Subgroups — C₃₇×#36546 #22657799

Order 9472.

2910 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#2848	C₂	1	2	yes	maximal, complemented
5	C₃₇×#2583	C₂	1	2	yes	maximal, complemented
6	C₃₇×#2579	C₂	1	2	yes	maximal, complemented
7	C₃₇×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₇×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₇×#2473	C₂	1	4	yes	maximal, complemented
10	C₃₇×#2449	C₂	1	4	yes	maximal, complemented
11	C₃₇×#2440	C₂	1	2	yes	maximal, complemented
12	C₃₇×#2417	C₂	1	2	yes	maximal, complemented
13	C₃₇×#2360	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₃₇	C₂	1	2	yes	maximal, complemented
15	C₃₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₃₇	C₂	1	1	yes	maximal, characteristic
17	C₄×#120×C₃₇	C₂	1	2	yes	maximal
18	C₂⁴×C₄×C₃₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₇	C₂²	1	2	yes	—
20	C₃₇×#554	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#125×C₃₇	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
29	C₂×#120×C₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₇	C₂²	1	4	yes	—
35	C₂²×C₄⋊C₄×C₃₇	—	2	8	no	—
36	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₃₇	C₂²	1	4	yes	—
39	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
43	C₃₇×#400	C₂²	1	2	yes	complemented
44	C₃₇×#399	C₂²	1	2	yes	complemented
45	C₃₇×#398	C₂²	1	4	yes	complemented
46	C₃₇×#398	C₂²	1	4	yes	complemented
47	C₃₇×#398	C₂²	1	4	yes	complemented
48	C₃₇×#396	C₂²	1	4	yes	complemented
49	C₃₇×#395	C₂²	1	4	yes	complemented
50	C₃₇×#391	C₂²	1	2	yes	complemented
51	C₃₇×#389	C₂²	1	2	yes	complemented
52	C₃₇×#389	C₂²	1	4	yes	complemented
53	C₃₇×#389	C₂²	1	2	yes	complemented
54	C₃₇×#389	C₂²	1	4	yes	complemented
55	C₃₇×#387	C₂²	1	4	yes	complemented
56	C₃₇×#387	C₂²	1	4	yes	complemented
57	C₃₇×#386	C₂²	1	4	yes	—
58	C₃₇×#386	C₂²	1	2	yes	—
59	C₃₇×#386	C₂²	1	2	yes	—
60	C₃₇×#386	C₂²	1	1	yes	characteristic
61	C₃₇×#385	C₂²	1	4	yes	—
62	C₃₇×#385	C₂²	1	4	yes	—
63	C₃₇×#385	C₂²	1	4	yes	—
64	C₃₇×#385	C₂²	1	2	yes	—
65	C₃₇×#385	C₂²	1	4	yes	—
66	C₃₇×#385	C₂²	1	2	yes	—
67	C₃₇×#385	C₂²	1	2	yes	—
68	C₃₇×#385	C₂²	1	2	yes	—
69	C₃₇×#385	C₂²	1	1	yes	characteristic
70	C₃₇×#385	C₂²	1	2	yes	—
71	C₃₇×#385	C₂²	1	4	yes	complemented
72	C₃₇×#384	C₂²	1	2	yes	complemented
73	C₃₇×#380	C₂²	1	4	yes	—
74	C₃₇×#380	C₂²	1	2	yes	—
75	C₃₇×#380	C₂²	1	1	yes	characteristic
76	C₃₇×#380	C₂²	1	2	yes	—
77	C₃₇×#380	C₂²	1	2	yes	complemented
78	C₃₇×#379	C₂²	1	1	yes	characteristic
79	C₃₇×#379	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₃₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₇	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
