Subgroups — C₁₃₇×#28663 #46878049

Order 35072.

740 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2640×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2331×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2068×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2067×C₁₃₇	C₂	1	2	yes	maximal
7	#1993×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1958×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1928×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1925×C₁₃₇	C₂	1	2	yes	maximal
11	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
15	#500×C₁₃₇	—	2	4	no	—
16	#489×C₁₃₇	—	2	4	no	—
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	#397×C₁₃₇	—	2	2	no	—
27	#393×C₁₃₇	—	2	2	no	—
28	#391×C₁₃₇	—	2	2	no	—
29	#391×C₁₃₇	C₂²	1	1	yes	characteristic
30	#391×C₁₃₇	C₂²	1	1	yes	characteristic
31	#390×C₁₃₇	C₂²	1	1	yes	characteristic
32	#390×C₁₃₇	C₂²	1	1	yes	characteristic
33	#389×C₁₃₇	C₂²	1	2	yes	—
34	#387×C₁₃₇	—	2	2	no	—
35	#382×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
37	#376×C₁₃₇	C₂²	1	1	yes	characteristic
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	—	2	1	no	—
42	C₂²×Q₈×C₁₃₇	—	2	1	no	—
43	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
48	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
51	#124×C₁₃₇	—	2	2	no	—
52	#124×C₁₃₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄²×C₁₃₇	—	2	2	no	—
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
68	#107×C₁₃₇	—	2	4	no	—
69	#107×C₁₃₇	—	2	4	no	—
70	C₄⋊C₈×C₁₃₇	—	2	4	no	—
71	#103×C₁₃₇	—	2	4	no	—
72	#103×C₁₃₇	—	2	4	no	—
73	#102×C₁₃₇	—	2	4	no	—
74	#102×C₁₃₇	—	2	4	no	—
75	#97×C₁₃₇	—	2	2	no	—
76	C₄×C₈×C₁₃₇	—	2	2	no	—
77	#95×C₁₃₇	—	2	2	no	—
78	#95×C₁₃₇	—	2	1	no	—
79	#95×C₁₃₇	—	2	1	no	—
80	#95×C₁₃₇	—	2	2	no	—
81	#95×C₁₃₇	—	2	2	no	—
82	#95×C₁₃₇	—	2	2	no	—
83	#95×C₁₃₇	D₄	1	2	yes	—
84	#95×C₁₃₇	D₄	1	2	yes	—
85	C₂⁴×C₁₃₇	—	2	1	no	—
86	C₂×Q₈×C₁₃₇	—	2	4	no	—
87	C₂×Q₈×C₁₃₇	—	2	1	no	—
88	C₂×Q₈×C₁₃₇	—	2	2	no	—
89	C₂×Q₈×C₁₃₇	—	2	1	no	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	4	2	no	—
92	C₂×Q₈×C₁₃₇	—	8	2	no	—
93	C₂×Q₈×C₁₃₇	—	8	2	no	—
94	C₂×D₄×C₁₃₇	—	2	1	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	2	2	no	—
99	C₂²×C₄×C₁₃₇	—	2	2	no	—
100	C₂²×C₄×C₁₃₇	—	2	1	no	—
101	C₂²×C₄×C₁₃₇	—	2	1	no	—
102	C₂²×C₄×C₁₃₇	—	2	1	no	—
103	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₃₇	—	2	2	no	—
109	C₂×C₈×C₁₃₇	—	2	2	no	—
110	C₂×C₈×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	—	2	2	no	—
113	C₂×C₈×C₁₃₇	#41	1	4	yes	—
114	C₄⋊C₄×C₁₃₇	—	2	4	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	1	no	—
117	C₄⋊C₄×C₁₃₇	—	2	1	no	—
118	C₄⋊C₄×C₁₃₇	—	2	2	no	—
119	C₄⋊C₄×C₁₃₇	—	2	2	no	—
120	C₄⋊C₄×C₁₃₇	—	2	1	no	—
121	C₄⋊C₄×C₁₃₇	—	2	1	no	—
122	C₄⋊C₄×C₁₃₇	—	4	2	no	—
123	C₄⋊C₄×C₁₃₇	—	8	2	no	—
124	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
126	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
128	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
