₂	semidirect
3. C₂×C₃₇×#468	C₂	semidirect
4. C₂×C₃₇×#467	C₂	semidirect
5. C₂×C₃₇×#465	C₂	semidirect
6. C₂×C₃₇×#435	C₂	semidirect
7. C₃₇×#2542	C₂	semidirect
9. C₃₇×#2001	C₂	semidirect
10. C₃₇×#2001	C₂	semidirect
11. C₃₇×#2000	C₂	semidirect
12. C₃₇×#2000	C₂	semidirect
13. C₃₇×#1983	C₂	semidirect
14. C₃₇×#1981	C₂	semidirect
15. C₃₇×#1776	C₂	semidirect
146. #107×C₃₇	D₄	semidirect
147. #106×C₃₇	D₄	semidirect
159. #97×C₃₇	D₄	semidirect
365. #28492	C₃₇	direct (N × H)
409. C₂×#497	C₂×C₃₇	semidirect
410. C₂×#470	C₂×C₃₇	semidirect
411. C₂×#468	C₂×C₃₇	semidirect
412. C₂×#467	C₂×C₃₇	semidirect
413. C₂×#465	C₂×C₃₇	semidirect
414. C₂×#435	C₂×C₃₇	semidirect
415. #2542	C₂×C₃₇	semidirect
417. #2001	C₂×C₃₇	semidirect
418. #2001	C₂×C₃₇	semidirect
419. #2000	C₂×C₃₇	semidirect
420. #2000	C₂×C₃₇	semidirect
421. #1983	C₂×C₃₇	semidirect
422. #1981	C₂×C₃₇	semidirect
423. #1776	C₂×C₃₇	semidirect
483. C₃₇	#28492	direct (N × H)
565. #107	D₄×C₃₇	semidirect
566. #106	D₄×C₃₇	semidirect
578. #97	D₄×C₃₇	semidirect

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×#470	2
C₂×C₃₇×#468	2
C₂×C₃₇×#467	2
C₂×C₃₇×#465	2
C₂×C₃₇×#435	2
C₃₇×#2542	2
C₃₇×#2540	2
C₃₇×#2001	2
C₃₇×#2000	2
C₃₇×#1983	2
C₃₇×#1981	2
C₃₇×#1776	2
#28492	37

Subgroups — C37×#28492 #22649745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#28492 #22649745