Subgroups — C₃₇×#60727 #22681980

Order 9472.

1902 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#3181	C₂	1	2	yes	maximal, complemented
4	C₃₇×#3180	C₂	1	2	yes	maximal, complemented
5	C₃₇×#3175	C₂	1	4	yes	maximal, complemented
6	C₃₇×#3173	C₂	1	4	yes	maximal, complemented
7	C₃₇×#3172	C₂	1	2	yes	maximal, complemented
8	C₃₇×#3171	C₂	1	2	yes	maximal, complemented
9	C₃₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#3063	C₂	1	2	yes	maximal, complemented
14	C₃₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₃₇×#2947	C₂	1	2	yes	maximal, complemented
16	C₃₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₃₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₃₇	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₃₇	C₂²	1	2	yes	—
20	C₂×#131×C₃₇	C₂²	1	2	yes	—
21	C₃₇×#559	—	2	1	no	—
22	C₃₇×#559	—	2	1	no	—
23	C₃₇×#556	—	2	1	no	—
24	C₃₇×#556	—	2	1	no	—
25	C₃₇×#556	—	2	1	no	—
26	C₃₇×#555	—	2	1	no	—
27	C₃₇×#554	—	2	1	no	—
28	C₃₇×#553	—	2	2	no	—
29	C₃₇×#551	—	2	2	no	—
30	C₃₇×#551	—	2	2	no	—
31	C₃₇×#548	—	2	2	no	—
32	C₃₇×#547	—	2	1	no	—
33	C₃₇×#542	C₂²	1	2	yes	—
34	C₃₇×#542	C₂²	1	2	yes	—
35	C₃₇×#542	C₂²	1	4	yes	complemented
36	C₃₇×#537	C₂²	1	2	yes	—
37	C₃₇×#536	C₂²	1	1	yes	characteristic
38	C₃₇×#535	C₂²	1	1	yes	characteristic
39	C₃₇×#533	C₂²	1	1	yes	characteristic
40	C₃₇×#533	C₂²	1	2	yes	complemented
41	C₃₇×#532	C₂²	1	1	yes	characteristic
42	C₃₇×#532	C₂²	1	2	yes	complemented
43	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
44	C₃₇×#529	C₂²	1	2	yes	—
45	C₃₇×#529	C₂²	1	2	yes	—
46	C₂×#124×C₃₇	C₂²	1	1	yes	characteristic
47	C₃₇×#520	C₂²	1	2	yes	—
48	C₃₇×#519	C₂²	1	1	yes	characteristic
49	C₃₇×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₇	C₂²	1	1	yes	characteristic
51	C₃₇×#501	C₂²	1	2	yes	complemented
52	C₃₇×#501	C₂²	1	2	yes	complemented
53	C₃₇×#500	C₂²	1	2	yes	complemented
54	C₃₇×#498	C₂²	1	2	yes	complemented
55	C₃₇×#497	C₂²	1	2	yes	—
56	C₃₇×#496	C₂²	1	2	yes	—
57	C₃₇×#495	C₂²	1	4	yes	—
58	C₃₇×#491	C₂²	1	1	yes	characteristic, complemented
59	C₃₇×#491	C₂²	1	1	yes	characteristic, complemented
60	C₃₇×#490	C₂²	1	1	yes	characteristic, complemented
61	C₃₇×#490	C₂²	1	1	yes	characteristic, complemented
62	C₃₇×#489	C₂²	1	2	yes	—
63	C₃₇×#489	C₂²	1	4	yes	—
64	C₃₇×#489	C₂²	1	2	yes	—
65	C₃₇×#489	C₂²	1	2	yes	complemented
66	C₃₇×#489	C₂²	1	2	yes	complemented
67	C₃₇×#470	C₂²	1	4	yes	complemented
68	C₃₇×#469	C₂²	1	4	yes	—
69	C₃₇×#468	C₂²	1	4	yes	—
70	C₃₇×#468	C₂²	1	4	yes	complemented
71	C₃₇×#467	C₂²	1	4	yes	complemented
72	C₃₇×#466	C₂²	1	4	yes	—
73	C₃₇×#465	C₂²	1	4	yes	—
74	C₃₇×#465	C₂²	1	4	yes	complemented
75	C₃₇×#442	C₂²	1	4	yes	—
76	C₃₇×#441	C₂²	1	4	yes	complemented
77	C₃₇×#440	C₂²	1	4	yes	—
78	C₃₇×#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₃₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₃₇	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₃₇	C₂²	1	4	yes	complemented
82	C₄×D₈×C₃₇	C₂²	1	4	yes	—
83	C₃₇×#428	C₂²	1	2	yes	—
84	C₃₇×#428	C₂²	1	2	yes	—
