Subgroups — #2473×C₁₃₇ #31777484

Order 17536.

520 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#400×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#398×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#398×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#398×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#389×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#387×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#387×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#385×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#385×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#385×C₁₃₇	C₂	1	1	yes	maximal, characteristic
13	#385×C₁₃₇	C₂	1	1	yes	maximal, characteristic
14	#380×C₁₃₇	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂²⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
19	#125×C₁₃₇	—	2	4	no	—
20	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
21	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
41	#95×C₁₃₇	C₂²	1	1	yes	characteristic
42	#95×C₁₃₇	C₂²	1	1	yes	characteristic
43	#95×C₁₃₇	C₂²	1	1	yes	characteristic
44	#95×C₁₃₇	C₂²	1	1	yes	characteristic
45	#95×C₁₃₇	C₂²	1	1	yes	characteristic
46	#95×C₁₃₇	C₂²	1	1	yes	characteristic
47	#95×C₁₃₇	C₂²	1	1	yes	characteristic
48	#95×C₁₃₇	C₂²	1	1	yes	characteristic
49	#95×C₁₃₇	C₂²	1	1	yes	characteristic
50	#95×C₁₃₇	C₂²	1	1	yes	characteristic
51	#95×C₁₃₇	C₂²	1	1	yes	characteristic
52	#95×C₁₃₇	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₃₇	—	2	2	no	—
55	C₂²×C₄×C₁₃₇	—	2	2	no	—
56	C₂²×C₄×C₁₃₇	—	2	2	no	—
57	C₂²×C₄×C₁₃₇	—	2	2	no	—
58	C₂²×C₄×C₁₃₇	—	2	2	no	—
59	C₂²×C₄×C₁₃₇	—	2	2	no	—
60	C₂²×C₄×C₁₃₇	—	2	2	no	—
61	C₂²×C₄×C₁₃₇	—	4	1	no	—
62	C₂²×C₄×C₁₃₇	—	4	1	no	—
63	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₄×C₁₃₇	—	2	2	no	—
78	C₄⋊C₄×C₁₃₇	—	2	2	no	—
79	C₄⋊C₄×C₁₃₇	—	2	2	no	—
80	C₄⋊C₄×C₁₃₇	—	2	2	no	—
81	C₄⋊C₄×C₁₃₇	—	2	2	no	—
82	C₄⋊C₄×C₁₃₇	—	2	2	no	—
83	C₄⋊C₄×C₁₃₇	—	2	2	no	—
84	C₄⋊C₄×C₁₃₇	—	2	2	no	—
85	C₄⋊C₄×C₁₃₇	—	2	2	no	—
86	C₄⋊C₄×C₁₃₇	—	2	2	no	—
87	C₄⋊C₄×C₁₃₇	—	4	1	no	—
88	C₄⋊C₄×C₁₃₇	—	4	1	no	—
89	C₄⋊C₄×C₁₃₇	—	4	1	no	—
90	C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
91	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
92	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
93	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
94	C₂²⋊C₄×C₁₃₇	Q₈	1	4	yes	—
95	C₄²×C₁₃₇	—	2	2	no	—
96	C₄²×C₁₃₇	—	4	1	no	—
97	C₂³×C₁₃₇	—	2	1	no	—
98	C₂³×C₁₃₇	—	2	1	no	—
99	C₂³×C₁₃₇	—	2	1	no	—
100	C₂³×C₁₃₇	—	2	1	no	—
101	C₂³×C₁₃₇	C₂×Q₈	1	2	yes	—
102	C₂³×C₁₃₇	#41	1	2	yes	—
103	C₂³×C₁₃₇	#41	1	2	yes	—
