Subgroups — C₃₇×#61684 #22682937

Order 9472.

2152 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₃₇×#3314	C₂	1	4	yes	maximal, complemented
5	C₃₇×#3294	C₂	1	2	yes	maximal, complemented
6	C₃₇×#3283	C₂	1	2	yes	maximal, complemented
7	C₃₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₃₇×#3268	C₂	1	4	yes	maximal, complemented
9	C₃₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3203	C₂	1	4	yes	maximal, complemented
12	C₃₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₇×#3012	C₂	1	4	yes	maximal, complemented
15	C₃₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₃₇	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	4	yes	complemented
18	C₂×#135×C₃₇	C₂²	1	4	yes	complemented
19	C₃₇×#562	—	2	2	no	—
20	C₃₇×#554	—	2	1	no	—
21	C₃₇×#554	C₂²	1	2	yes	complemented
22	C₃₇×#550	—	2	1	no	—
23	C₃₇×#550	C₂²	1	2	yes	complemented
24	C₃₇×#547	—	2	1	no	—
25	C₃₇×#547	C₂²	1	2	yes	—
26	C₃₇×#547	C₂²	1	2	yes	complemented
27	C₃₇×#547	C₂²	1	2	yes	complemented
28	C₃₇×#546	—	2	2	no	—
29	C₃₇×#546	C₂²	1	4	yes	—
30	D₄²×C₃₇	—	2	1	no	—
31	D₄²×C₃₇	C₂²	1	2	yes	—
32	C₃₇×#540	—	2	2	no	—
33	C₃₇×#537	—	2	2	no	—
34	C₃₇×#537	C₂²	1	2	yes	—
35	C₃₇×#537	C₂²	1	4	yes	complemented
36	C₃₇×#534	—	2	2	no	—
37	C₃₇×#533	C₂²	1	1	yes	characteristic, complemented
38	C₃₇×#532	C₂²	1	1	yes	characteristic
39	C₃₇×#532	C₂²	1	1	yes	characteristic
40	C₃₇×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₃₇	—	2	2	no	—
42	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
43	C₃₇×#496	C₂²	1	2	yes	complemented
44	C₃₇×#494	C₂²	1	1	yes	characteristic, complemented
45	C₃₇×#492	C₂²	1	1	yes	characteristic, complemented
46	C₃₇×#489	C₂²	1	2	yes	complemented
47	C₃₇×#487	C₂²	1	1	yes	characteristic, complemented
48	C₃₇×#486	C₂²	1	1	yes	characteristic, complemented
49	C₃₇×#484	C₂²	1	2	yes	complemented
50	C₃₇×#484	C₂²	1	4	yes	complemented
51	C₃₇×#480	C₂²	1	2	yes	complemented
52	C₃₇×#480	C₂²	1	4	yes	complemented
53	C₃₇×#474	C₂²	1	2	yes	complemented
54	C₃₇×#474	C₂²	1	2	yes	complemented
55	C₃₇×#468	C₂²	1	4	yes	complemented
56	C₃₇×#468	C₂²	1	4	yes	complemented
57	C₃₇×#467	C₂²	1	4	yes	complemented
58	C₃₇×#466	C₂²	1	4	yes	complemented
59	C₃₇×#464	C₂²	1	4	yes	complemented
60	C₃₇×#461	C₂²	1	2	yes	complemented
61	C₃₇×#461	C₂²	1	2	yes	complemented
62	C₃₇×#459	C₂²	1	2	yes	complemented
63	C₃₇×#459	C₂²	1	2	yes	complemented
64	C₃₇×#452	C₂²	1	4	yes	complemented
65	C₃₇×#452	C₂²	1	4	yes	complemented
66	C₃₇×#452	C₂²	1	4	yes	complemented
67	C₃₇×#450	C₂²	1	2	yes	—
68	C₃₇×#450	C₂²	1	4	yes	complemented
69	C₃₇×#449	C₂²	1	4	yes	complemented
70	C₃₇×#449	C₂²	1	4	yes	complemented
71	C₃₇×#449	C₂²	1	4	yes	complemented
72	C₃₇×#447	C₂²	1	2	yes	—
73	C₃₇×#447	C₂²	1	4	yes	complemented
74	C₃₇×#440	C₂²	1	4	yes	complemented
75	C₄×D₈×C₃₇	C₂²	1	2	yes	complemented
76	C₄×D₈×C₃₇	C₂²	1	2	yes	complemented
77	C₃₇×#436	C₂²	1	2	yes	complemented
78	C₃₇×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₃₇	C₂²	1	2	yes	complemented
