Subgroups — C₁₃₇×#28760 #46878146

Order 35072.

804 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#491×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#488×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2658×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2330×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2043×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2042×C₁₃₇	C₂	1	2	yes	maximal
7	#1983×C₁₃₇	C₂	1	2	yes	maximal
8	#1981×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1959×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#1956×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
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×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
19	#491×C₁₃₇	—	2	4	no	—
20	#488×C₁₃₇	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
32	#399×C₁₃₇	—	2	2	no	—
33	#399×C₁₃₇	—	2	2	no	—
34	#389×C₁₃₇	—	2	2	no	—
35	#389×C₁₃₇	C₂²	1	2	yes	—
36	#387×C₁₃₇	—	2	2	no	—
37	#384×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
39	#376×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
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	4	no	—
50	C₄⋊Q₈×C₁₃₇	—	4	2	no	—
51	#125×C₁₃₇	—	2	2	no	—
52	#125×C₁₃₇	D₄	1	4	yes	—
53	#124×C₁₃₇	—	2	2	no	—
54	#124×C₁₃₇	—	2	2	no	—
55	#124×C₁₃₇	—	2	4	no	—
56	#124×C₁₃₇	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₄²×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₇	—	2	4	no	—
75	#103×C₁₃₇	—	2	4	no	—
76	#103×C₁₃₇	—	2	4	no	—
77	#103×C₁₃₇	—	2	4	no	—
78	#103×C₁₃₇	—	4	2	no	—
79	#103×C₁₃₇	—	4	2	no	—
80	#103×C₁₃₇	—	4	2	no	—
81	#102×C₁₃₇	—	2	4	no	—
82	#102×C₁₃₇	—	4	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	C₄×C₈×C₁₃₇	—	2	2	no	—
85	#95×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	—	2	2	no	—
87	#95×C₁₃₇	D₄	1	2	yes	—
88	#95×C₁₃₇	D₄	1	2	yes	—
89	C₂⁴×C₁₃₇	—	2	1	no	—
90	C₂×Q₈×C₁₃₇	—	2	1	no	—
91	C₂×Q₈×C₁₃₇	—	2	1	no	—
92	C₂×Q₈×C₁₃₇	—	2	1	no	—
93	C₂×Q₈×C₁₃₇	—	2	1	no	—
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	2	2	no	—
100	C₂×Q₈×C₁₃₇	—	2	2	no	—
101	C₂×Q₈×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	1	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	1	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂²×C₄×C₁₃₇	—	2	2	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	2	1	no	—
109	C₂²×C₄×C₁₃₇	—	2	1	no	—
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	2	8	no	—
123	C₄⋊C₄×C₁₃₇	—	2	2	no	—
124	C₄⋊C₄×C₁₃₇	—	2	2	no	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	4	2	no	—
127	C₄⋊C₄×C₁₃₇	—	4	2	no	—
128	C₄⋊C₄×C₁₃₇	—	4	4	no	—
129	C₄⋊C₄×C₁₃₇	—	4	4	no	—
130	C₄⋊C₄×C₁₃₇	—	8	2	no	—
131	C₄⋊C₄×C₁₃₇	—	8	2	no	—
132	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
134	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
135	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
137	C₄²×C₁₃₇	—	2	2	no	—
138	C₄²×C₁₃₇	—	8	2	no	—
139	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
140	C₄²×C₁₃₇	#41	1	2	yes	—
141	C₄²×C₁₃₇	#41	1	4	yes	—
142	C₂³×C₁₃₇	—	4	1	no	—
143	C₂³×C₁₃₇	—	4	1	no	—
144	C₂³×C₁₃₇	—	4	1	no	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	—	4	2	no	—
147	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	4	2	no	—
149	Q₈×C₁₃₇	—	4	2	no	—
150	Q₈×C₁₃₇	—	4	2	no	—
151	Q₈×C₁₃₇	—	4	2	no	—
152	Q₈×C₁₃₇	—	4	2	no	—
153	Q₈×C₁₃₇	—	4	2	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	D₄×C₁₃₇	—	4	2	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	4	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	4	2	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	1	no	—
169	C₂×C₄×C₁₃₇	—	4	1	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	1	no	—
172	C₂×C₄×C₁₃₇	—	4	1	no	—
173	C₂×C₄×C₁₃₇	—	4	1	no	—
174	C₂×C₄×C₁₃₇	—	4	2	no	—
175	C₂×C₄×C₁₃₇	—	4	1	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	4	2	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	#121	1	4	yes	—
180	C₂×C₄×C₁₃₇	#124	1	4	yes	—
181	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
183	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₁₃₇	—	4	2	no	—
186	C₈×C₁₃₇	—	4	2	no	—
187	C₂²×C₁₃₇	—	8	2	no	—
188	C₂²×C₁₃₇	—	8	1	no	—
189	C₂²×C₁₃₇	—	8	1	no	—
190	C₂²×C₁₃₇	—	8	2	no	—
191	C₂²×C₁₃₇	—	8	1	no	—
192	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
193	C₂²×C₁₃₇	C₂×#124	1	1	yes	characteristic
194	C₂²×C₁₃₇	#535	1	1	yes	characteristic
195	C₂²×C₁₃₇	#577	1	2	yes	—