85	C₂⁵×C₃₇	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₃₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₇	—	2	4	no	—
91	C₂³×C₄×C₃₇	—	2	8	no	—
92	C₂³×C₄×C₃₇	—	2	8	no	—
93	C₂³×C₄×C₃₇	—	4	8	no	—
94	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₃₇	C₂³	1	4	yes	—
99	C₂³×C₄×C₃₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
101	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
102	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₇	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₃₇	—	2	4	no	—
105	#125×C₃₇	—	2	8	no	—
106	C₂²⋊Q₈×C₃₇	—	2	8	no	—
107	C₂²⋊Q₈×C₃₇	—	2	4	no	—
108	C₂²⋊Q₈×C₃₇	—	2	8	no	—
109	C₂²⋊Q₈×C₃₇	—	2	8	no	—
110	C₂²⋊Q₈×C₃₇	—	2	4	no	—
111	C₂²⋊Q₈×C₃₇	—	4	8	no	—
112	#120×C₃₇	Q₈	1	8	yes	complemented
113	C₄×Q₈×C₃₇	—	2	4	no	—
114	C₄×D₄×C₃₇	—	2	8	no	—
115	C₄×D₄×C₃₇	—	2	4	no	—
116	C₄×D₄×C₃₇	—	2	8	no	—
117	C₄×D₄×C₃₇	—	4	8	no	—
118	C₂×C₄⋊C₄×C₃₇	—	2	8	no	—
119	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
120	C₂×C₄⋊C₄×C₃₇	—	2	4	no	—
121	C₂×C₄⋊C₄×C₃₇	—	2	8	no	—
122	C₂×C₄⋊C₄×C₃₇	—	2	16	no	—
123	C₂×C₄⋊C₄×C₃₇	—	2	8	no	—
124	C₂×C₄⋊C₄×C₃₇	D₄	1	8	yes	complemented
125	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
161	C₂×C₄²×C₃₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₃₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₇	C₂³	1	4	yes	—
164	#95×C₃₇	C₂³	1	2	yes	—
165	#95×C₃₇	C₂³	1	2	yes	—
166	#95×C₃₇	C₂³	1	4	yes	—
167	#95×C₃₇	C₂³	1	4	yes	—
168	#95×C₃₇	C₂³	1	2	yes	—
169	#95×C₃₇	C₂³	1	4	yes	—
170	#95×C₃₇	C₂³	1	4	yes	—
171	#95×C₃₇	C₂³	1	4	yes	—
172	#95×C₃₇	C₂³	1	4	yes	—
173	#95×C₃₇	C₂³	1	2	yes	—
174	#95×C₃₇	C₂³	1	4	yes	—
175	C₂⁴×C₃₇	—	2	2	no	—
176	C₂⁴×C₃₇	—	2	4	no	—
177	C₂⁴×C₃₇	—	2	4	no	—
178	C₂⁴×C₃₇	—	2	2	no	—
179	C₂⁴×C₃₇	C₂×Q₈	1	4	yes	—
180	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₃₇	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₃₇	C₂⁴	1	2	yes	—
183	C₂×Q₈×C₃₇	—	2	2	no	—
184	C₂×Q₈×C₃₇	—	2	4	no	—
185	C₂×Q₈×C₃₇	—	2	4	no	—
186	C₂×Q₈×C₃₇	—	4	4	no	—
187	C₂×D₄×C₃₇	—	2	2	no	—
188	C₂×D₄×C₃₇	—	2	4	no	—
189	C₂×D₄×C₃₇	—	2	4	no	—
190	C₂×D₄×C₃₇	—	2	2	no	—
191	C₂×D₄×C₃₇	C₂×Q₈	1	4	yes	—
192	C₂×D₄×C₃₇	C₂×Q₈	1	8	yes	—
193	C₂²×C₄×C₃₇	—	2	32	no	—
194	C₂²×C₄×C₃₇	—	2	2	no	—
195	C₂²×C₄×C₃₇	—	2	4	no	—
196	C₂²×C₄×C₃₇	—	2	4	no	—
197	C₂²×C₄×C₃₇	—	2	4	no	—
198	C₂²×C₄×C₃₇	—	2	4	no	—
199	C₂²×C₄×C₃₇	—	2	4	no	—
200	C₂²×C₄×C₃₇	—	2	4	no	—
201	C₂²×C₄×C₃₇	—	2	4	no	—
202	C₂²×C₄×C₃₇	—	2	4	no	—
203	C₂²×C₄×C₃₇	—	2	8	no	—
204	C₂²×C₄×C₃₇	—	2	8	no	—
205	C₂²×C₄×C₃₇	—	2	8	no	—
206	C₂²×C₄×C₃₇	—	2	8	no	—
207	C₂²×C₄×C₃₇	—	2	2	no	—
208	C₂²×C₄×C₃₇	—	2	4	no	—
209	C₂²×C₄×C₃₇	—	2	4	no	—
210	C₂²×C₄×C₃₇	—	4	4	no	—