80	C₃₇×#432	C₂²	1	1	yes	characteristic, complemented
81	C₃₇×#431	C₂²	1	1	yes	characteristic, complemented
82	C₃₇×#417	C₂²	1	4	yes	complemented
83	C₂×#102×C₃₇	C₂²	1	4	yes	complemented
84	C₃₇×#408	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₃₇	—	4	8	no	—
86	C₂×#41×C₃₇	—	2	2	no	—
87	C₂×#41×C₃₇	—	2	2	no	—
88	C₂×#41×C₃₇	—	2	1	no	—
89	C₂×#41×C₃₇	C₂³	1	4	yes	—
90	C₂×#41×C₃₇	C₂³	1	2	yes	—
91	C₂×#41×C₃₇	C₂³	1	4	yes	—
92	C₂×#41×C₃₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₃₇	—	2	4	no	—
94	C₂²×D₄×C₃₇	—	2	2	no	—
95	C₂²×D₄×C₃₇	—	2	2	no	—
96	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₃₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₃₇	—	2	1	no	—
99	AGL(1,ℤ/8)×C₃₇	—	4	8	no	—
100	#135×C₃₇	—	4	8	no	—
101	C₂×Q₁₆×C₃₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
105	C₂×D₈×C₃₇	C₂³	1	2	yes	—
106	C₂×D₈×C₃₇	C₂³	1	2	yes	—
107	C₂×D₈×C₃₇	C₂³	1	4	yes	—
108	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
109	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₃₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
115	#127×C₃₇	—	2	2	no	—
116	#127×C₃₇	D₄	1	1	yes	characteristic
117	#127×C₃₇	C₂³	1	1	yes	characteristic
118	#127×C₃₇	C₂³	1	1	yes	characteristic
119	#125×C₃₇	—	2	2	no	—
120	#125×C₃₇	—	2	1	no	—
121	#124×C₃₇	—	2	1	no	—
122	#124×C₃₇	D₄	1	2	yes	—
123	#124×C₃₇	C₂³	1	2	yes	—
124	#123×C₃₇	—	2	4	no	—
125	#123×C₃₇	—	2	4	no	—
126	#123×C₃₇	—	2	4	no	—
127	#123×C₃₇	—	2	4	no	—
128	C₂²⋊Q₈×C₃₇	—	2	2	no	—
129	C₂²⋊Q₈×C₃₇	—	2	4	no	—
130	C₂²⋊Q₈×C₃₇	—	2	1	no	—
131	C₂²⋊Q₈×C₃₇	—	2	2	no	—
132	C₂²⋊Q₈×C₃₇	—	2	4	no	—
133	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
136	#121×C₃₇	—	2	4	no	—
137	#121×C₃₇	—	2	2	no	—
138	#121×C₃₇	—	2	4	no	—
139	#121×C₃₇	—	2	4	no	—
140	#121×C₃₇	—	2	2	no	—
141	#121×C₃₇	—	2	2	no	—
142	#121×C₃₇	—	2	4	no	—
143	#121×C₃₇	—	2	1	no	—
144	#121×C₃₇	—	2	1	no	—
145	#121×C₃₇	—	2	1	no	—
146	#121×C₃₇	—	2	2	no	—
147	#121×C₃₇	—	2	4	no	—
148	#121×C₃₇	—	2	4	no	—
149	#121×C₃₇	D₄	1	2	yes	—
150	#121×C₃₇	D₄	1	2	yes	—
151	#121×C₃₇	C₂³	1	2	yes	—
152	#121×C₃₇	C₂³	1	4	yes	—
153	#121×C₃₇	C₂³	1	4	yes	—
154	#120×C₃₇	—	2	4	no	—
155	#120×C₃₇	—	2	4	no	—
156	C₄×Q₈×C₃₇	—	2	1	no	—
157	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
158	C₄×D₄×C₃₇	—	2	2	no	—
159	C₄×D₄×C₃₇	—	2	2	no	—
160	C₄×D₄×C₃₇	—	2	1	no	—
161	C₄×D₄×C₃₇	—	2	1	no	—
162	C₄×D₄×C₃₇	—	2	1	no	—
163	C₄×D₄×C₃₇	—	2	1	no	—
164	C₄×D₄×C₃₇	—	2	1	no	—
165	C₄×D₄×C₃₇	C₂³	1	2	yes	—
166	C₄×D₄×C₃₇	C₂³	1	2	yes	—
167	C₄×D₄×C₃₇	C₂³	1	2	yes	—
168	C₄×D₄×C₃₇	C₂³	1	2	yes	—
169	C₄×D₄×C₃₇	C₂³	1	2	yes	—
170	#117×C₃₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
173	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₃₇	—	2	4	no	—
177	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
178	#107×C₃₇	C₂³	1	2	yes	—
179	#107×C₃₇	C₂³	1	2	yes	—
180	#107×C₃₇	C₂³	1	4	yes	—
181	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₃₇	C₂³	1	2	yes	—