85	C₃₇×#416	C₂²	1	2	yes	—
86	C₃₇×#416	C₂²	1	2	yes	—
87	C₂×#103×C₃₇	C₂²	1	2	yes	—
88	C₂×#102×C₃₇	C₂²	1	2	yes	—
89	C₃₇×#405	C₂²	1	2	yes	—
90	C₃₇×#405	C₂²	1	4	yes	complemented
91	C₄×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
92	C₄×M₁₆×C₃₇	C₂²	1	2	yes	complemented
93	C₂×#97×C₃₇	C₂²	1	1	yes	characteristic
94	C₂×#97×C₃₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₃₇	—	2	2	no	—
96	C₂×#41×C₃₇	C₂³	1	2	yes	—
97	C₂×#41×C₃₇	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₇	—	2	1	no	—
99	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
101	#137×C₃₇	—	2	8	no	—
102	AGL(1,ℤ/8)×C₃₇	—	2	8	no	—
103	C₂×Q₁₆×C₃₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₃₇	C₂³	1	4	yes	—
106	C₂×D₈×C₃₇	C₂³	1	4	yes	—
107	#131×C₃₇	—	2	8	no	—
108	C₂×M₁₆×C₃₇	C₂³	1	4	yes	—
109	C₂×M₁₆×C₃₇	C₂³	1	2	yes	—
110	C₂²×C₈×C₃₇	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₇	C₂³	1	4	yes	—
112	C₄⋊Q₈×C₃₇	—	2	1	no	—
113	C₄⋊Q₈×C₃₇	—	2	1	no	—
114	C₄⋊Q₈×C₃₇	—	2	1	no	—
115	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₃₇	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₃₇	C₂³	1	1	yes	characteristic
120	#127×C₃₇	—	2	1	no	—
121	#127×C₃₇	C₂³	1	1	yes	characteristic
122	#126×C₃₇	—	2	2	no	—
123	#126×C₃₇	—	2	2	no	—
124	#126×C₃₇	—	2	4	no	—
125	#126×C₃₇	—	2	2	no	—
126	#126×C₃₇	—	2	2	no	—
127	#125×C₃₇	—	2	2	no	—
128	#125×C₃₇	C₂³	1	1	yes	characteristic
129	#125×C₃₇	C₂³	1	1	yes	characteristic
130	#124×C₃₇	—	2	1	no	—
131	#124×C₃₇	—	2	1	no	—
132	#124×C₃₇	—	2	2	no	—
133	#124×C₃₇	—	2	2	no	—
134	#124×C₃₇	—	2	4	no	—
135	#124×C₃₇	—	2	1	no	—
136	#124×C₃₇	—	2	1	no	—
137	#124×C₃₇	—	2	2	no	—
138	#124×C₃₇	C₂³	1	2	yes	—
139	#124×C₃₇	C₂³	1	2	yes	—
140	#124×C₃₇	C₂³	1	2	yes	—
141	#123×C₃₇	—	2	2	no	—
142	#123×C₃₇	—	2	2	no	—
143	#123×C₃₇	—	2	2	no	—
144	#123×C₃₇	—	2	2	no	—
145	#123×C₃₇	—	2	2	no	—
146	#123×C₃₇	—	2	4	no	—
147	C₂²⋊Q₈×C₃₇	—	2	2	no	—
148	C₂²⋊Q₈×C₃₇	—	2	1	no	—
149	C₂²⋊Q₈×C₃₇	—	2	1	no	—
150	C₂²⋊Q₈×C₃₇	—	2	2	no	—
151	C₂²⋊Q₈×C₃₇	—	2	2	no	—
152	C₂²⋊Q₈×C₃₇	—	2	2	no	—
153	C₂²⋊Q₈×C₃₇	—	2	4	no	—
154	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₃₇	C₂³	1	2	yes	—
156	C₂²⋊Q₈×C₃₇	C₂³	1	4	yes	—
157	#121×C₃₇	—	2	2	no	—
158	#121×C₃₇	—	2	4	no	—
159	#121×C₃₇	—	2	1	no	—
160	#121×C₃₇	—	2	1	no	—
161	#121×C₃₇	—	2	2	no	—
162	#121×C₃₇	C₂³	1	2	yes	—
163	#121×C₃₇	C₂³	1	2	yes	—
164	#121×C₃₇	C₂³	1	4	yes	—
165	#120×C₃₇	—	2	2	no	—
166	C₄×Q₈×C₃₇	—	2	1	no	—
167	C₄×Q₈×C₃₇	—	2	1	no	—
168	C₄×Q₈×C₃₇	—	2	1	no	—
169	C₄×Q₈×C₃₇	—	2	1	no	—
170	C₄×Q₈×C₃₇	—	2	2	no	—
171	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₃₇	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
174	C₄×Q₈×C₃₇	C₂³	1	2	yes	—
175	C₄×Q₈×C₃₇	C₂³	1	4	yes	—
176	C₄×D₄×C₃₇	—	2	2	no	—
177	C₄×D₄×C₃₇	—	2	2	no	—
178	C₄×D₄×C₃₇	—	2	1	no	—
179	C₄×D₄×C₃₇	—	2	1	no	—
180	C₄×D₄×C₃₇	—	2	4	no	—
181	C₄×D₄×C₃₇	—	2	1	no	—
182	C₄×D₄×C₃₇	—	2	1	no	—
183	C₄×D₄×C₃₇	—	2	2	no	—
184	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
185	C₄×D₄×C₃₇	D₄	1	2	yes	—
186	C₄×D₄×C₃₇	D₄	1	2	yes	—
