Subgroups — C₁₃₇×#28665 #46878051

Order 35072.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#490×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2641×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2330×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2067×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1992×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1926×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1925×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
15	#499×C₁₃₇	—	2	4	no	—
16	#490×C₁₃₇	—	2	4	no	—
17	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	#394×C₁₃₇	—	2	2	no	—
28	#394×C₁₃₇	—	2	2	no	—
29	#390×C₁₃₇	C₂²	1	2	yes	—
30	#390×C₁₃₇	C₂²	1	2	yes	—
31	#389×C₁₃₇	—	2	2	no	—
32	#389×C₁₃₇	C₂²	1	2	yes	—
33	#387×C₁₃₇	—	2	2	no	—
34	#384×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	#376×C₁₃₇	C₂²	1	1	yes	characteristic
37	#340×C₁₃₇	C₂²	1	2	yes	—
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₇	—	2	2	no	—
42	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	#127×C₁₃₇	—	2	2	no	—
48	#127×C₁₃₇	—	2	2	no	—
49	#125×C₁₃₇	—	2	2	no	—
50	#125×C₁₃₇	—	2	2	no	—
51	#125×C₁₃₇	—	2	2	no	—
52	#125×C₁₃₇	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	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	#106×C₁₃₇	—	2	4	no	—
70	C₄⋊C₈×C₁₃₇	—	2	2	no	—
71	C₄⋊C₈×C₁₃₇	—	2	2	no	—
72	#102×C₁₃₇	—	2	4	no	—
73	#102×C₁₃₇	—	2	4	no	—
74	#102×C₁₃₇	—	2	4	no	—
75	#102×C₁₃₇	—	2	4	no	—
76	#97×C₁₃₇	—	2	2	no	—
77	C₄×C₈×C₁₃₇	—	2	2	no	—
78	#95×C₁₃₇	—	2	2	no	—
79	#95×C₁₃₇	—	2	2	no	—
80	#95×C₁₃₇	D₄	1	2	yes	—
81	#95×C₁₃₇	D₄	1	2	yes	—
82	C₂⁴×C₁₃₇	—	2	2	no	—
83	C₂×D₄×C₁₃₇	—	2	2	no	—
84	C₂×D₄×C₁₃₇	—	2	2	no	—
85	C₂×D₄×C₁₃₇	—	2	2	no	—
86	C₂×D₄×C₁₃₇	—	2	2	no	—
87	C₂×D₄×C₁₃₇	—	2	2	no	—
88	C₂×D₄×C₁₃₇	—	2	2	no	—
89	C₂×D₄×C₁₃₇	—	4	4	no	—
90	C₂×D₄×C₁₃₇	—	8	2	no	—
91	C₂×D₄×C₁₃₇	—	8	2	no	—
92	C₂²×C₄×C₁₃₇	—	2	2	no	—
93	C₂²×C₄×C₁₃₇	—	2	2	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₁₃₇	—	2	1	no	—
101	C₂×C₈×C₁₃₇	—	2	1	no	—
102	C₂×C₈×C₁₃₇	—	2	1	no	—
103	C₂×C₈×C₁₃₇	—	2	1	no	—
104	C₂×C₈×C₁₃₇	—	2	1	no	—
105	C₂×C₈×C₁₃₇	—	2	1	no	—
106	C₂×C₈×C₁₃₇	—	2	1	no	—
107	C₂×C₈×C₁₃₇	—	2	1	no	—
108	C₂×C₈×C₁₃₇	—	2	1	no	—
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	#41	1	2	yes	—
111	C₂×C₈×C₁₃₇	#41	1	2	yes	—
112	C₄⋊C₄×C₁₃₇	—	2	8	no	—
113	C₄⋊C₄×C₁₃₇	—	2	2	no	—
114	C₄⋊C₄×C₁₃₇	—	2	2	no	—
115	C₄⋊C₄×C₁₃₇	—	2	2	no	—
116	C₄⋊C₄×C₁₃₇	—	2	2	no	—
117	C₄⋊C₄×C₁₃₇	—	2	2	no	—
118	C₄⋊C₄×C₁₃₇	—	4	4	no	—
119	C₄⋊C₄×C₁₃₇	—	8	2	no	—
120	C₄⋊C₄×C₁₃₇	—	8	2	no	—
121	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
122	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
123	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
124	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
125	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
126	C₄²×C₁₃₇	—	2	1	no	—
127	C₄²×C₁₃₇	—	2	1	no	—
128	C₄²×C₁₃₇	—	2	1	no	—
129	C₄²×C₁₃₇	—	2	1	no	—