183	#103×C₃₇	C₂³	1	4	yes	—
184	#103×C₃₇	C₂³	1	4	yes	—
185	#103×C₃₇	C₂³	1	4	yes	—
186	#102×C₃₇	C₂³	1	2	yes	—
187	#102×C₃₇	C₂³	1	4	yes	—
188	#102×C₃₇	C₂³	1	4	yes	—
189	#102×C₃₇	C₂³	1	4	yes	—
190	#102×C₃₇	C₂³	1	2	yes	—
191	#102×C₃₇	C₂³	1	2	yes	—
192	#102×C₃₇	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₃₇	C₂³	1	2	yes	—
195	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₃₇	C₂³	1	4	yes	—
197	#97×C₃₇	C₂³	1	2	yes	—
198	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₃₇	C₂³	1	1	yes	characteristic
200	C₂⁴×C₃₇	—	2	1	no	—
201	C₂⁴×C₃₇	—	2	4	no	—
202	#41×C₃₇	—	2	8	no	—
203	#41×C₃₇	—	4	4	no	—
204	#41×C₃₇	—	4	4	no	—
205	#41×C₃₇	—	4	4	no	—
206	#41×C₃₇	—	4	4	no	—
207	#41×C₃₇	—	4	4	no	—
208	#41×C₃₇	—	4	8	no	—
209	#41×C₃₇	—	8	2	no	—
210	#41×C₃₇	—	8	4	no	—
211	C₂×Q₈×C₃₇	—	2	1	no	—
212	C₂×Q₈×C₃₇	—	2	1	no	—
213	C₂×Q₈×C₃₇	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
216	C₂×D₄×C₃₇	—	2	4	no	—
217	C₂×D₄×C₃₇	—	2	8	no	—
218	C₂×D₄×C₃₇	—	2	4	no	—
219	C₂×D₄×C₃₇	—	2	2	no	—
220	C₂×D₄×C₃₇	—	2	4	no	—
221	C₂×D₄×C₃₇	—	2	2	no	—
222	C₂×D₄×C₃₇	—	2	4	no	—
223	C₂×D₄×C₃₇	—	2	4	no	—
224	C₂×D₄×C₃₇	—	2	1	no	—
225	C₂×D₄×C₃₇	—	2	1	no	—
226	C₂×D₄×C₃₇	—	2	1	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	4	no	—
231	C₂×D₄×C₃₇	—	4	8	no	—
232	C₂×D₄×C₃₇	—	4	16	no	—
233	C₂×D₄×C₃₇	—	8	4	no	—
234	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₃₇	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
239	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
240	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₇	—	2	1	no	—
242	C₂²×C₄×C₃₇	—	2	4	no	—
243	C₂²×C₄×C₃₇	—	2	4	no	—
244	C₂²×C₄×C₃₇	—	2	2	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	4	no	—
249	C₂²×C₄×C₃₇	—	8	2	no	—
250	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
254	Q₁₆×C₃₇	—	4	4	no	—
255	SD₁₆×C₃₇	—	2	8	no	—
256	SD₁₆×C₃₇	—	4	4	no	—
257	SD₁₆×C₃₇	—	4	4	no	—
258	D₈×C₃₇	—	2	4	no	—
259	D₈×C₃₇	—	2	4	no	—
260	D₈×C₃₇	—	4	4	no	—
261	M₁₆×C₃₇	—	4	4	no	—
262	C₂×C₈×C₃₇	—	4	4	no	—
263	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
265	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₃₇	—	2	1	no	—
267	C₄⋊C₄×C₃₇	—	2	1	no	—
268	C₄⋊C₄×C₃₇	—	2	4	no	—
269	C₄⋊C₄×C₃₇	—	2	4	no	—
270	C₄⋊C₄×C₃₇	—	2	1	no	—
271	C₄⋊C₄×C₃₇	—	2	4	no	—
272	C₄⋊C₄×C₃₇	—	2	1	no	—
273	C₄⋊C₄×C₃₇	—	2	1	no	—
274	C₄⋊C₄×C₃₇	—	2	1	no	—
275	C₄⋊C₄×C₃₇	—	2	1	no	—
276	C₄⋊C₄×C₃₇	—	2	2	no	—
277	C₄⋊C₄×C₃₇	—	2	2	no	—
278	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₃₇	—	2	4	no	—
284	C₂²⋊C₄×C₃₇	—	2	2	no	—
285	C₂²⋊C₄×C₃₇	—	2	4	no	—
286	C₂²⋊C₄×C₃₇	—	2	2	no	—
287	C₂²⋊C₄×C₃₇	—	2	2	no	—
288	C₂²⋊C₄×C₃₇	—	2	2	no	—
289	C₂²⋊C₄×C₃₇	—	2	4	no	—
290	C₂²⋊C₄×C₃₇	—	2	2	no	—
291	C₂²⋊C₄×C₃₇	—	2	4	no	—
292	C₂²⋊C₄×C₃₇	—	2	2	no	—
293	C₂²⋊C₄×C₃₇	—	2	2	no	—
294	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
296	C₄²×C₃₇	—	2	2	no	—
297	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