187	C₄×D₄×C₃₇	D₄	1	1	yes	characteristic
188	C₄×D₄×C₃₇	C₂³	1	4	yes	—
189	C₄×D₄×C₃₇	C₂³	1	2	yes	—
190	C₄×D₄×C₃₇	C₂³	1	2	yes	—
191	#117×C₃₇	—	2	2	no	—
192	#117×C₃₇	—	2	2	no	—
193	#117×C₃₇	—	2	2	no	—
194	#117×C₃₇	—	2	2	no	—
195	#117×C₃₇	—	2	2	no	—
196	#117×C₃₇	C₂³	1	1	yes	characteristic
197	#117×C₃₇	C₂³	1	1	yes	characteristic
198	#117×C₃₇	C₂³	1	1	yes	characteristic
199	#117×C₃₇	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₃₇	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₇	—	2	2	no	—
202	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₃₇	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₃₇	—	2	2	no	—
206	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
208	#107×C₃₇	C₂³	1	4	yes	—
209	#107×C₃₇	C₂³	1	4	yes	—
210	#106×C₃₇	C₂³	1	4	yes	—
211	#106×C₃₇	C₂³	1	4	yes	—
212	#103×C₃₇	C₂³	1	4	yes	—
213	#103×C₃₇	C₂³	1	4	yes	—
214	#103×C₃₇	C₂³	1	2	yes	—
215	#103×C₃₇	C₂³	1	2	yes	—
216	#103×C₃₇	C₂³	1	2	yes	—
217	#103×C₃₇	C₂³	1	2	yes	—
218	#102×C₃₇	C₂³	1	4	yes	—
219	#102×C₃₇	C₂³	1	4	yes	—
220	#102×C₃₇	C₂³	1	2	yes	—
221	#102×C₃₇	C₂³	1	2	yes	—
222	#102×C₃₇	C₂³	1	2	yes	—
223	#102×C₃₇	C₂³	1	2	yes	—
224	#97×C₃₇	C₂³	1	1	yes	characteristic
225	#97×C₃₇	C₂³	1	1	yes	characteristic
226	#97×C₃₇	C₂³	1	2	yes	—
227	#97×C₃₇	C₂³	1	2	yes	—
228	#97×C₃₇	C₂³	1	4	yes	—
229	C₄×C₈×C₃₇	C₂³	1	2	yes	—
230	C₄×C₈×C₃₇	C₂³	1	4	yes	—
231	C₂⁴×C₃₇	—	2	1	no	—
232	#41×C₃₇	—	2	4	no	—
233	#41×C₃₇	—	2	4	no	—
234	#41×C₃₇	—	2	4	no	—
235	#41×C₃₇	—	8	4	no	—
236	C₂×Q₈×C₃₇	—	2	1	no	—
237	C₂×Q₈×C₃₇	—	2	2	no	—
238	C₂×Q₈×C₃₇	—	2	1	no	—
239	C₂×Q₈×C₃₇	—	2	1	no	—
240	C₂×Q₈×C₃₇	—	2	2	no	—
241	C₂×Q₈×C₃₇	—	2	4	no	—
242	C₂×Q₈×C₃₇	—	8	2	no	—
243	C₂×Q₈×C₃₇	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₇	C₂⁴	1	2	yes	—
246	C₂×D₄×C₃₇	—	2	2	no	—
247	C₂×D₄×C₃₇	—	2	2	no	—
248	C₂×D₄×C₃₇	—	2	2	no	—
249	C₂×D₄×C₃₇	—	2	4	no	—
250	C₂×D₄×C₃₇	—	2	1	no	—
251	C₂×D₄×C₃₇	—	2	1	no	—
252	C₂×D₄×C₃₇	—	2	1	no	—
253	C₂×D₄×C₃₇	—	2	4	no	—
254	C₂×D₄×C₃₇	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₃₇	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
257	C₂×D₄×C₃₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₃₇	—	2	1	no	—
259	C₂²×C₄×C₃₇	—	2	2	no	—
260	C₂²×C₄×C₃₇	—	2	2	no	—
261	C₂²×C₄×C₃₇	—	2	2	no	—
262	C₂²×C₄×C₃₇	—	2	2	no	—
263	C₂²×C₄×C₃₇	—	2	4	no	—
264	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₇	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₃₇	—	2	8	no	—
271	SD₁₆×C₃₇	—	2	8	no	—
272	SD₁₆×C₃₇	—	2	8	no	—
273	D₈×C₃₇	—	2	8	no	—
274	M₁₆×C₃₇	—	2	8	no	—
275	M₁₆×C₃₇	#41	1	8	yes	complemented
276	C₂×C₈×C₃₇	—	2	4	no	—
277	C₂×C₈×C₃₇	—	2	8	no	—
278	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
279	C₂×C₈×C₃₇	C₂⁴	1	2	yes	—
280	C₂×C₈×C₃₇	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₃₇	—	2	2	no	—
282	C₄⋊C₄×C₃₇	—	2	2	no	—
283	C₄⋊C₄×C₃₇	—	2	4	no	—
284	C₄⋊C₄×C₃₇	—	2	2	no	—
285	C₄⋊C₄×C₃₇	—	2	1	no	—
286	C₄⋊C₄×C₃₇	—	2	1	no	—
287	C₄⋊C₄×C₃₇	—	2	1	no	—
288	C₄⋊C₄×C₃₇	—	2	2	no	—
289	C₄⋊C₄×C₃₇	—	2	2	no	—
290	C₄⋊C₄×C₃₇	—	2	2	no	—