130	C₄²×C₁₃₇	—	8	2	no	—
131	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
132	C₄²×C₁₃₇	#41	1	2	yes	—
133	C₂³×C₁₃₇	—	4	2	no	—
134	C₂³×C₁₃₇	—	4	2	no	—
135	C₂³×C₁₃₇	—	4	2	no	—
136	C₂³×C₁₃₇	—	4	2	no	—
137	C₂³×C₁₃₇	—	4	2	no	—
138	C₂³×C₁₃₇	—	4	2	no	—
139	C₂³×C₁₃₇	—	4	2	no	—
140	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₁₃₇	—	4	2	no	—
142	D₄×C₁₃₇	—	4	2	no	—
143	D₄×C₁₃₇	—	4	2	no	—
144	D₄×C₁₃₇	—	4	2	no	—
145	D₄×C₁₃₇	—	8	8	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	1	no	—
150	C₂×C₄×C₁₃₇	—	2	1	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	—	2	2	no	—
156	C₂×C₄×C₁₃₇	—	4	2	no	—
157	C₂×C₄×C₁₃₇	—	4	2	no	—
158	C₂×C₄×C₁₃₇	—	4	2	no	—
159	C₂×C₄×C₁₃₇	—	4	2	no	—
160	C₂×C₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	4	2	no	—
162	C₂×C₄×C₁₃₇	—	4	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	#121	1	4	yes	—
165	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
171	C₈×C₁₃₇	—	2	2	no	—
172	C₈×C₁₃₇	—	2	2	no	—
173	C₈×C₁₃₇	—	4	1	no	—
174	C₈×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	—	8	2	no	—
179	C₂²×C₁₃₇	—	8	2	no	—
180	C₂²×C₁₃₇	—	8	2	no	—
181	C₂²×C₁₃₇	—	8	2	no	—
182	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
183	C₂²×C₁₃₇	#532	1	1	yes	characteristic
184	C₂²×C₁₃₇	#536	1	1	yes	characteristic
185	C₂²×C₁₃₇	#576	1	2	yes	—
186	C₂²×C₁₃₇	#577	1	2	yes	—
187	C₄×C₁₃₇	—	2	4	no	—
188	C₄×C₁₃₇	—	4	1	no	—
189	C₄×C₁₃₇	—	4	1	no	—
190	C₄×C₁₃₇	—	4	2	no	—
191	C₄×C₁₃₇	—	4	4	no	—
192	C₄×C₁₃₇	—	8	2	no	—
193	C₄×C₁₃₇	—	8	2	no	—
194	C₄×C₁₃₇	#548	1	1	yes	characteristic
195	C₄×C₁₃₇	#548	1	1	yes	characteristic
196	C₄×C₁₃₇	#556	1	1	yes	characteristic
197	C₄×C₁₃₇	#556	1	1	yes	characteristic
198	C₂×C₁₃₇	—	16	2	no	—
199	C₂×C₁₃₇	#2545	1	1	yes	characteristic
200	C₂×C₁₃₇	#3045	1	2	yes	—
201	C₂×C₁₃₇	#3174	1	1	yes	characteristic
202	C₂×C₁₃₇	#3176	1	1	yes	characteristic
203	C₂×C₁₃₇	#3241	1	2	yes	—
204	#28665	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₇	#28665	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#499	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	C₂×#490	C₂×C₁₃₇	1	1	yes	characteristic
208	#2641	C₂×C₁₃₇	1	1	yes	characteristic
209	#2330	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#2067	C₂×C₁₃₇	1	2	yes	complemented
211	#2065	C₂×C₁₃₇	1	2	yes	complemented
212	#1992	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	#1957	C₂×C₁₃₇	1	1	yes	characteristic
214	#1926	C₂×C₁₃₇	1	2	yes	complemented
215	#1925	C₂×C₁₃₇	1	2	yes	complemented
216	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
220	#499	—	2	4	no	—
221	#490	—	2	4	no	—
222	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
223	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
227	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
228	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
229	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
230	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