211	C₂²×C₄×C₃₇	—	4	4	no	—
212	C₂²×C₄×C₃₇	—	4	4	no	—
213	C₂²×C₄×C₃₇	—	4	4	no	—
214	C₂²×C₄×C₃₇	—	4	4	no	—
215	C₂²×C₄×C₃₇	—	4	32	no	—
216	C₂²×C₄×C₃₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₃₇	C₂×D₄	1	8	yes	—
218	C₂²×C₄×C₃₇	#41	1	8	yes	—
219	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₇	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₃₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₃₇	—	2	8	no	—
234	C₄⋊C₄×C₃₇	—	2	8	no	—
235	C₄⋊C₄×C₃₇	—	2	4	no	—
236	C₄⋊C₄×C₃₇	—	2	4	no	—
237	C₄⋊C₄×C₃₇	—	2	4	no	—
238	C₄⋊C₄×C₃₇	—	2	2	no	—
239	C₄⋊C₄×C₃₇	—	2	2	no	—
240	C₄⋊C₄×C₃₇	—	2	4	no	—
241	C₄⋊C₄×C₃₇	—	2	4	no	—
242	C₄⋊C₄×C₃₇	—	2	4	no	—
243	C₄⋊C₄×C₃₇	—	2	4	no	—
244	C₄⋊C₄×C₃₇	—	2	4	no	—
245	C₄⋊C₄×C₃₇	—	2	4	no	—
246	C₄⋊C₄×C₃₇	—	2	8	no	—
247	C₄⋊C₄×C₃₇	—	4	4	no	—
248	C₄⋊C₄×C₃₇	—	4	4	no	—
249	C₄⋊C₄×C₃₇	—	4	4	no	—
250	C₄⋊C₄×C₃₇	—	4	4	no	—
251	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₃₇	C₂×D₄	1	8	yes	—
253	C₄⋊C₄×C₃₇	C₂×D₄	1	4	yes	—
254	C₂²⋊C₄×C₃₇	—	2	4	no	—
255	C₂²⋊C₄×C₃₇	—	2	2	no	—
256	C₂²⋊C₄×C₃₇	—	2	4	no	—
257	C₂²⋊C₄×C₃₇	—	2	8	no	—
258	C₂²⋊C₄×C₃₇	—	2	8	no	—
259	C₂²⋊C₄×C₃₇	—	2	4	no	—
260	C₂²⋊C₄×C₃₇	—	2	2	no	—
261	C₂²⋊C₄×C₃₇	—	2	4	no	—
262	C₂²⋊C₄×C₃₇	—	2	4	no	—
263	C₂²⋊C₄×C₃₇	—	2	2	no	—
264	C₂²⋊C₄×C₃₇	—	2	4	no	—
265	C₂²⋊C₄×C₃₇	—	4	4	no	—
266	C₂²⋊C₄×C₃₇	C₂×Q₈	1	4	yes	—
267	C₂²⋊C₄×C₃₇	C₂×Q₈	1	8	yes	—
268	C₄²×C₃₇	—	2	4	no	—
269	C₄²×C₃₇	—	2	2	no	—
270	C₄²×C₃₇	—	2	4	no	—
271	C₄²×C₃₇	—	4	4	no	—
272	C₂³×C₃₇	—	2	8	no	—
273	C₂³×C₃₇	—	2	8	no	—
274	C₂³×C₃₇	—	2	16	no	—
275	C₂³×C₃₇	—	2	8	no	—
276	C₂³×C₃₇	—	2	16	no	—
277	C₂³×C₃₇	—	2	2	no	—
278	C₂³×C₃₇	—	2	2	no	—
279	C₂³×C₃₇	—	2	2	no	—
280	C₂³×C₃₇	—	2	2	no	—
281	C₂³×C₃₇	—	2	2	no	—
282	C₂³×C₃₇	—	2	2	no	—
283	C₂³×C₃₇	—	2	1	no	—
284	C₂³×C₃₇	—	2	2	no	—
285	C₂³×C₃₇	—	2	2	no	—
286	C₂³×C₃₇	—	2	1	no	—
287	C₂³×C₃₇	C₂²×D₄	1	2	yes	—
288	C₂³×C₃₇	C₂²×Q₈	1	2	yes	—
289	C₂³×C₃₇	C₂²×Q₈	1	2	yes	—
290	C₂³×C₃₇	C₂²×Q₈	1	4	yes	—
291	C₂³×C₃₇	C₂×#41	1	4	yes	—
292	C₂³×C₃₇	H(5,𝔽₂)	1	4	yes	—
293	C₂³×C₃₇	2₋¹⁺⁴	1	2	yes	—
294	C₂³×C₃₇	C₂⁵	1	1	yes	characteristic
295	Q₈×C₃₇	—	4	4	no	—
296	Q₈×C₃₇	—	8	4	no	—
297	D₄×C₃₇	—	2	8	no	—
298	D₄×C₃₇	—	2	16	no	—
299	C₂×C₄×C₃₇	—	2	16	no	—
300	C₂×C₄×C₃₇	—	2	8	no	—
301	C₂×C₄×C₃₇	—	2	1	no	—
302	C₂×C₄×C₃₇	—	2	2	no	—
303	C₂×C₄×C₃₇	—	2	2	no	—
304	C₂×C₄×C₃₇	—	2	2	no	—
305	C₂×C₄×C₃₇	—	2	2	no	—
306	C₂×C₄×C₃₇	—	2	2	no	—
307	C₂×C₄×C₃₇	—	2	4	no	—
308	C₂×C₄×C₃₇	—	2	4	no	—
309	C₂×C₄×C₃₇	—	2	1	no	—
310	C₂×C₄×C₃₇	—	2	8	no	—
311	C₂×C₄×C₃₇	—	2	16	no	—
312	C₂×C₄×C₃₇	—	2	2	no	—
313	C₂×C₄×C₃₇	—	2	1	no	—
314	C₂×C₄×C₃₇	—	2	1	no	—
315	C₂×C₄×C₃₇	—	2	2	no	—
316	C₂×C₄×C₃₇	—	2	4	no	—