291	C₄⋊C₄×C₃₇	—	2	2	no	—
292	C₄⋊C₄×C₃₇	—	2	1	no	—
293	C₄⋊C₄×C₃₇	—	2	1	no	—
294	C₄⋊C₄×C₃₇	—	2	1	no	—
295	C₄⋊C₄×C₃₇	—	2	4	no	—
296	C₄⋊C₄×C₃₇	—	2	1	no	—
297	C₄⋊C₄×C₃₇	—	2	1	no	—
298	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₇	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₃₇	C₂⁴	1	1	yes	characteristic
307	C₂²⋊C₄×C₃₇	—	2	1	no	—
308	C₂²⋊C₄×C₃₇	—	2	1	no	—
309	C₂²⋊C₄×C₃₇	—	2	4	no	—
310	C₂²⋊C₄×C₃₇	—	2	2	no	—
311	C₂²⋊C₄×C₃₇	—	2	2	no	—
312	C₂²⋊C₄×C₃₇	—	2	2	no	—
313	C₂²⋊C₄×C₃₇	—	2	2	no	—
314	C₂²⋊C₄×C₃₇	—	2	2	no	—
315	C₂²⋊C₄×C₃₇	—	2	2	no	—
316	C₂²⋊C₄×C₃₇	—	2	2	no	—
317	C₂²⋊C₄×C₃₇	—	2	2	no	—
318	C₂²⋊C₄×C₃₇	—	2	4	no	—
319	C₂²⋊C₄×C₃₇	—	2	2	no	—
320	C₂²⋊C₄×C₃₇	—	2	2	no	—
321	C₂²⋊C₄×C₃₇	—	2	4	no	—
322	C₂²⋊C₄×C₃₇	—	2	2	no	—
323	C₂²⋊C₄×C₃₇	—	2	2	no	—
324	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₃₇	C₂×D₄	1	2	yes	—
327	C₄²×C₃₇	—	2	2	no	—
328	C₄²×C₃₇	—	2	2	no	—
329	C₄²×C₃₇	—	2	4	no	—
330	C₄²×C₃₇	—	2	1	no	—
331	C₄²×C₃₇	—	2	1	no	—
332	C₄²×C₃₇	C₂×D₄	1	2	yes	—
333	C₄²×C₃₇	C₂×D₄	1	2	yes	—
334	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₃₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₃₇	C₂⁴	1	2	yes	—
337	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
338	C₄²×C₃₇	C₂⁴	1	1	yes	characteristic
339	C₂³×C₃₇	—	2	2	no	—
340	C₂³×C₃₇	—	2	2	no	—
341	C₂³×C₃₇	—	4	2	no	—
342	C₂³×C₃₇	—	8	1	no	—
343	C₂³×C₃₇	—	8	1	no	—
344	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
345	C₂³×C₃₇	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₃₇	—	2	2	no	—
347	Q₈×C₃₇	—	2	2	no	—
348	Q₈×C₃₇	—	2	4	no	—
349	Q₈×C₃₇	—	2	2	no	—
350	Q₈×C₃₇	—	4	4	no	—
351	Q₈×C₃₇	—	4	2	no	—
352	Q₈×C₃₇	—	8	1	no	—
353	Q₈×C₃₇	—	8	1	no	—
354	Q₈×C₃₇	—	8	2	no	—
355	D₄×C₃₇	—	2	4	no	—
356	D₄×C₃₇	—	2	2	no	—
357	D₄×C₃₇	—	2	2	no	—
358	D₄×C₃₇	—	2	4	no	—
359	D₄×C₃₇	—	2	2	no	—
360	D₄×C₃₇	—	4	2	no	—
361	D₄×C₃₇	—	4	2	no	—
362	D₄×C₃₇	—	4	4	no	—
363	D₄×C₃₇	—	4	2	no	—
364	D₄×C₃₇	—	8	2	no	—
365	D₄×C₃₇	—	8	2	no	—
366	D₄×C₃₇	—	8	4	no	—
367	C₂×C₄×C₃₇	—	2	4	no	—
368	C₂×C₄×C₃₇	—	2	1	no	—
369	C₂×C₄×C₃₇	—	2	1	no	—
370	C₂×C₄×C₃₇	—	2	2	no	—
371	C₂×C₄×C₃₇	—	2	2	no	—
372	C₂×C₄×C₃₇	—	2	1	no	—
373	C₂×C₄×C₃₇	—	2	1	no	—
374	C₂×C₄×C₃₇	—	2	4	no	—
375	C₂×C₄×C₃₇	—	4	2	no	—
376	C₂×C₄×C₃₇	—	4	1	no	—
377	C₂×C₄×C₃₇	—	4	1	no	—
378	C₂×C₄×C₃₇	—	4	2	no	—
379	C₂×C₄×C₃₇	—	4	2	no	—
380	C₂×C₄×C₃₇	—	4	4	no	—
381	C₂×C₄×C₃₇	—	8	2	no	—
382	C₂×C₄×C₃₇	—	8	2	no	—
383	C₂×C₄×C₃₇	—	8	4	no	—
384	C₂×C₄×C₃₇	—	8	2	no	—
385	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
394	C₂×C₄×C₃₇	C₂⁵	1	1	yes	characteristic
395	C₈×C₃₇	—	2	2	no	—
396	C₈×C₃₇	—	2	2	no	—
397	C₈×C₃₇	C₂×#41	1	8	yes	—
398	#60727	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂²×C₃₇	—	2	1	no	—
400	C₂²×C₃₇	—	2	1	no	—
401	C₂²×C₃₇	—	2	2	no	—
402	C₂²×C₃₇	—	2	2	no	—
403	C₂²×C₃₇	—	2	2	no	—
404	C₂²×C₃₇	—	4	2	no	—
405	C₂²×C₃₇	—	4	2	no	—
406	C₂²×C₃₇	—	4	2	no	—
407	C₂²×C₃₇	—	4	2	no	—
408	C₂²×C₃₇	—	4	2	no	—
409	C₂²×C₃₇	—	4	2	no	—
410	C₂²×C₃₇	—	16	2	no	—
411	C₂²×C₃₇	#532	1	2	yes	—