129	C₄²×C₁₃₇	—	2	2	no	—
130	C₄²×C₁₃₇	—	2	2	no	—
131	C₄²×C₁₃₇	—	8	2	no	—
132	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
133	C₄²×C₁₃₇	#41	1	2	yes	—
134	C₂³×C₁₃₇	—	4	1	no	—
135	C₂³×C₁₃₇	—	4	1	no	—
136	C₂³×C₁₃₇	—	4	1	no	—
137	C₂³×C₁₃₇	—	4	2	no	—
138	C₂³×C₁₃₇	—	4	2	no	—
139	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₃₇	—	4	2	no	—
141	Q₈×C₁₃₇	—	4	2	no	—
142	Q₈×C₁₃₇	—	8	4	no	—
143	Q₈×C₁₃₇	—	8	4	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	D₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄×C₁₃₇	—	2	2	no	—
147	C₂×C₄×C₁₃₇	—	2	2	no	—
148	C₂×C₄×C₁₃₇	—	2	4	no	—
149	C₂×C₄×C₁₃₇	—	2	2	no	—
150	C₂×C₄×C₁₃₇	—	2	2	no	—
151	C₂×C₄×C₁₃₇	—	2	2	no	—
152	C₂×C₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	2	no	—
154	C₂×C₄×C₁₃₇	—	2	2	no	—
155	C₂×C₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	4	2	no	—
157	C₂×C₄×C₁₃₇	—	4	1	no	—
158	C₂×C₄×C₁₃₇	—	4	1	no	—
159	C₂×C₄×C₁₃₇	—	4	1	no	—
160	C₂×C₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	4	1	no	—
162	C₂×C₄×C₁₃₇	—	4	1	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	#121	1	2	yes	—
168	C₂×C₄×C₁₃₇	#121	1	2	yes	—
169	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₁₃₇	—	2	4	no	—
174	C₈×C₁₃₇	—	4	2	no	—
175	C₂²×C₁₃₇	—	8	2	no	—
176	C₂²×C₁₃₇	—	8	2	no	—
177	C₂²×C₁₃₇	—	8	1	no	—
178	C₂²×C₁₃₇	—	8	1	no	—
179	C₂²×C₁₃₇	—	8	1	no	—
180	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
181	C₂²×C₁₃₇	#532	1	1	yes	characteristic
182	C₂²×C₁₃₇	#536	1	1	yes	characteristic
183	C₂²×C₁₃₇	#576	1	2	yes	—
184	C₂²×C₁₃₇	#578	1	2	yes	—
185	C₄×C₁₃₇	—	2	2	no	—
186	C₄×C₁₃₇	—	2	2	no	—
187	C₄×C₁₃₇	—	4	2	no	—
188	C₄×C₁₃₇	—	4	2	no	—
189	C₄×C₁₃₇	—	4	4	no	—
190	C₄×C₁₃₇	—	8	2	no	—
191	C₄×C₁₃₇	—	8	1	no	—
192	C₄×C₁₃₇	—	8	1	no	—
193	C₄×C₁₃₇	—	8	1	no	—
194	C₄×C₁₃₇	#548	1	2	yes	—
195	C₄×C₁₃₇	#556	1	2	yes	—
196	C₂×C₁₃₇	—	16	1	no	—
197	C₂×C₁₃₇	#2545	1	1	yes	characteristic
198	C₂×C₁₃₇	#3041	1	1	yes	characteristic
199	C₂×C₁₃₇	#3044	1	1	yes	characteristic
200	C₂×C₁₃₇	#3175	1	2	yes	—
201	C₂×C₁₃₇	#3243	1	2	yes	—
202	#28663	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₇	#28663	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×#500	C₂×C₁₃₇	1	1	yes	characteristic, complemented
205	C₂×#489	C₂×C₁₃₇	1	1	yes	characteristic
206	#2640	C₂×C₁₃₇	1	1	yes	characteristic
207	#2331	C₂×C₁₃₇	1	1	yes	characteristic, complemented
208	#2068	C₂×C₁₃₇	1	2	yes	complemented
209	#2067	C₂×C₁₃₇	1	2	yes	—
210	#1993	C₂×C₁₃₇	1	1	yes	characteristic, complemented
211	#1958	C₂×C₁₃₇	1	1	yes	characteristic
212	#1928	C₂×C₁₃₇	1	2	yes	complemented
213	#1925	C₂×C₁₃₇	1	2	yes	—
214	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
215	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
218	#500	—	2	4	no	—
219	#489	—	2	4	no	—
220	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
221	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
223	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