317	C₂×C₄×C₃₇	—	2	2	no	—
318	C₂×C₄×C₃₇	—	2	4	no	—
319	C₂×C₄×C₃₇	—	2	2	no	—
320	C₂×C₄×C₃₇	—	2	4	no	—
321	C₂×C₄×C₃₇	—	2	4	no	—
322	C₂×C₄×C₃₇	—	2	2	no	—
323	C₂×C₄×C₃₇	—	2	4	no	—
324	C₂×C₄×C₃₇	—	2	2	no	—
325	C₂×C₄×C₃₇	—	2	4	no	—
326	C₂×C₄×C₃₇	—	2	4	no	—
327	C₂×C₄×C₃₇	—	2	2	no	—
328	C₂×C₄×C₃₇	—	2	4	no	—
329	C₂×C₄×C₃₇	—	4	8	no	—
330	C₂×C₄×C₃₇	—	4	16	no	—
331	C₂×C₄×C₃₇	—	4	16	no	—
332	C₂×C₄×C₃₇	—	4	8	no	—
333	C₂×C₄×C₃₇	—	4	4	no	—
334	C₂×C₄×C₃₇	—	8	4	no	—
335	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₇	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₃₇	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₃₇	C₂²×Q₈	1	2	yes	—
340	C₂×C₄×C₃₇	C₂²×Q₈	1	4	yes	—
341	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
342	C₂×C₄×C₃₇	C₂×#41	1	4	yes	—
343	#36546	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂²×C₃₇	—	2	32	no	—
345	C₂²×C₃₇	—	2	2	no	—
346	C₂²×C₃₇	—	2	4	no	—
347	C₂²×C₃₇	—	2	4	no	—
348	C₂²×C₃₇	—	2	4	no	—
349	C₂²×C₃₇	—	2	4	no	—
350	C₂²×C₃₇	—	2	2	no	—
351	C₂²×C₃₇	—	2	4	no	—
352	C₂²×C₃₇	—	2	4	no	—
353	C₂²×C₃₇	—	2	4	no	—
354	C₂²×C₃₇	—	2	4	no	—
355	C₂²×C₃₇	—	2	2	no	—
356	C₂²×C₃₇	—	2	4	no	—
357	C₂²×C₃₇	—	4	1	no	—
358	C₂²×C₃₇	—	4	1	no	—
359	C₂²×C₃₇	—	4	2	no	—
360	C₂²×C₃₇	D₄×Q₈	1	4	yes	—
361	C₂²×C₃₇	#554	1	8	yes	complemented
362	C₂²×C₃₇	C₂³×D₄	1	1	yes	characteristic
363	C₂²×C₃₇	C₂³×Q₈	1	1	yes	characteristic
364	C₂²×C₃₇	C₂²×#41	1	2	yes	—
365	C₂²×C₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂²×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₄×C₃₇	—	2	2	no	—
368	C₄×C₃₇	—	2	4	no	—
369	C₄×C₃₇	—	2	2	no	—
370	C₄×C₃₇	—	2	4	no	—
371	C₄×C₃₇	—	2	4	no	—
372	C₄×C₃₇	—	2	4	no	—
373	C₄×C₃₇	—	4	1	no	—
374	C₄×C₃₇	—	4	2	no	—
375	C₄×C₃₇	—	4	4	no	—
376	C₄×C₃₇	—	4	2	no	—
377	C₄×C₃₇	—	4	1	no	—
378	C₄×C₃₇	—	4	2	no	—
379	C₄×C₃₇	—	4	4	no	—
380	C₄×C₃₇	#525	1	4	yes	—
381	C₂×#554	C₂×C₃₇	1	1	yes	characteristic, complemented
382	C₂³×C₄⋊C₄	C₂×C₃₇	1	1	yes	characteristic, complemented
383	#2848	C₂×C₃₇	1	2	yes	complemented
384	#2848	C₂×C₃₇	1	1	yes	characteristic, complemented
385	#2583	C₂×C₃₇	1	2	yes	complemented
386	#2579	C₂×C₃₇	1	2	yes	complemented
387	#2502	C₂×C₃₇	1	1	yes	characteristic, complemented
388	#2487	C₂×C₃₇	1	1	yes	characteristic, complemented
389	#2473	C₂×C₃₇	1	4	yes	complemented
390	#2449	C₂×C₃₇	1	4	yes	complemented
391	#2440	C₂×C₃₇	1	2	yes	complemented
392	#2417	C₂×C₃₇	1	2	yes	complemented
393	#2360	C₂×C₃₇	1	2	yes	complemented
394	D₄×C₄⋊C₄	C₂×C₃₇	1	2	yes	complemented
395	#2345	C₂×C₃₇	1	1	yes	characteristic, complemented
396	C₄×#120	C₂×C₃₇	1	2	yes	—
397	C₄×#120	C₂×C₃₇	1	1	yes	characteristic
398	C₂×C₃₇	—	2	4	no	—