412	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
419	C₄×C₃₇	—	2	2	no	—
420	C₄×C₃₇	—	4	4	no	—
421	C₄×C₃₇	—	4	1	no	—
422	C₄×C₃₇	—	4	1	no	—
423	C₄×C₃₇	—	4	1	no	—
424	C₄×C₃₇	—	4	1	no	—
425	C₄×C₃₇	—	4	2	no	—
426	C₄×C₃₇	—	4	2	no	—
427	C₄×C₃₇	#532	1	2	yes	—
428	C₄×C₃₇	C₂²×#41	1	2	yes	—
429	#3511	C₂×C₃₇	1	1	yes	characteristic, complemented
430	#3510	C₂×C₃₇	1	1	yes	characteristic, complemented
431	#3181	C₂×C₃₇	1	2	yes	complemented
432	#3180	C₂×C₃₇	1	2	yes	complemented
433	#3175	C₂×C₃₇	1	4	yes	complemented
434	#3173	C₂×C₃₇	1	4	yes	complemented
435	#3172	C₂×C₃₇	1	2	yes	complemented
436	#3171	C₂×C₃₇	1	2	yes	complemented
437	#3165	C₂×C₃₇	1	1	yes	characteristic, complemented
438	#3153	C₂×C₃₇	1	1	yes	characteristic, complemented
439	#3135	C₂×C₃₇	1	1	yes	characteristic, complemented
440	C₂×#489	C₂×C₃₇	1	1	yes	characteristic, complemented
441	#3063	C₂×C₃₇	1	2	yes	complemented
442	#3062	C₂×C₃₇	1	2	yes	complemented
443	#2947	C₂×C₃₇	1	2	yes	complemented
444	#2946	C₂×C₃₇	1	2	yes	complemented
445	#2875	C₂×C₃₇	1	1	yes	characteristic, complemented
446	C₂×C₃₇	—	2	2	no	—
447	C₂×C₃₇	—	4	2	no	—
448	C₂×C₃₇	—	8	2	no	—
449	C₂×C₃₇	—	8	2	no	—
450	C₂×C₃₇	C₂×#532	1	1	yes	characteristic
451	C₂×C₃₇	#3585	1	1	yes	characteristic
452	C₂×C₃₇	#3586	1	1	yes	characteristic
453	C₂×#137	C₂²×C₃₇	1	2	yes	—
454	C₂×AGL(1,ℤ/8)	C₂²×C₃₇	1	2	yes	—
455	C₂×#131	C₂²×C₃₇	1	2	yes	—
456	#559	—	2	1	no	—
457	#559	—	2	1	no	—
458	#556	—	2	1	no	—
459	#556	—	2	1	no	—
460	#556	—	2	1	no	—
461	#555	—	2	1	no	—
462	#554	—	2	1	no	—
463	#553	—	2	2	no	—
464	#551	—	2	2	no	—
465	#551	—	2	2	no	—
466	#548	—	2	2	no	—
467	#547	—	2	1	no	—
468	#542	C₂²×C₃₇	1	2	yes	—
469	#542	C₂²×C₃₇	1	2	yes	—
470	#542	C₂²×C₃₇	1	4	yes	complemented
471	#537	C₂²×C₃₇	1	2	yes	—
472	#536	C₂²×C₃₇	1	1	yes	characteristic
473	#535	C₂²×C₃₇	1	1	yes	characteristic
474	#533	C₂²×C₃₇	1	1	yes	characteristic
475	#533	C₂²×C₃₇	1	2	yes	complemented
476	#532	C₂²×C₃₇	1	1	yes	characteristic
477	#532	C₂²×C₃₇	1	2	yes	complemented
478	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
479	#529	C₂²×C₃₇	1	2	yes	—
480	#529	C₂²×C₃₇	1	2	yes	—
481	C₂×#124	C₂²×C₃₇	1	1	yes	characteristic
482	#520	C₂²×C₃₇	1	2	yes	—
483	#519	C₂²×C₃₇	1	1	yes	characteristic
484	#518	C₂²×C₃₇	1	1	yes	characteristic
485	C₄×#41	C₂²×C₃₇	1	1	yes	characteristic
486	#501	C₂²×C₃₇	1	2	yes	complemented
487	#501	C₂²×C₃₇	1	2	yes	complemented
488	#500	C₂²×C₃₇	1	2	yes	complemented
489	#498	C₂²×C₃₇	1	2	yes	complemented
490	#497	C₂²×C₃₇	1	2	yes	—
491	#496	C₂²×C₃₇	1	2	yes	—
492	#495	C₂²×C₃₇	1	4	yes	—
493	#491	C₂²×C₃₇	1	1	yes	characteristic, complemented
494	#491	C₂²×C₃₇	1	1	yes	characteristic, complemented
495	#490	C₂²×C₃₇	1	1	yes	characteristic, complemented
496	#490	C₂²×C₃₇	1	1	yes	characteristic, complemented
497	#489	C₂²×C₃₇	1	2	yes	—
498	#489	C₂²×C₃₇	1	4	yes	—
499	#489	C₂²×C₃₇	1	2	yes	—
500	#489	C₂²×C₃₇	1	2	yes	complemented
501	#489	C₂²×C₃₇	1	2	yes	complemented
502	#470	C₂²×C₃₇	1	4	yes	complemented
503	#469	C₂²×C₃₇	1	4	yes	—
504	#468	C₂²×C₃₇	1	4	yes	—