196	C₂²×C₁₃₇	#578	1	2	yes	—
197	C₄×C₁₃₇	—	2	4	no	—
198	C₄×C₁₃₇	—	2	4	no	—
199	C₄×C₁₃₇	—	4	1	no	—
200	C₄×C₁₃₇	—	4	1	no	—
201	C₄×C₁₃₇	—	4	4	no	—
202	C₄×C₁₃₇	—	8	2	no	—
203	C₄×C₁₃₇	—	8	1	no	—
204	C₄×C₁₃₇	—	8	1	no	—
205	C₄×C₁₃₇	—	8	1	no	—
206	C₄×C₁₃₇	#550	1	2	yes	—
207	C₄×C₁₃₇	#559	1	2	yes	—
208	C₂×C₁₃₇	—	16	1	no	—
209	C₂×C₁₃₇	#2548	1	1	yes	characteristic
210	C₂×C₁₃₇	#3046	1	2	yes	—
211	C₂×C₁₃₇	#3137	1	2	yes	—
212	C₂×C₁₃₇	#3221	1	1	yes	characteristic
213	C₂×C₁₃₇	#3223	1	1	yes	characteristic
214	#28760	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₇	#28760	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×#491	C₂×C₁₃₇	1	1	yes	characteristic, complemented
217	C₂×#488	C₂×C₁₃₇	1	1	yes	characteristic
218	#2658	C₂×C₁₃₇	1	1	yes	characteristic
219	#2330	C₂×C₁₃₇	1	1	yes	characteristic, complemented
220	#2043	C₂×C₁₃₇	1	2	yes	complemented
221	#2042	C₂×C₁₃₇	1	2	yes	—
222	#1983	C₂×C₁₃₇	1	2	yes	—
223	#1981	C₂×C₁₃₇	1	2	yes	complemented
224	#1959	C₂×C₁₃₇	1	1	yes	characteristic
225	#1956	C₂×C₁₃₇	1	1	yes	characteristic, complemented
226	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
227	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
230	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
231	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
232	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
234	#491	—	2	4	no	—
235	#488	—	2	4	no	—
236	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
237	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
239	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
240	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
242	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
243	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
244	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
245	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
247	#399	—	2	2	no	—
248	#399	—	2	2	no	—
249	#389	—	2	2	no	—
250	#389	C₂²×C₁₃₇	1	2	yes	—
251	#387	—	2	2	no	—
252	#384	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
254	#376	C₂²×C₁₃₇	1	1	yes	characteristic
255	#336	C₂²×C₁₃₇	1	2	yes	—
256	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	4	no	—
265	C₄⋊Q₈	—	4	2	no	—
266	#125	—	2	2	no	—
267	#125	D₄×C₁₃₇	1	4	yes	—
268	#124	—	2	2	no	—
269	#124	—	2	2	no	—
270	#124	—	2	4	no	—
271	#124	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
289	C₄⋊C₈	—	2	4	no	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	4	2	no	—
294	#103	—	4	2	no	—
295	#103	—	4	2	no	—
296	#102	—	2	4	no	—
297	#102	—	4	2	no	—
298	#97	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	D₄×C₁₃₇	1	2	yes	—
303	#95	D₄×C₁₃₇	1	2	yes	—
304	C₂⁴	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	4	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	8	2	no	—
354	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
355	C₄²	#41×C₁₃₇	1	2	yes	—
356	C₄²	#41×C₁₃₇	1	4	yes	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	#121×C₁₃₇	1	4	yes	—
395	C₂×C₄	#124×C₁₃₇	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
398	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
399	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
408	C₂²	C₂×#124×C₁₃₇	1	1	yes	characteristic
409	C₂²	#535×C₁₃₇	1	1	yes	characteristic
410	C₂²	#577×C₁₃₇	1	2	yes	—
411	C₂²	#578×C₁₃₇	1	2	yes	—
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	#550×C₁₃₇	1	2	yes	—
422	C₄	#559×C₁₃₇	1	2	yes	—
423	C₂	—	16	1	no	—
424	C₂	#2548×C₁₃₇	1	1	yes	characteristic
425	C₂	#3046×C₁₃₇	1	2	yes	—
426	C₂	#3137×C₁₃₇	1	2	yes	—
427	C₂	#3221×C₁₃₇	1	1	yes	characteristic
428	C₂	#3223×C₁₃₇	1	1	yes	characteristic

	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×#491×C₁₃₇	C₂	semidirect
4. #2330×C₁₃₇	C₂	semidirect
5. #2043×C₁₃₇	C₂	semidirect
8. #1981×C₁₃₇	C₂	semidirect
10. #1956×C₁₃₇	C₂	semidirect
11. #1768×C₁₃₇	C₂	semidirect
214. #28760	C₁₃₇	direct (N × H)
215. C₁₃₇	#28760	direct (N × H)
216. C₂×#491	C₂×C₁₃₇	semidirect
219. #2330	C₂×C₁₃₇	semidirect
220. #2043	C₂×C₁₃₇	semidirect
223. #1981	C₂×C₁₃₇	semidirect
225. #1956	C₂×C₁₃₇	semidirect
226. #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×#491×C₁₃₇	2
C₂×#488×C₁₃₇	2
#2658×C₁₃₇	2
#2330×C₁₃₇	2
#2043×C₁₃₇	2
#2042×C₁₃₇	2
#1983×C₁₃₇	2
#1981×C₁₃₇	2
#1959×C₁₃₇	2
#1956×C₁₃₇	2
#1768×C₁₃₇	2
#28760	137

Subgroups — C137×#28760 #46878146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28760 #46878146