399	C₂×C₃₇	—	2	8	no	—
400	C₂×C₃₇	—	4	2	no	—
401	C₂×C₃₇	C₂×#525	1	1	yes	characteristic
402	C₂×C₃₇	C₂×D₄×Q₈	1	1	yes	characteristic
403	C₂×C₃₇	C₂×#554	1	2	yes	—
404	C₂×C₃₇	#3484	1	1	yes	characteristic
405	C₂×C₃₇	#3492	1	2	yes	—
406	C₂⁴×C₄	C₂²×C₃₇	1	1	yes	characteristic
407	C₂⁴×C₄	C₂²×C₃₇	1	2	yes	—
408	#554	—	2	8	no	—
409	C₂×C₄⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
410	C₂×#125	C₂²×C₃₇	1	2	yes	complemented
411	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	4	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
416	C₂×C₂²⋊Q₈	C₂²×C₃₇	1	2	yes	complemented
417	C₂×#120	C₂²×C₃₇	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₃₇	1	1	yes	characteristic, complemented
419	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₃₇	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₃₇	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₃₇	1	4	yes	—
423	C₂²×C₄⋊C₄	—	2	8	no	—
424	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
425	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×C₃₇	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₃₇	1	4	yes	—
428	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₃₇	1	1	yes	characteristic, complemented
431	#400	C₂²×C₃₇	1	2	yes	complemented
432	#399	C₂²×C₃₇	1	2	yes	complemented
433	#398	C₂²×C₃₇	1	4	yes	complemented
434	#398	C₂²×C₃₇	1	4	yes	complemented
435	#398	C₂²×C₃₇	1	4	yes	complemented
436	#396	C₂²×C₃₇	1	4	yes	complemented
437	#395	C₂²×C₃₇	1	4	yes	complemented
438	#391	C₂²×C₃₇	1	2	yes	complemented
439	#389	C₂²×C₃₇	1	4	yes	complemented
440	#389	C₂²×C₃₇	1	4	yes	complemented
441	#389	C₂²×C₃₇	1	2	yes	complemented
442	#389	C₂²×C₃₇	1	2	yes	complemented
443	#387	C₂²×C₃₇	1	4	yes	complemented
444	#387	C₂²×C₃₇	1	4	yes	complemented
445	#386	C₂²×C₃₇	1	1	yes	characteristic
446	#386	C₂²×C₃₇	1	2	yes	—
447	#386	C₂²×C₃₇	1	4	yes	—
448	#386	C₂²×C₃₇	1	2	yes	—
449	#385	C₂²×C₃₇	1	2	yes	—
450	#385	C₂²×C₃₇	1	2	yes	—
451	#385	C₂²×C₃₇	1	1	yes	characteristic
452	#385	C₂²×C₃₇	1	2	yes	—
453	#385	C₂²×C₃₇	1	2	yes	—
454	#385	C₂²×C₃₇	1	4	yes	—
455	#385	C₂²×C₃₇	1	4	yes	—
456	#385	C₂²×C₃₇	1	4	yes	—
457	#385	C₂²×C₃₇	1	4	yes	—
458	#385	C₂²×C₃₇	1	2	yes	—
459	#385	C₂²×C₃₇	1	4	yes	complemented
460	#384	C₂²×C₃₇	1	2	yes	complemented
461	#380	C₂²×C₃₇	1	2	yes	—
462	#380	C₂²×C₃₇	1	1	yes	characteristic
463	#380	C₂²×C₃₇	1	2	yes	—
464	#380	C₂²×C₃₇	1	4	yes	—
465	#380	C₂²×C₃₇	1	2	yes	complemented
466	#379	C₂²×C₃₇	1	2	yes	—
467	#379	C₂²×C₃₇	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₃₇	1	2	yes	complemented
469	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₃₇	1	1	yes	characteristic