232	#394	—	2	2	no	—
233	#394	—	2	2	no	—
234	#390	C₂²×C₁₃₇	1	2	yes	—
235	#390	C₂²×C₁₃₇	1	2	yes	—
236	#389	—	2	2	no	—
237	#389	C₂²×C₁₃₇	1	2	yes	—
238	#387	—	2	2	no	—
239	#384	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
241	#376	C₂²×C₁₃₇	1	1	yes	characteristic
242	#340	C₂²×C₁₃₇	1	2	yes	—
243	#340	C₂²×C₁₃₇	1	2	yes	—
244	#336	C₂²×C₁₃₇	1	1	yes	characteristic
245	#336	C₂²×C₁₃₇	1	1	yes	characteristic
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
252	#127	—	2	2	no	—
253	#127	—	2	2	no	—
254	#125	—	2	2	no	—
255	#125	—	2	2	no	—
256	#125	—	2	2	no	—
257	#125	D₄×C₁₃₇	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
273	#107	—	2	4	no	—
274	#106	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#102	—	2	4	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	D₄×C₁₃₇	1	2	yes	—
286	#95	D₄×C₁₃₇	1	2	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	#41×C₁₃₇	1	2	yes	—
316	C₂×C₈	#41×C₁₃₇	1	2	yes	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	8	2	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	8	2	no	—
336	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
337	C₄²	#41×C₁₃₇	1	2	yes	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	#121×C₁₃₇	1	4	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
374	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
375	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	1	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
388	C₂²	#532×C₁₃₇	1	1	yes	characteristic
389	C₂²	#536×C₁₃₇	1	1	yes	characteristic
390	C₂²	#576×C₁₃₇	1	2	yes	—
391	C₂²	#577×C₁₃₇	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	#548×C₁₃₇	1	1	yes	characteristic
400	C₄	#548×C₁₃₇	1	1	yes	characteristic
401	C₄	#556×C₁₃₇	1	1	yes	characteristic
402	C₄	#556×C₁₃₇	1	1	yes	characteristic
403	C₂	—	16	2	no	—
404	C₂	#2545×C₁₃₇	1	1	yes	characteristic
405	C₂	#3045×C₁₃₇	1	2	yes	—
406	C₂	#3174×C₁₃₇	1	1	yes	characteristic
407	C₂	#3176×C₁₃₇	1	1	yes	characteristic
408	C₂	#3241×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
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×#499×C₁₃₇	C₂	semidirect
4. #2330×C₁₃₇	C₂	semidirect
5. #2067×C₁₃₇	C₂	semidirect
6. #2065×C₁₃₇	C₂	semidirect
7. #1992×C₁₃₇	C₂	semidirect
9. #1926×C₁₃₇	C₂	semidirect
10. #1925×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
204. #28665	C₁₃₇	direct (N × H)
205. C₁₃₇	#28665	direct (N × H)
206. C₂×#499	C₂×C₁₃₇	semidirect
209. #2330	C₂×C₁₃₇	semidirect
210. #2067	C₂×C₁₃₇	semidirect
211. #2065	C₂×C₁₃₇	semidirect
212. #1992	C₂×C₁₃₇	semidirect
214. #1926	C₂×C₁₃₇	semidirect
215. #1925	C₂×C₁₃₇	semidirect
216. #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×#499×C₁₃₇	2
C₂×#490×C₁₃₇	2
#2641×C₁₃₇	2
#2330×C₁₃₇	2
#2067×C₁₃₇	2
#2065×C₁₃₇	2
#1992×C₁₃₇	2
#1957×C₁₃₇	2
#1926×C₁₃₇	2
#1925×C₁₃₇	2
#1768×C₁₃₇	2
#28665	137

Subgroups — C137×#28665 #46878051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28665 #46878051