301	C₂³×C₃₇	—	2	4	no	—
302	C₂³×C₃₇	—	2	2	no	—
303	C₂³×C₃₇	—	2	2	no	—
304	C₂³×C₃₇	—	2	2	no	—
305	C₂³×C₃₇	—	4	8	no	—
306	C₂³×C₃₇	—	8	1	no	—
307	C₂³×C₃₇	—	8	1	no	—
308	C₂³×C₃₇	—	8	4	no	—
309	C₂³×C₃₇	—	8	4	no	—
310	C₂³×C₃₇	C₂²×D₄	1	4	yes	—
311	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₃₇	—	2	4	no	—
313	Q₈×C₃₇	—	2	4	no	—
314	Q₈×C₃₇	—	4	2	no	—
315	Q₈×C₃₇	—	4	2	no	—
316	Q₈×C₃₇	—	8	1	no	—
317	D₄×C₃₇	—	2	4	no	—
318	D₄×C₃₇	—	2	4	no	—
319	D₄×C₃₇	—	2	2	no	—
320	D₄×C₃₇	—	2	2	no	—
321	D₄×C₃₇	—	2	2	no	—
322	D₄×C₃₇	—	2	4	no	—
323	D₄×C₃₇	—	4	2	no	—
324	D₄×C₃₇	—	4	4	no	—
325	D₄×C₃₇	—	4	2	no	—
326	D₄×C₃₇	—	4	8	no	—
327	D₄×C₃₇	—	4	2	no	—
328	D₄×C₃₇	—	4	8	no	—
329	D₄×C₃₇	—	4	4	no	—
330	D₄×C₃₇	—	4	2	no	—
331	D₄×C₃₇	—	8	1	no	—
332	D₄×C₃₇	—	8	1	no	—
333	D₄×C₃₇	—	8	4	no	—
334	D₄×C₃₇	—	8	4	no	—
335	D₄×C₃₇	—	8	2	no	—
336	D₄×C₃₇	—	8	4	no	—
337	D₄×C₃₇	H(5,𝔽₂)	1	4	yes	—
338	C₂×C₄×C₃₇	—	2	2	no	—
339	C₂×C₄×C₃₇	—	2	4	no	—
340	C₂×C₄×C₃₇	—	2	4	no	—
341	C₂×C₄×C₃₇	—	2	2	no	—
342	C₂×C₄×C₃₇	—	2	2	no	—
343	C₂×C₄×C₃₇	—	2	2	no	—
344	C₂×C₄×C₃₇	—	2	2	no	—
345	C₂×C₄×C₃₇	—	2	2	no	—
346	C₂×C₄×C₃₇	—	2	2	no	—
347	C₂×C₄×C₃₇	—	4	1	no	—
348	C₂×C₄×C₃₇	—	4	8	no	—
349	C₂×C₄×C₃₇	—	4	4	no	—
350	C₂×C₄×C₃₇	—	4	4	no	—
351	C₂×C₄×C₃₇	—	4	4	no	—
352	C₂×C₄×C₃₇	—	8	2	no	—
353	C₂×C₄×C₃₇	—	8	4	no	—
354	C₂×C₄×C₃₇	—	8	1	no	—
355	C₂×C₄×C₃₇	—	8	4	no	—
356	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
363	C₈×C₃₇	—	2	2	no	—
364	C₈×C₃₇	—	2	4	no	—
365	C₈×C₃₇	—	2	2	no	—
366	#61684	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂²×C₃₇	—	2	1	no	—
368	C₂²×C₃₇	—	2	4	no	—
369	C₂²×C₃₇	—	2	1	no	—
370	C₂²×C₃₇	—	2	4	no	—
371	C₂²×C₃₇	—	2	4	no	—
372	C₂²×C₃₇	—	2	1	no	—
373	C₂²×C₃₇	—	2	4	no	—
374	C₂²×C₃₇	—	4	2	no	—
375	C₂²×C₃₇	—	4	2	no	—
376	C₂²×C₃₇	—	4	2	no	—
377	C₂²×C₃₇	—	4	2	no	—
378	C₂²×C₃₇	—	4	2	no	—
379	C₂²×C₃₇	—	4	2	no	—
380	C₂²×C₃₇	—	4	2	no	—
381	C₂²×C₃₇	—	4	2	no	—
382	C₂²×C₃₇	—	8	4	no	—
383	C₂²×C₃₇	—	16	8	no	—
384	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₃₇	—	2	1	no	—
386	C₄×C₃₇	—	2	1	no	—
387	C₄×C₃₇	—	2	1	no	—
388	C₄×C₃₇	—	2	4	no	—
389	C₄×C₃₇	—	2	1	no	—
390	C₄×C₃₇	—	4	2	no	—
391	C₄×C₃₇	—	4	2	no	—
392	C₄×C₃₇	—	4	2	no	—
393	C₄×C₃₇	—	4	2	no	—
394	C₄×C₃₇	—	4	2	no	—
395	C₄×C₃₇	#576	1	2	yes	—
396	C₄×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
397	#3548	C₂×C₃₇	1	1	yes	characteristic, complemented
398	#3496	C₂×C₃₇	1	1	yes	characteristic, complemented
399	#3330	C₂×C₃₇	1	2	yes	complemented
400	#3314	C₂×C₃₇	1	4	yes	complemented
401	#3294	C₂×C₃₇	1	2	yes	complemented
402	#3283	C₂×C₃₇	1	2	yes	complemented
403	#3272	C₂×C₃₇	1	2	yes	complemented
404	#3268	C₂×C₃₇	1	4	yes	complemented
405	#3214	C₂×C₃₇	1	1	yes	characteristic, complemented
406	#3210	C₂×C₃₇	1	1	yes	characteristic, complemented
407	#3203	C₂×C₃₇	1	4	yes	complemented
408	#3110	C₂×C₃₇	1	1	yes	characteristic, complemented
409	#3100	C₂×C₃₇	1	1	yes	characteristic, complemented