471	C₄×C₂²⋊C₄	C₂²×C₃₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₃₇	1	4	yes	—
473	C₃₇	#36546	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁵	C₂³×C₃₇	1	1	yes	characteristic
475	C₂²×Q₈	C₂³×C₃₇	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₃₇	1	2	yes	—
477	C₂²×D₄	C₂³×C₃₇	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₃₇	1	2	yes	—
479	C₂³×C₄	—	2	4	no	—
480	C₂³×C₄	—	2	8	no	—
481	C₂³×C₄	—	2	8	no	—
482	C₂³×C₄	—	4	8	no	—
483	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
485	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
487	C₂³×C₄	C₂³×C₃₇	1	4	yes	—
488	C₂³×C₄	C₂³×C₃₇	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
490	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
491	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
492	C₂³×C₄	C₂³×C₃₇	1	2	yes	—
493	C₄⋊Q₈	—	2	4	no	—
494	#125	—	2	8	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	C₂²⋊Q₈	—	2	8	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	4	8	no	—
501	#120	Q₈×C₃₇	1	8	yes	complemented
502	C₄×Q₈	—	2	4	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	4	8	no	—
507	C₂×C₄⋊C₄	—	2	8	no	—
508	C₂×C₄⋊C₄	—	2	4	no	—
509	C₂×C₄⋊C₄	—	2	8	no	—
510	C₂×C₄⋊C₄	—	2	16	no	—
511	C₂×C₄⋊C₄	—	2	8	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	D₄×C₃₇	1	8	yes	complemented
514	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₃₇	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃₇	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃₇	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₃₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₃₇	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃₇	1	2	yes	—
552	C₂×C₄²	C₂³×C₃₇	1	4	yes	—
553	#95	C₂³×C₃₇	1	2	yes	—
554	#95	C₂³×C₃₇	1	2	yes	—
555	#95	C₂³×C₃₇	1	4	yes	—
556	#95	C₂³×C₃₇	1	4	yes	—
557	#95	C₂³×C₃₇	1	2	yes	—
558	#95	C₂³×C₃₇	1	4	yes	—
559	#95	C₂³×C₃₇	1	4	yes	—
560	#95	C₂³×C₃₇	1	4	yes	—
561	#95	C₂³×C₃₇	1	4	yes	—
562	#95	C₂³×C₃₇	1	2	yes	—
563	#95	C₂³×C₃₇	1	4	yes	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	2	no	—
568	C₂⁴	C₂×Q₈×C₃₇	1	4	yes	—
569	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
570	C₂⁴	C₂⁴×C₃₇	1	1	yes	characteristic
571	C₂⁴	C₂⁴×C₃₇	1	2	yes	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	C₂×Q₈×C₃₇	1	4	yes	—
581	C₂×D₄	C₂×Q₈×C₃₇	1	8	yes	—
582	C₂²×C₄	—	2	32	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	8	no	—
593	C₂²×C₄	—	2	8	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	32	no	—
605	C₂²×C₄	C₂×D₄×C₃₇	1	4	yes	—
606	C₂²×C₄	C₂×D₄×C₃₇	1	8	yes	—
607	C₂²×C₄	#41×C₃₇	1	8	yes	—
