Subgroups — C₁₃₇×#20012 #46869398

Order 35072.

606 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3396×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3361×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#3338×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1706×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1678×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1676×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1667×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1630×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1622×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₁₃₇	C₂²	1	2	yes	—
13	#554×C₁₃₇	C₂²	1	2	yes	—
14	#500×C₁₃₇	C₂²	1	1	yes	characteristic
15	#495×C₁₃₇	—	2	1	no	—
16	#493×C₁₃₇	C₂²	1	1	yes	characteristic
17	#492×C₁₃₇	C₂²	1	2	yes	—
18	#488×C₁₃₇	—	2	2	no	—
19	#486×C₁₃₇	C₂²	1	2	yes	—
20	#484×C₁₃₇	—	2	2	no	—
21	#478×C₁₃₇	—	2	2	no	—
22	#477×C₁₃₇	C₂²	1	2	yes	—
23	#477×C₁₃₇	C₂²	1	2	yes	—
24	#467×C₁₃₇	—	2	1	no	—
25	#463×C₁₃₇	—	2	2	no	—
26	#463×C₁₃₇	—	2	2	no	—
27	#460×C₁₃₇	C₂²	1	2	yes	—
28	#459×C₁₃₇	C₂²	1	2	yes	—
29	C₈×Q₈×C₁₃₇	C₂²	1	2	yes	—
30	C₈×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₁₃₇	—	2	1	no	—
34	C₄×D₈×C₁₃₇	—	2	2	no	—
35	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₁₃₇	—	2	1	no	—
37	#335×C₁₃₇	C₂²	1	1	yes	characteristic
38	#334×C₁₃₇	C₂²	1	1	yes	characteristic
39	#333×C₁₃₇	C₂²	1	2	yes	—
40	#331×C₁₃₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
43	D₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
47	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
48	C₂×SD₁₆×C₁₃₇	D₄	1	1	yes	characteristic
49	C₂×D₈×C₁₃₇	—	2	2	no	—
50	C₂×D₈×C₁₃₇	—	2	1	no	—
51	C₂×D₈×C₁₃₇	—	2	1	no	—
52	C₂²×C₈×C₁₃₇	—	2	1	no	—
53	C₄⋊Q₈×C₁₃₇	C₂³	1	2	yes	—
54	#127×C₁₃₇	C₂³	1	2	yes	—
55	#125×C₁₃₇	—	2	2	no	—
56	#124×C₁₃₇	—	2	2	no	—
57	#124×C₁₃₇	—	2	2	no	—
58	#123×C₁₃₇	—	4	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
61	C₄×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
63	C₄×D₄×C₁₃₇	—	2	2	no	—
64	C₄×D₄×C₁₃₇	—	2	2	no	—
65	C₄×D₄×C₁₃₇	—	2	2	no	—
66	C₄×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
68	#107×C₁₃₇	—	2	1	no	—
69	#107×C₁₃₇	—	2	1	no	—
70	#107×C₁₃₇	—	2	2	no	—
71	#107×C₁₃₇	—	2	2	no	—
72	#107×C₁₃₇	D₄	1	1	yes	characteristic
73	#106×C₁₃₇	D₄	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₇	—	2	1	no	—
75	C₄⋊C₈×C₁₃₇	—	2	2	no	—
76	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
78	C₄⋊C₈×C₁₃₇	C₂³	1	1	yes	characteristic
79	#103×C₁₃₇	—	2	2	no	—
80	#103×C₁₃₇	—	2	2	no	—
81	#103×C₁₃₇	D₄	1	1	yes	characteristic
82	#103×C₁₃₇	D₄	1	2	yes	—
83	#102×C₁₃₇	—	2	2	no	—
84	#102×C₁₃₇	—	2	2	no	—
85	#102×C₁₃₇	—	2	2	no	—
86	#102×C₁₃₇	—	2	2	no	—
87	#102×C₁₃₇	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	—	2	2	no	—
90	C₄×C₈×C₁₃₇	—	2	1	no	—
91	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	4	2	no	—
103	C₂²×C₄×C₁₃₇	—	4	2	no	—
104	Q₁₆×C₁₃₇	—	2	2	no	—
105	SD₁₆×C₁₃₇	—	2	2	no	—
106	SD₁₆×C₁₃₇	—	8	4	no	—
107	SD₁₆×C₁₃₇	—	8	2	no	—
108	D₈×C₁₃₇	—	4	4	no	—
109	D₈×C₁₃₇	—	4	2	no	—
110	D₈×C₁₃₇	—	8	1	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	—	4	2	no	—
116	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₁₃₇	—	2	2	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	2	2	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	4	2	no	—