505	#468	C₂²×C₃₇	1	4	yes	complemented
506	#467	C₂²×C₃₇	1	4	yes	complemented
507	#466	C₂²×C₃₇	1	4	yes	—
508	#465	C₂²×C₃₇	1	4	yes	—
509	#465	C₂²×C₃₇	1	4	yes	complemented
510	#442	C₂²×C₃₇	1	4	yes	—
511	#441	C₂²×C₃₇	1	4	yes	complemented
512	#440	C₂²×C₃₇	1	4	yes	—
513	#440	C₂²×C₃₇	1	4	yes	complemented
514	C₄×Q₁₆	C₂²×C₃₇	1	4	yes	complemented
515	C₄×SD₁₆	C₂²×C₃₇	1	4	yes	—
516	C₄×SD₁₆	C₂²×C₃₇	1	4	yes	complemented
517	C₄×D₈	C₂²×C₃₇	1	4	yes	—
518	#428	C₂²×C₃₇	1	2	yes	—
519	#428	C₂²×C₃₇	1	2	yes	—
520	#416	C₂²×C₃₇	1	2	yes	—
521	#416	C₂²×C₃₇	1	2	yes	—
522	C₂×#103	C₂²×C₃₇	1	2	yes	—
523	C₂×#102	C₂²×C₃₇	1	2	yes	—
524	#405	C₂²×C₃₇	1	2	yes	—
525	#405	C₂²×C₃₇	1	4	yes	complemented
526	C₄×M₁₆	C₂²×C₃₇	1	1	yes	characteristic
527	C₄×M₁₆	C₂²×C₃₇	1	2	yes	complemented
528	C₂×#97	C₂²×C₃₇	1	1	yes	characteristic
529	C₂×#97	C₂²×C₃₇	1	2	yes	complemented
530	C₃₇	#60727	1	1	yes	characteristic, direct product factor, Sylow
531	C₂×#41	—	2	2	no	—
532	C₂×#41	C₂³×C₃₇	1	2	yes	—
533	C₂×#41	C₂³×C₃₇	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
537	#137	—	2	8	no	—
538	AGL(1,ℤ/8)	—	2	8	no	—
539	C₂×Q₁₆	C₂³×C₃₇	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₃₇	1	4	yes	—
542	C₂×D₈	C₂³×C₃₇	1	4	yes	—
543	#131	—	2	8	no	—
544	C₂×M₁₆	C₂³×C₃₇	1	4	yes	—
545	C₂×M₁₆	C₂³×C₃₇	1	2	yes	—
546	C₂²×C₈	C₂³×C₃₇	1	2	yes	—
547	C₂²×C₈	C₂³×C₃₇	1	4	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
552	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₃₇	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₃₇	1	1	yes	characteristic
556	#127	—	2	1	no	—
557	#127	C₂³×C₃₇	1	1	yes	characteristic
558	#126	—	2	2	no	—
559	#126	—	2	2	no	—
560	#126	—	2	4	no	—
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	C₂³×C₃₇	1	1	yes	characteristic
565	#125	C₂³×C₃₇	1	1	yes	characteristic
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	4	no	—
571	#124	—	2	1	no	—
572	#124	—	2	1	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₃₇	1	2	yes	—
575	#124	C₂³×C₃₇	1	2	yes	—
576	#124	C₂³×C₃₇	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
591	C₂²⋊Q₈	C₂³×C₃₇	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₃₇	1	4	yes	—
593	#121	—	2	2	no	—
594	#121	—	2	4	no	—
595	#121	—	2	1	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	#121	C₂³×C₃₇	1	2	yes	—
599	#121	C₂³×C₃₇	1	2	yes	—
600	#121	C₂³×C₃₇	1	4	yes	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
608	C₄×Q₈	D₄×C₃₇	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
610	C₄×Q₈	C₂³×C₃₇	1	2	yes	—
611	C₄×Q₈	C₂³×C₃₇	1	4	yes	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
621	C₄×D₄	D₄×C₃₇	1	2	yes	—
622	C₄×D₄	D₄×C₃₇	1	2	yes	—
623	C₄×D₄	D₄×C₃₇	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₃₇	1	2	yes	—
625	C₄×D₄	C₂³×C₃₇	1	2	yes	—
626	C₄×D₄	C₂³×C₃₇	1	4	yes	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	C₂³×C₃₇	1	1	yes	characteristic
633	#117	C₂³×C₃₇	1	1	yes	characteristic
634	#117	C₂³×C₃₇	1	1	yes	characteristic
635	#117	C₂³×C₃₇	1	2	yes	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