410	#3012	C₂×C₃₇	1	4	yes	complemented
411	#2981	C₂×C₃₇	1	1	yes	characteristic, complemented
412	C₂×C₃₇	—	4	1	no	—
413	C₂×C₃₇	—	4	4	no	—
414	C₂×C₃₇	—	4	4	no	—
415	C₂×C₃₇	—	8	2	no	—
416	C₂×C₃₇	—	8	2	no	—
417	C₂×C₃₇	#3484	1	1	yes	characteristic
418	C₂×C₃₇	C₂×#576	1	1	yes	characteristic
419	C₂×C₃₇	#3586	1	1	yes	characteristic
420	C₂×H(5,𝔽₂)	C₂²×C₃₇	1	2	yes	—
421	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	4	yes	complemented
422	C₂×#135	C₂²×C₃₇	1	4	yes	complemented
423	#562	—	2	2	no	—
424	#554	—	2	1	no	—
425	#554	C₂²×C₃₇	1	2	yes	complemented
426	#550	—	2	1	no	—
427	#550	C₂²×C₃₇	1	2	yes	complemented
428	#547	—	2	1	no	—
429	#547	C₂²×C₃₇	1	2	yes	—
430	#547	C₂²×C₃₇	1	2	yes	complemented
431	#547	C₂²×C₃₇	1	2	yes	complemented
432	#546	—	2	2	no	—
433	#546	C₂²×C₃₇	1	4	yes	—
434	D₄²	—	2	1	no	—
435	D₄²	C₂²×C₃₇	1	2	yes	—
436	#540	—	2	2	no	—
437	#537	—	2	2	no	—
438	#537	C₂²×C₃₇	1	2	yes	—
439	#537	C₂²×C₃₇	1	4	yes	complemented
440	#534	—	2	2	no	—
441	#533	C₂²×C₃₇	1	1	yes	characteristic, complemented
442	#532	C₂²×C₃₇	1	1	yes	characteristic
443	#532	C₂²×C₃₇	1	1	yes	characteristic
444	#532	C₂²×C₃₇	1	1	yes	characteristic, complemented
445	C₂×#121	—	2	2	no	—
446	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
447	#496	C₂²×C₃₇	1	2	yes	complemented
448	#494	C₂²×C₃₇	1	1	yes	characteristic, complemented
449	#492	C₂²×C₃₇	1	1	yes	characteristic, complemented
450	#489	C₂²×C₃₇	1	2	yes	complemented
451	#487	C₂²×C₃₇	1	1	yes	characteristic, complemented
452	#486	C₂²×C₃₇	1	1	yes	characteristic, complemented
453	#484	C₂²×C₃₇	1	4	yes	complemented
454	#484	C₂²×C₃₇	1	2	yes	complemented
455	#480	C₂²×C₃₇	1	2	yes	complemented
456	#480	C₂²×C₃₇	1	4	yes	complemented
457	#474	C₂²×C₃₇	1	2	yes	complemented
458	#474	C₂²×C₃₇	1	2	yes	complemented
459	#468	C₂²×C₃₇	1	4	yes	complemented
460	#468	C₂²×C₃₇	1	4	yes	complemented
461	#467	C₂²×C₃₇	1	4	yes	complemented
462	#466	C₂²×C₃₇	1	4	yes	complemented
463	#464	C₂²×C₃₇	1	4	yes	complemented
464	#461	C₂²×C₃₇	1	2	yes	complemented
465	#461	C₂²×C₃₇	1	2	yes	complemented
466	#459	C₂²×C₃₇	1	2	yes	complemented
467	#459	C₂²×C₃₇	1	2	yes	complemented
468	#452	C₂²×C₃₇	1	4	yes	complemented
469	#452	C₂²×C₃₇	1	4	yes	complemented
470	#452	C₂²×C₃₇	1	4	yes	complemented
471	#450	C₂²×C₃₇	1	2	yes	—
472	#450	C₂²×C₃₇	1	4	yes	complemented
473	#449	C₂²×C₃₇	1	4	yes	complemented
474	#449	C₂²×C₃₇	1	4	yes	complemented
475	#449	C₂²×C₃₇	1	4	yes	complemented
476	#447	C₂²×C₃₇	1	2	yes	—
477	#447	C₂²×C₃₇	1	4	yes	complemented
478	#440	C₂²×C₃₇	1	4	yes	complemented
479	C₄×D₈	C₂²×C₃₇	1	2	yes	complemented
480	C₄×D₈	C₂²×C₃₇	1	2	yes	complemented
481	#436	C₂²×C₃₇	1	2	yes	complemented
482	#435	C₂²×C₃₇	1	4	yes	complemented
483	C₈×D₄	C₂²×C₃₇	1	2	yes	complemented
484	#432	C₂²×C₃₇	1	1	yes	characteristic, complemented
485	#431	C₂²×C₃₇	1	1	yes	characteristic, complemented
486	#417	C₂²×C₃₇	1	4	yes	complemented
487	C₂×#102	C₂²×C₃₇	1	4	yes	complemented