125	C₄⋊C₄×C₁₃₇	—	4	2	no	—
126	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
134	C₄²×C₁₃₇	—	2	1	no	—
135	C₄²×C₁₃₇	—	2	2	no	—
136	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
137	C₂³×C₁₃₇	—	2	1	no	—
138	C₂³×C₁₃₇	—	4	2	no	—
139	Q₈×C₁₃₇	—	2	1	no	—
140	Q₈×C₁₃₇	—	2	2	no	—
141	Q₈×C₁₃₇	—	2	2	no	—
142	Q₈×C₁₃₇	—	2	1	no	—
143	Q₈×C₁₃₇	—	8	2	no	—
144	D₄×C₁₃₇	—	2	1	no	—
145	D₄×C₁₃₇	—	4	2	no	—
146	D₄×C₁₃₇	—	4	2	no	—
147	D₄×C₁₃₇	—	4	2	no	—
148	D₄×C₁₃₇	—	4	2	no	—
149	D₄×C₁₃₇	—	8	2	no	—
150	D₄×C₁₃₇	#135	1	2	yes	—
151	C₂×C₄×C₁₃₇	—	2	1	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	4	1	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	16	2	no	—
160	C₂×C₄×C₁₃₇	—	16	2	no	—
161	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₁₃₇	—	2	2	no	—
165	C₈×C₁₃₇	—	2	1	no	—
166	C₈×C₁₃₇	—	2	1	no	—
167	C₈×C₁₃₇	—	2	1	no	—
168	C₈×C₁₃₇	—	4	1	no	—
169	C₈×C₁₃₇	—	4	2	no	—
170	C₈×C₁₃₇	—	4	1	no	—
171	C₈×C₁₃₇	#135	1	2	yes	—
172	C₂²×C₁₃₇	—	2	2	no	—
173	C₂²×C₁₃₇	—	4	1	no	—
174	C₂²×C₁₃₇	—	4	1	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	2	no	—
177	C₂²×C₁₃₇	—	8	2	no	—
178	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
179	C₄×C₁₃₇	—	2	1	no	—
180	C₄×C₁₃₇	—	4	1	no	—
181	C₄×C₁₃₇	—	4	2	no	—
182	C₄×C₁₃₇	—	4	1	no	—
183	C₄×C₁₃₇	—	4	1	no	—
184	C₄×C₁₃₇	—	4	2	no	—
185	C₄×C₁₃₇	—	8	2	no	—
186	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
187	C₄×C₁₃₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₁₃₇	#577	1	1	yes	characteristic
189	C₄×C₁₃₇	#578	1	1	yes	characteristic
190	C₂×C₁₃₇	—	4	2	no	—
191	C₂×C₁₃₇	—	16	2	no	—
192	C₂×C₁₃₇	#3284	1	1	yes	characteristic
193	C₂×C₁₃₇	#3285	1	1	yes	characteristic
194	C₂×C₁₃₇	#3292	1	1	yes	characteristic
195	#20012	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₇	#20012	1	1	yes	characteristic, direct product factor, Sylow
197	#3396	C₂×C₁₃₇	1	1	yes	characteristic, complemented
198	#3361	C₂×C₁₃₇	1	2	yes	complemented
199	#3338	C₂×C₁₃₇	1	1	yes	characteristic, complemented
200	#1706	C₂×C₁₃₇	1	1	yes	characteristic, complemented
201	#1678	C₂×C₁₃₇	1	2	yes	complemented
202	#1676	C₂×C₁₃₇	1	1	yes	characteristic, complemented
203	#1667	C₂×C₁₃₇	1	1	yes	characteristic
204	#1630	C₂×C₁₃₇	1	2	yes	complemented
205	#1622	C₂×C₁₃₇	1	2	yes	complemented
206	C₈×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	C₈×SD₁₆	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	#559	C₂²×C₁₃₇	1	2	yes	—
209	#554	C₂²×C₁₃₇	1	2	yes	—
210	#500	C₂²×C₁₃₇	1	1	yes	characteristic
211	#495	—	2	1	no	—
212	#493	C₂²×C₁₃₇	1	1	yes	characteristic
213	#492	C₂²×C₁₃₇	1	2	yes	—
214	#488	—	2	2	no	—
215	#486	C₂²×C₁₃₇	1	2	yes	—
216	#484	—	2	2	no	—
217	#478	—	2	2	no	—
218	#477	C₂²×C₁₃₇	1	2	yes	—
219	#477	C₂²×C₁₃₇	1	2	yes	—
220	#467	—	2	1	no	—
221	#463	—	2	2	no	—
222	#463	—	2	2	no	—
223	#460	C₂²×C₁₃₇	1	2	yes	—
224	#459	C₂²×C₁₃₇	1	2	yes	—
225	C₈×Q₈	C₂²×C₁₃₇	1	2	yes	—
226	C₈×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₄×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	—	2	2	no	—
231	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×#107	—	2	1	no	—
233	#335	C₂²×C₁₃₇	1	1	yes	characteristic
234	#334	C₂²×C₁₃₇	1	1	yes	characteristic
235	#333	C₂²×C₁₃₇	1	2	yes	—