644	#107	C₂³×C₃₇	1	4	yes	—
645	#107	C₂³×C₃₇	1	4	yes	—
646	#106	C₂³×C₃₇	1	4	yes	—
647	#106	C₂³×C₃₇	1	4	yes	—
648	#103	C₂³×C₃₇	1	4	yes	—
649	#103	C₂³×C₃₇	1	4	yes	—
650	#103	C₂³×C₃₇	1	2	yes	—
651	#103	C₂³×C₃₇	1	2	yes	—
652	#103	C₂³×C₃₇	1	2	yes	—
653	#103	C₂³×C₃₇	1	2	yes	—
654	#102	C₂³×C₃₇	1	4	yes	—
655	#102	C₂³×C₃₇	1	4	yes	—
656	#102	C₂³×C₃₇	1	2	yes	—
657	#102	C₂³×C₃₇	1	2	yes	—
658	#102	C₂³×C₃₇	1	2	yes	—
659	#102	C₂³×C₃₇	1	2	yes	—
660	#97	C₂³×C₃₇	1	1	yes	characteristic
661	#97	C₂³×C₃₇	1	1	yes	characteristic
662	#97	C₂³×C₃₇	1	2	yes	—
663	#97	C₂³×C₃₇	1	2	yes	—
664	#97	C₂³×C₃₇	1	4	yes	—
665	C₄×C₈	C₂³×C₃₇	1	2	yes	—
666	C₄×C₈	C₂³×C₃₇	1	4	yes	—
667	C₂⁴	—	2	1	no	—
668	#41	—	2	4	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	8	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	8	2	no	—
679	C₂×Q₈	C₂×D₄×C₃₇	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₃₇	1	2	yes	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	C₂×D₄×C₃₇	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₃₇	1	1	yes	characteristic
692	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
693	C₂×D₄	C₂⁴×C₃₇	1	2	yes	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₃₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
706	Q₁₆	—	2	8	no	—
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	8	no	—
709	D₈	—	2	8	no	—
710	M₁₆	—	2	8	no	—
711	M₁₆	#41×C₃₇	1	8	yes	complemented
712	C₂×C₈	—	2	4	no	—
713	C₂×C₈	—	2	8	no	—
714	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
715	C₂×C₈	C₂⁴×C₃₇	1	2	yes	—
716	C₂×C₈	C₂⁴×C₃₇	1	4	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₃₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₃₇	1	4	yes	—
741	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₃₇	1	1	yes	characteristic
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₃₇	1	2	yes	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₃₇	1	2	yes	—
769	C₄²	C₂×D₄×C₃₇	1	2	yes	—
770	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₃₇	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₇	1	2	yes	—
773	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
774	C₄²	C₂⁴×C₃₇	1	1	yes	characteristic
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
781	C₂³	C₂²×D₄×C₃₇	1	1	yes	characteristic
782	Q₈	—	2	2	no	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	4	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	1	no	—
790	Q₈	—	8	1	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₃₇	1	1	yes	characteristic
829	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
830	C₂×C₄	C₂⁵×C₃₇	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	C₂×#41×C₃₇	1	8	yes	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	16	2	no	—
846	C₂²	C₃₇×#532	1	2	yes	—
847	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	C₃₇×#532	1	2	yes	—
863	C₄	C₂²×#41×C₃₇	1	2	yes	—
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₃₇×#532	1	1	yes	characteristic
869	C₂	C₃₇×#3585	1	1	yes	characteristic