488	#408	C₂²×C₃₇	1	4	yes	complemented
489	C₃₇	#61684	1	1	yes	characteristic, direct product factor, Sylow
490	H(5,𝔽₂)	—	4	8	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	C₂³×C₃₇	1	4	yes	—
495	C₂×#41	C₂³×C₃₇	1	2	yes	—
496	C₂×#41	C₂³×C₃₇	1	4	yes	—
497	C₂×#41	C₂³×C₃₇	1	2	yes	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₃₇	1	4	yes	—
503	C₂³×C₄	—	2	1	no	—
504	AGL(1,ℤ/8)	—	4	8	no	—
505	#135	—	4	8	no	—
506	C₂×Q₁₆	C₂³×C₃₇	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
510	C₂×D₈	C₂³×C₃₇	1	2	yes	—
511	C₂×D₈	C₂³×C₃₇	1	2	yes	—
512	C₂×D₈	C₂³×C₃₇	1	4	yes	—
513	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
514	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
515	C₄⋊Q₈	D₄×C₃₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
520	#127	—	2	2	no	—
521	#127	D₄×C₃₇	1	1	yes	characteristic
522	#127	C₂³×C₃₇	1	1	yes	characteristic
523	#127	C₂³×C₃₇	1	1	yes	characteristic
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	D₄×C₃₇	1	2	yes	—
528	#124	C₂³×C₃₇	1	2	yes	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
539	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
541	#121	—	2	4	no	—
542	#121	—	2	2	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	D₄×C₃₇	1	2	yes	—
555	#121	D₄×C₃₇	1	2	yes	—
556	#121	C₂³×C₃₇	1	2	yes	—
557	#121	C₂³×C₃₇	1	4	yes	—
558	#121	C₂³×C₃₇	1	4	yes	—
559	#120	—	2	4	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₃₇	1	2	yes	—
571	C₄×D₄	C₂³×C₃₇	1	2	yes	—
572	C₄×D₄	C₂³×C₃₇	1	2	yes	—
573	C₄×D₄	C₂³×C₃₇	1	2	yes	—
574	C₄×D₄	C₂³×C₃₇	1	2	yes	—
575	#117	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	4	no	—
582	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
583	#107	C₂³×C₃₇	1	2	yes	—
584	#107	C₂³×C₃₇	1	2	yes	—
585	#107	C₂³×C₃₇	1	4	yes	—
586	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
587	C₄⋊C₈	C₂³×C₃₇	1	2	yes	—
588	#103	C₂³×C₃₇	1	4	yes	—
589	#103	C₂³×C₃₇	1	4	yes	—
590	#103	C₂³×C₃₇	1	4	yes	—
591	#102	C₂³×C₃₇	1	2	yes	—
592	#102	C₂³×C₃₇	1	4	yes	—
593	#102	C₂³×C₃₇	1	4	yes	—
594	#102	C₂³×C₃₇	1	4	yes	—
595	#102	C₂³×C₃₇	1	2	yes	—
596	#102	C₂³×C₃₇	1	2	yes	—
597	#102	C₂³×C₃₇	1	2	yes	—
598	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
599	C₂²⋊C₈	C₂³×C₃₇	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₃₇	1	4	yes	—
602	#97	C₂³×C₃₇	1	2	yes	—
603	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₃₇	1	1	yes	characteristic
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	#41	—	8	2	no	—
615	#41	—	8	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	C₂×D₄×C₃₇	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	8	4	no	—
639	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
640	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
641	C₂×D₄	C₂×D₄×C₃₇	1	4	yes	—
642	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
643	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
645	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