236	#331	C₂²×C₁₃₇	1	2	yes	—
237	Q₈⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
238	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
239	D₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₈²	C₂²×C₁₃₇	1	1	yes	characteristic
241	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×SD₁₆	D₄×C₁₃₇	1	1	yes	characteristic
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₄⋊Q₈	C₂³×C₁₃₇	1	2	yes	—
250	#127	C₂³×C₁₃₇	1	2	yes	—
251	#125	—	2	2	no	—
252	#124	—	2	2	no	—
253	#124	—	2	2	no	—
254	#123	—	4	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
258	C₄×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	2	no	—
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#107	D₄×C₁₃₇	1	1	yes	characteristic
269	#106	D₄×C₁₃₇	1	1	yes	characteristic
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	D₄×C₁₃₇	1	1	yes	characteristic
278	#103	D₄×C₁₃₇	1	2	yes	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	D₄×C₁₃₇	1	1	yes	characteristic
284	C₂²⋊C₈	—	2	1	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
292	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	Q₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	8	4	no	—
303	SD₁₆	—	8	2	no	—
304	D₈	—	4	4	no	—
305	D₈	—	4	2	no	—
306	D₈	—	8	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
323	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
324	C₄⋊C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
333	C₂³	—	2	1	no	—
334	C₂³	—	4	2	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	2	1	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	8	2	no	—
346	D₄	#135×C₁₃₇	1	2	yes	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	16	2	no	—
356	C₂×C₄	—	16	2	no	—
357	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₈	#135×C₁₃₇	1	2	yes	—
368	C₂²	—	2	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	2	no	—
382	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
383	C₄	C₂×#135×C₁₃₇	1	1	yes	characteristic
384	C₄	#577×C₁₃₇	1	1	yes	characteristic
385	C₄	#578×C₁₃₇	1	1	yes	characteristic
386	C₂	—	4	2	no	—
387	C₂	—	16	2	no	—
388	C₂	#3284×C₁₃₇	1	1	yes	characteristic
389	C₂	#3285×C₁₃₇	1	1	yes	characteristic
390	C₂	#3292×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#1667×C₁₃₇	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3396×C₁₃₇	C₂	semidirect
2. #3361×C₁₃₇	C₂	semidirect
3. #3338×C₁₃₇	C₂	semidirect
4. #1706×C₁₃₇	C₂	semidirect
5. #1678×C₁₃₇	C₂	semidirect
6. #1676×C₁₃₇	C₂	semidirect
8. #1630×C₁₃₇	C₂	semidirect
9. #1622×C₁₃₇	C₂	semidirect
10. C₈×Q₁₆×C₁₃₇	C₂	semidirect
11. C₈×SD₁₆×C₁₃₇	C₂	semidirect
195. #20012	C₁₃₇	direct (N × H)
196. C₁₃₇	#20012	direct (N × H)
197. #3396	C₂×C₁₃₇	semidirect
198. #3361	C₂×C₁₃₇	semidirect
199. #3338	C₂×C₁₃₇	semidirect
200. #1706	C₂×C₁₃₇	semidirect
201. #1678	C₂×C₁₃₇	semidirect
202. #1676	C₂×C₁₃₇	semidirect
204. #1630	C₂×C₁₃₇	semidirect
205. #1622	C₂×C₁₃₇	semidirect
206. C₈×Q₁₆	C₂×C₁₃₇	semidirect
207. C₈×SD₁₆	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3396×C₁₃₇	2
#3361×C₁₃₇	2
#3338×C₁₃₇	2
#1706×C₁₃₇	2
#1678×C₁₃₇	2
#1676×C₁₃₇	2
#1667×C₁₃₇	2
#1630×C₁₃₇	2
#1622×C₁₃₇	2
C₈×Q₁₆×C₁₃₇	2
C₈×SD₁₆×C₁₃₇	2
#20012	137

Subgroups — C137×#20012 #46869398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20012 #46869398