870	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 ◁ C₄×#41×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₇×#3511	C₂	semidirect
2. C₃₇×#3510	C₂	semidirect
3. C₃₇×#3181	C₂	semidirect
4. C₃₇×#3180	C₂	semidirect
5. C₃₇×#3175	C₂	semidirect
6. C₃₇×#3173	C₂	semidirect
7. C₃₇×#3172	C₂	semidirect
8. C₃₇×#3171	C₂	semidirect
9. C₃₇×#3165	C₂	semidirect
10. C₃₇×#3153	C₂	semidirect
11. C₃₇×#3135	C₂	semidirect
12. C₂×C₃₇×#489	C₂	semidirect
13. C₃₇×#3063	C₂	semidirect
14. C₃₇×#3062	C₂	semidirect
15. C₃₇×#2947	C₂	semidirect
16. C₃₇×#2946	C₂	semidirect
17. C₃₇×#2875	C₂	semidirect
35. C₃₇×#542	C₂²	semidirect
40. C₃₇×#533	C₂²	semidirect
42. C₃₇×#532	C₂²	semidirect
51. C₃₇×#501	C₂²	semidirect
52. C₃₇×#501	C₂²	semidirect
53. C₃₇×#500	C₂²	semidirect
54. C₃₇×#498	C₂²	semidirect
58. C₃₇×#491	C₂²	semidirect
59. C₃₇×#491	C₂²	semidirect
60. C₃₇×#490	C₂²	semidirect
61. C₃₇×#490	C₂²	semidirect
65. C₃₇×#489	C₂²	semidirect
66. C₃₇×#489	C₂²	semidirect
67. C₃₇×#470	C₂²	semidirect
70. C₃₇×#468	C₂²	semidirect
71. C₃₇×#467	C₂²	semidirect
74. C₃₇×#465	C₂²	semidirect
76. C₃₇×#441	C₂²	semidirect
78. C₃₇×#440	C₂²	semidirect
79. C₄×Q₁₆×C₃₇	C₂²	semidirect
81. C₄×SD₁₆×C₃₇	C₂²	semidirect
90. C₃₇×#405	C₂²	semidirect
92. C₄×M₁₆×C₃₇	C₂²	semidirect
94. C₂×#97×C₃₇	C₂²	semidirect
275. M₁₆×C₃₇	#41	semidirect
398. #60727	C₃₇	direct (N × H)
429. #3511	C₂×C₃₇	semidirect
430. #3510	C₂×C₃₇	semidirect
431. #3181	C₂×C₃₇	semidirect
432. #3180	C₂×C₃₇	semidirect
433. #3175	C₂×C₃₇	semidirect
434. #3173	C₂×C₃₇	semidirect
435. #3172	C₂×C₃₇	semidirect
436. #3171	C₂×C₃₇	semidirect
437. #3165	C₂×C₃₇	semidirect
438. #3153	C₂×C₃₇	semidirect
439. #3135	C₂×C₃₇	semidirect
440. C₂×#489	C₂×C₃₇	semidirect
441. #3063	C₂×C₃₇	semidirect
442. #3062	C₂×C₃₇	semidirect
443. #2947	C₂×C₃₇	semidirect
444. #2946	C₂×C₃₇	semidirect
445. #2875	C₂×C₃₇	semidirect
470. #542	C₂²×C₃₇	semidirect
475. #533	C₂²×C₃₇	semidirect
477. #532	C₂²×C₃₇	semidirect
486. #501	C₂²×C₃₇	semidirect
487. #501	C₂²×C₃₇	semidirect
488. #500	C₂²×C₃₇	semidirect
489. #498	C₂²×C₃₇	semidirect
493. #491	C₂²×C₃₇	semidirect
494. #491	C₂²×C₃₇	semidirect
495. #490	C₂²×C₃₇	semidirect
496. #490	C₂²×C₃₇	semidirect
500. #489	C₂²×C₃₇	semidirect
501. #489	C₂²×C₃₇	semidirect
502. #470	C₂²×C₃₇	semidirect
505. #468	C₂²×C₃₇	semidirect
506. #467	C₂²×C₃₇	semidirect
509. #465	C₂²×C₃₇	semidirect
511. #441	C₂²×C₃₇	semidirect
513. #440	C₂²×C₃₇	semidirect
514. C₄×Q₁₆	C₂²×C₃₇	semidirect
516. C₄×SD₁₆	C₂²×C₃₇	semidirect
525. #405	C₂²×C₃₇	semidirect
527. C₄×M₁₆	C₂²×C₃₇	semidirect
529. C₂×#97	C₂²×C₃₇	semidirect
530. C₃₇	#60727	direct (N × H)
711. M₁₆	#41×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×#3511	2
C₃₇×#3510	2
C₃₇×#3181	2
C₃₇×#3180	2
C₃₇×#3175	2
C₃₇×#3173	2
C₃₇×#3172	2
C₃₇×#3171	2
C₃₇×#3165	2
C₃₇×#3153	2
C₃₇×#3135	2
C₂×C₃₇×#489	2
C₃₇×#3063	2
C₃₇×#3062	2
C₃₇×#2947	2
C₃₇×#2946	2
C₃₇×#2875	2
#60727	37

Subgroups — C37×#60727 #22681980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#60727 #22681980