659	Q₁₆	—	4	4	no	—
660	SD₁₆	—	2	8	no	—
661	SD₁₆	—	4	4	no	—
662	SD₁₆	—	4	4	no	—
663	D₈	—	2	4	no	—
664	D₈	—	2	4	no	—
665	D₈	—	4	4	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
669	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
670	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₃₇	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
700	C₂²⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
704	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	—	8	4	no	—
714	C₂³	—	8	4	no	—
715	C₂³	C₂²×D₄×C₃₇	1	4	yes	—
716	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
717	Q₈	—	2	4	no	—
718	Q₈	—	2	4	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	8	1	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	4	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	8	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	4	no	—
742	D₄	H(5,𝔽₂)×C₃₇	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
766	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
767	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	4	no	—
770	C₈	—	2	2	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	8	no	—
788	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
789	C₄	—	2	1	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	C₃₇×#576	1	2	yes	—
800	C₄	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
801	C₂	—	4	1	no	—
802	C₂	—	4	4	no	—
803	C₂	—	4	4	no	—
804	C₂	—	8	2	no	—
805	C₂	—	8	2	no	—
806	C₂	C₃₇×#3484	1	1	yes	characteristic
807	C₂	C₂×C₃₇×#576	1	1	yes	characteristic
808	C₂	C₃₇×#3586	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 ◁ C₃₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3548	C₂	semidirect
2. C₃₇×#3496	C₂	semidirect
3. C₃₇×#3330	C₂	semidirect
4. C₃₇×#3314	C₂	semidirect
5. C₃₇×#3294	C₂	semidirect
6. C₃₇×#3283	C₂	semidirect
7. C₃₇×#3272	C₂	semidirect
8. C₃₇×#3268	C₂	semidirect
9. C₃₇×#3214	C₂	semidirect
10. C₃₇×#3210	C₂	semidirect
11. C₃₇×#3203	C₂	semidirect
12. C₃₇×#3110	C₂	semidirect
13. C₃₇×#3100	C₂	semidirect
14. C₃₇×#3012	C₂	semidirect
15. C₃₇×#2981	C₂	semidirect
17. C₂×AGL(1,ℤ/8)×C₃₇	C₂²	semidirect
18. C₂×#135×C₃₇	C₂²	semidirect
21. C₃₇×#554	C₂²	semidirect
23. C₃₇×#550	C₂²	semidirect
26. C₃₇×#547	C₂²	semidirect
27. C₃₇×#547	C₂²	semidirect
35. C₃₇×#537	C₂²	semidirect
37. C₃₇×#533	C₂²	semidirect
40. C₃₇×#532	C₂²	semidirect
43. C₃₇×#496	C₂²	semidirect
44. C₃₇×#494	C₂²	semidirect
45. C₃₇×#492	C₂²	semidirect
46. C₃₇×#489	C₂²	semidirect
47. C₃₇×#487	C₂²	semidirect
48. C₃₇×#486	C₂²	semidirect
49. C₃₇×#484	C₂²	semidirect
50. C₃₇×#484	C₂²	semidirect
51. C₃₇×#480	C₂²	semidirect
52. C₃₇×#480	C₂²	semidirect
53. C₃₇×#474	C₂²	semidirect
54. C₃₇×#474	C₂²	semidirect
55. C₃₇×#468	C₂²	semidirect
56. C₃₇×#468	C₂²	semidirect
57. C₃₇×#467	C₂²	semidirect
58. C₃₇×#466	C₂²	semidirect
59. C₃₇×#464	C₂²	semidirect
60. C₃₇×#461	C₂²	semidirect
61. C₃₇×#461	C₂²	semidirect