608	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₇	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₃₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃₇	1	1	yes	characteristic
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	2	8	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	8	no	—
636	C₄⋊C₄	—	4	4	no	—
637	C₄⋊C₄	—	4	4	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
641	C₄⋊C₄	C₂×D₄×C₃₇	1	8	yes	—
642	C₄⋊C₄	C₂×D₄×C₃₇	1	4	yes	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	C₂×Q₈×C₃₇	1	4	yes	—
656	C₂²⋊C₄	C₂×Q₈×C₃₇	1	8	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	4	4	no	—
661	C₂³	—	2	8	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	16	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	16	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	C₂²×D₄×C₃₇	1	2	yes	—
677	C₂³	C₂²×Q₈×C₃₇	1	2	yes	—
678	C₂³	C₂²×Q₈×C₃₇	1	2	yes	—
679	C₂³	C₂²×Q₈×C₃₇	1	4	yes	—
680	C₂³	C₂×#41×C₃₇	1	4	yes	—
681	C₂³	H(5,𝔽₂)×C₃₇	1	4	yes	—
682	C₂³	2₋¹⁺⁴×C₃₇	1	2	yes	—
683	C₂³	C₂⁵×C₃₇	1	1	yes	characteristic
684	Q₈	—	4	4	no	—
685	Q₈	—	8	4	no	—
686	D₄	—	2	8	no	—
687	D₄	—	2	16	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	16	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	16	no	—
720	C₂×C₄	—	4	16	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₃₇	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₃₇	1	2	yes	—
728	C₂×C₄	C₂²×Q₈×C₃₇	1	2	yes	—
729	C₂×C₄	C₂²×Q₈×C₃₇	1	4	yes	—
730	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
731	C₂×C₄	C₂×#41×C₃₇	1	4	yes	—
732	C₂²	—	2	32	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	D₄×Q₈×C₃₇	1	4	yes	—
749	C₂²	C₃₇×#554	1	8	yes	complemented
750	C₂²	C₂³×D₄×C₃₇	1	1	yes	characteristic
751	C₂²	C₂³×Q₈×C₃₇	1	1	yes	characteristic
752	C₂²	C₂²×#41×C₃₇	1	2	yes	—
753	C₂²	C₂×H(5,𝔽₂)×C₃₇	1	2	yes	—
754	C₂²	C₂×2₋¹⁺⁴×C₃₇	1	1	yes	characteristic
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	C₃₇×#525	1	4	yes	—
769	C₂	—	2	4	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	2	no	—
772	C₂	C₂×C₃₇×#525	1	1	yes	characteristic
773	C₂	C₂×D₄×Q₈×C₃₇	1	1	yes	characteristic
774	C₂	C₂×C₃₇×#554	1	2	yes	—
775	C₂	C₃₇×#3484	1	1	yes	characteristic
776	C₂	C₃₇×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₇
prime radical	C₂×#120×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₇×#554	C₂	semidirect
2. C₂³×C₄⋊C₄×C₃₇	C₂	semidirect
3. C₃₇×#2848	C₂	semidirect
4. C₃₇×#2848	C₂	semidirect
5. C₃₇×#2583	C₂	semidirect
6. C₃₇×#2579	C₂	semidirect
7. C₃₇×#2502	C₂	semidirect
8. C₃₇×#2487	C₂	semidirect
9. C₃₇×#2473	C₂	semidirect
10. C₃₇×#2449	C₂	semidirect
11. C₃₇×#2440	C₂	semidirect
12. C₃₇×#2417	C₂	semidirect
13. C₃₇×#2360	C₂	semidirect