224	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
225	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
226	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
227	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
229	#397	—	2	2	no	—
230	#393	—	2	2	no	—
231	#391	—	2	2	no	—
232	#391	C₂²×C₁₃₇	1	1	yes	characteristic
233	#391	C₂²×C₁₃₇	1	1	yes	characteristic
234	#390	C₂²×C₁₃₇	1	1	yes	characteristic
235	#390	C₂²×C₁₃₇	1	1	yes	characteristic
236	#389	C₂²×C₁₃₇	1	2	yes	—
237	#387	—	2	2	no	—
238	#382	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
240	#376	C₂²×C₁₃₇	1	1	yes	characteristic
241	#340	C₂²×C₁₃₇	1	2	yes	—
242	#340	C₂²×C₁₃₇	1	2	yes	—
243	#336	C₂²×C₁₃₇	1	2	yes	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
254	#124	—	2	2	no	—
255	#124	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
271	#107	—	2	4	no	—
272	#107	—	2	4	no	—
273	C₄⋊C₈	—	2	4	no	—
274	#103	—	2	4	no	—
275	#103	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	4	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	D₄×C₁₃₇	1	2	yes	—
287	#95	D₄×C₁₃₇	1	2	yes	—
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	8	2	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	#41×C₁₃₇	1	4	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
336	C₄²	#41×C₁₃₇	1	2	yes	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	8	4	no	—
346	Q₈	—	8	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	#121×C₁₃₇	1	2	yes	—
371	C₂×C₄	#121×C₁₃₇	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
374	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
376	C₈	—	2	4	no	—
377	C₈	—	4	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
384	C₂²	#532×C₁₃₇	1	1	yes	characteristic
385	C₂²	#536×C₁₃₇	1	1	yes	characteristic
386	C₂²	#576×C₁₃₇	1	2	yes	—
387	C₂²	#578×C₁₃₇	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	#548×C₁₃₇	1	2	yes	—
398	C₄	#556×C₁₃₇	1	2	yes	—
399	C₂	—	16	1	no	—
400	C₂	#2545×C₁₃₇	1	1	yes	characteristic
401	C₂	#3041×C₁₃₇	1	1	yes	characteristic
402	C₂	#3044×C₁₃₇	1	1	yes	characteristic
403	C₂	#3175×C₁₃₇	1	2	yes	—
404	C₂	#3243×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ #376×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#500×C₁₃₇	C₂	semidirect
4. #2331×C₁₃₇	C₂	semidirect
5. #2068×C₁₃₇	C₂	semidirect
7. #1993×C₁₃₇	C₂	semidirect
9. #1928×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
202. #28663	C₁₃₇	direct (N × H)
203. C₁₃₇	#28663	direct (N × H)
204. C₂×#500	C₂×C₁₃₇	semidirect
207. #2331	C₂×C₁₃₇	semidirect
208. #2068	C₂×C₁₃₇	semidirect
210. #1993	C₂×C₁₃₇	semidirect
212. #1928	C₂×C₁₃₇	semidirect
214. #1768	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#500×C₁₃₇	2
C₂×#489×C₁₃₇	2
#2640×C₁₃₇	2
#2331×C₁₃₇	2
#2068×C₁₃₇	2
#2067×C₁₃₇	2
#1993×C₁₃₇	2
#1958×C₁₃₇	2
#1928×C₁₃₇	2
#1925×C₁₃₇	2
#1768×C₁₃₇	2
#28663	137

Subgroups — C137×#28663 #46878049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28663 #46878049