62. C₃₇×#459	C₂²	semidirect
63. C₃₇×#459	C₂²	semidirect
64. C₃₇×#452	C₂²	semidirect
65. C₃₇×#452	C₂²	semidirect
66. C₃₇×#452	C₂²	semidirect
68. C₃₇×#450	C₂²	semidirect
69. C₃₇×#449	C₂²	semidirect
70. C₃₇×#449	C₂²	semidirect
71. C₃₇×#449	C₂²	semidirect
73. C₃₇×#447	C₂²	semidirect
74. C₃₇×#440	C₂²	semidirect
75. C₄×D₈×C₃₇	C₂²	semidirect
76. C₄×D₈×C₃₇	C₂²	semidirect
77. C₃₇×#436	C₂²	semidirect
78. C₃₇×#435	C₂²	semidirect
79. C₈×D₄×C₃₇	C₂²	semidirect
80. C₃₇×#432	C₂²	semidirect
81. C₃₇×#431	C₂²	semidirect
82. C₃₇×#417	C₂²	semidirect
83. C₂×#102×C₃₇	C₂²	semidirect
84. C₃₇×#408	C₂²	semidirect
366. #61684	C₃₇	direct (N × H)
397. #3548	C₂×C₃₇	semidirect
398. #3496	C₂×C₃₇	semidirect
399. #3330	C₂×C₃₇	semidirect
400. #3314	C₂×C₃₇	semidirect
401. #3294	C₂×C₃₇	semidirect
402. #3283	C₂×C₃₇	semidirect
403. #3272	C₂×C₃₇	semidirect
404. #3268	C₂×C₃₇	semidirect
405. #3214	C₂×C₃₇	semidirect
406. #3210	C₂×C₃₇	semidirect
407. #3203	C₂×C₃₇	semidirect
408. #3110	C₂×C₃₇	semidirect
409. #3100	C₂×C₃₇	semidirect
410. #3012	C₂×C₃₇	semidirect
411. #2981	C₂×C₃₇	semidirect
421. C₂×AGL(1,ℤ/8)	C₂²×C₃₇	semidirect
422. C₂×#135	C₂²×C₃₇	semidirect
425. #554	C₂²×C₃₇	semidirect
427. #550	C₂²×C₃₇	semidirect
430. #547	C₂²×C₃₇	semidirect
431. #547	C₂²×C₃₇	semidirect
439. #537	C₂²×C₃₇	semidirect
441. #533	C₂²×C₃₇	semidirect
444. #532	C₂²×C₃₇	semidirect
447. #496	C₂²×C₃₇	semidirect
448. #494	C₂²×C₃₇	semidirect
449. #492	C₂²×C₃₇	semidirect
450. #489	C₂²×C₃₇	semidirect
451. #487	C₂²×C₃₇	semidirect
452. #486	C₂²×C₃₇	semidirect
453. #484	C₂²×C₃₇	semidirect
454. #484	C₂²×C₃₇	semidirect
455. #480	C₂²×C₃₇	semidirect
456. #480	C₂²×C₃₇	semidirect
457. #474	C₂²×C₃₇	semidirect
458. #474	C₂²×C₃₇	semidirect
459. #468	C₂²×C₃₇	semidirect
460. #468	C₂²×C₃₇	semidirect
461. #467	C₂²×C₃₇	semidirect
462. #466	C₂²×C₃₇	semidirect
463. #464	C₂²×C₃₇	semidirect
464. #461	C₂²×C₃₇	semidirect
465. #461	C₂²×C₃₇	semidirect
466. #459	C₂²×C₃₇	semidirect
467. #459	C₂²×C₃₇	semidirect
468. #452	C₂²×C₃₇	semidirect
469. #452	C₂²×C₃₇	semidirect
470. #452	C₂²×C₃₇	semidirect
472. #450	C₂²×C₃₇	semidirect
473. #449	C₂²×C₃₇	semidirect
474. #449	C₂²×C₃₇	semidirect
475. #449	C₂²×C₃₇	semidirect
477. #447	C₂²×C₃₇	semidirect
478. #440	C₂²×C₃₇	semidirect
479. C₄×D₈	C₂²×C₃₇	semidirect
480. C₄×D₈	C₂²×C₃₇	semidirect
481. #436	C₂²×C₃₇	semidirect
482. #435	C₂²×C₃₇	semidirect
483. C₈×D₄	C₂²×C₃₇	semidirect
484. #432	C₂²×C₃₇	semidirect
485. #431	C₂²×C₃₇	semidirect
486. #417	C₂²×C₃₇	semidirect
487. C₂×#102	C₂²×C₃₇	semidirect
488. #408	C₂²×C₃₇	semidirect
489. C₃₇	#61684	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×#3548	2
C₃₇×#3496	2
C₃₇×#3330	2
C₃₇×#3314	2
C₃₇×#3294	2
C₃₇×#3283	2
C₃₇×#3272	2
C₃₇×#3268	2
C₃₇×#3214	2
C₃₇×#3210	2
C₃₇×#3203	2
C₃₇×#3110	2
C₃₇×#3100	2
C₃₇×#3012	2
C₃₇×#2981	2
#61684	37

Subgroups — C37×#61684 #22682937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#61684 #22682937