14. D₄×C₄⋊C₄×C₃₇	C₂	semidirect
15. C₃₇×#2345	C₂	semidirect
21. C₂×C₄⋊Q₈×C₃₇	C₂²	semidirect
22. C₂×#125×C₃₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₃₇	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₃₇	C₂²	semidirect
30. C₂×C₄×Q₈×C₃₇	C₂²	semidirect
42. C₂²×C₄⋊C₄×C₃₇	C₂²	semidirect
43. C₃₇×#400	C₂²	semidirect
44. C₃₇×#399	C₂²	semidirect
45. C₃₇×#398	C₂²	semidirect
46. C₃₇×#398	C₂²	semidirect
47. C₃₇×#398	C₂²	semidirect
48. C₃₇×#396	C₂²	semidirect
49. C₃₇×#395	C₂²	semidirect
50. C₃₇×#391	C₂²	semidirect
51. C₃₇×#389	C₂²	semidirect
52. C₃₇×#389	C₂²	semidirect
53. C₃₇×#389	C₂²	semidirect
54. C₃₇×#389	C₂²	semidirect
55. C₃₇×#387	C₂²	semidirect
56. C₃₇×#387	C₂²	semidirect
71. C₃₇×#385	C₂²	semidirect
72. C₃₇×#384	C₂²	semidirect
77. C₃₇×#380	C₂²	semidirect
80. C₄×C₄⋊C₄×C₃₇	C₂²	semidirect
112. #120×C₃₇	Q₈	semidirect
124. C₂×C₄⋊C₄×C₃₇	D₄	semidirect
343. #36546	C₃₇	direct (N × H)
361. C₂²×C₃₇	#554	semidirect
381. C₂×#554	C₂×C₃₇	semidirect
382. C₂³×C₄⋊C₄	C₂×C₃₇	semidirect
383. #2848	C₂×C₃₇	semidirect
384. #2848	C₂×C₃₇	semidirect
385. #2583	C₂×C₃₇	semidirect
386. #2579	C₂×C₃₇	semidirect
387. #2502	C₂×C₃₇	semidirect
388. #2487	C₂×C₃₇	semidirect
389. #2473	C₂×C₃₇	semidirect
390. #2449	C₂×C₃₇	semidirect
391. #2440	C₂×C₃₇	semidirect
392. #2417	C₂×C₃₇	semidirect
393. #2360	C₂×C₃₇	semidirect
394. D₄×C₄⋊C₄	C₂×C₃₇	semidirect
395. #2345	C₂×C₃₇	semidirect
409. C₂×C₄⋊Q₈	C₂²×C₃₇	semidirect
410. C₂×#125	C₂²×C₃₇	semidirect
415. C₂×C₂²⋊Q₈	C₂²×C₃₇	semidirect
416. C₂×C₂²⋊Q₈	C₂²×C₃₇	semidirect
418. C₂×C₄×Q₈	C₂²×C₃₇	semidirect
430. C₂²×C₄⋊C₄	C₂²×C₃₇	semidirect
431. #400	C₂²×C₃₇	semidirect
432. #399	C₂²×C₃₇	semidirect
433. #398	C₂²×C₃₇	semidirect
434. #398	C₂²×C₃₇	semidirect
435. #398	C₂²×C₃₇	semidirect
436. #396	C₂²×C₃₇	semidirect
437. #395	C₂²×C₃₇	semidirect
438. #391	C₂²×C₃₇	semidirect
439. #389	C₂²×C₃₇	semidirect
440. #389	C₂²×C₃₇	semidirect
441. #389	C₂²×C₃₇	semidirect
442. #389	C₂²×C₃₇	semidirect
443. #387	C₂²×C₃₇	semidirect
444. #387	C₂²×C₃₇	semidirect
459. #385	C₂²×C₃₇	semidirect
460. #384	C₂²×C₃₇	semidirect
465. #380	C₂²×C₃₇	semidirect
468. C₄×C₄⋊C₄	C₂²×C₃₇	semidirect
473. C₃₇	#36546	direct (N × H)
501. #120	Q₈×C₃₇	semidirect
513. C₂×C₄⋊C₄	D₄×C₃₇	semidirect
749. C₂²	C₃₇×#554	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₇×#554	2
C₂³×C₄⋊C₄×C₃₇	2
C₃₇×#2848	2
C₃₇×#2583	2
C₃₇×#2579	2
C₃₇×#2502	2
C₃₇×#2487	2
C₃₇×#2473	2
C₃₇×#2449	2
C₃₇×#2440	2
C₃₇×#2417	2
C₃₇×#2360	2
D₄×C₄⋊C₄×C₃₇	2
C₃₇×#2345	2
C₄×#120×C₃₇	2
#36546	37

Subgroups — C37×#36546 #22657799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#36546 #22657799