104	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₄×C₁₃₇	—	2	8	no	—
106	C₂×C₄×C₁₃₇	—	2	1	no	—
107	C₂×C₄×C₁₃₇	—	2	1	no	—
108	C₂×C₄×C₁₃₇	—	2	1	no	—
109	C₂×C₄×C₁₃₇	—	2	1	no	—
110	C₂×C₄×C₁₃₇	—	2	1	no	—
111	C₂×C₄×C₁₃₇	—	2	1	no	—
112	C₂×C₄×C₁₃₇	—	2	1	no	—
113	C₂×C₄×C₁₃₇	—	2	1	no	—
114	C₂×C₄×C₁₃₇	—	2	1	no	—
115	C₂×C₄×C₁₃₇	—	2	1	no	—
116	C₂×C₄×C₁₃₇	—	2	1	no	—
117	C₂×C₄×C₁₃₇	—	2	1	no	—
118	C₂×C₄×C₁₃₇	—	2	1	no	—
119	C₂×C₄×C₁₃₇	—	2	1	no	—
120	C₂×C₄×C₁₃₇	—	2	1	no	—
121	C₂×C₄×C₁₃₇	—	2	1	no	—
122	C₂×C₄×C₁₃₇	—	2	1	no	—
123	C₂×C₄×C₁₃₇	—	2	1	no	—
124	C₂×C₄×C₁₃₇	—	2	1	no	—
125	C₂×C₄×C₁₃₇	—	2	1	no	—
126	C₂×C₄×C₁₃₇	—	2	1	no	—
127	C₂×C₄×C₁₃₇	—	2	1	no	—
128	C₂×C₄×C₁₃₇	—	2	1	no	—
129	C₂×C₄×C₁₃₇	—	2	1	no	—
130	C₂×C₄×C₁₃₇	—	2	1	no	—
131	C₂×C₄×C₁₃₇	—	2	1	no	—
132	C₂×C₄×C₁₃₇	—	2	1	no	—
133	C₂×C₄×C₁₃₇	—	2	1	no	—
134	C₂×C₄×C₁₃₇	—	2	1	no	—
135	C₂×C₄×C₁₃₇	—	2	1	no	—
136	C₂×C₄×C₁₃₇	—	2	1	no	—
137	C₂×C₄×C₁₃₇	—	2	1	no	—
138	C₂×C₄×C₁₃₇	—	2	1	no	—
139	C₂×C₄×C₁₃₇	—	2	1	no	—
140	C₂×C₄×C₁₃₇	—	2	1	no	—
141	C₂×C₄×C₁₃₇	—	2	1	no	—
142	C₂×C₄×C₁₃₇	—	4	4	no	—
143	C₂×C₄×C₁₃₇	—	4	4	no	—
144	C₂×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
148	C₂×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
149	C₂×C₄×C₁₃₇	#41	1	2	yes	—
150	C₂²×C₁₃₇	—	2	2	no	—
151	C₂²×C₁₃₇	—	2	2	no	—
152	C₂²×C₁₃₇	—	2	2	no	—
153	C₂²×C₁₃₇	—	2	2	no	—
154	C₂²×C₁₃₇	—	2	2	no	—
155	C₂²×C₁₃₇	—	2	2	no	—
156	C₂²×C₁₃₇	#125	1	4	yes	complemented
157	C₂²×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
159	C₂²×C₁₃₇	C₂×#41	1	1	yes	characteristic
160	C₂²×C₁₃₇	C₂×#41	1	1	yes	characteristic
161	C₂²×C₁₃₇	C₂×#41	1	1	yes	characteristic
162	C₂²×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₄×C₁₃₇	—	2	2	no	—
165	C₄×C₁₃₇	—	2	2	no	—
166	C₄×C₁₃₇	—	2	2	no	—
167	C₄×C₁₃₇	—	2	2	no	—
168	C₄×C₁₃₇	—	2	2	no	—
169	C₄×C₁₃₇	—	2	2	no	—
170	C₄×C₁₃₇	—	4	1	no	—
171	C₄×C₁₃₇	—	4	1	no	—
172	C₄×C₁₃₇	—	4	1	no	—
173	C₄×C₁₃₇	—	4	1	no	—
174	C₄×C₁₃₇	—	4	1	no	—
175	C₄×C₁₃₇	—	4	1	no	—
176	C₄×C₁₃₇	—	4	1	no	—
177	C₄×C₁₃₇	—	4	1	no	—
178	C₂×C₁₃₇	—	2	4	no	—
179	C₂×C₁₃₇	#525	1	1	yes	characteristic
180	C₂×C₁₃₇	C₂×#125	1	1	yes	characteristic
181	C₂×C₁₃₇	#539	1	1	yes	characteristic
182	C₂×C₁₃₇	#546	1	1	yes	characteristic
183	C₂×C₁₃₇	D₄×Q₈	1	1	yes	characteristic
184	C₂×C₁₃₇	#552	1	1	yes	characteristic
185	C₂×C₁₃₇	#554	1	1	yes	characteristic
186	C₁₃₇	#2473	1	1	yes	characteristic, direct product factor, Sylow
187	#2473	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×#125	C₂×C₁₃₇	1	1	yes	characteristic, complemented
189	C₂²×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
190	#400	C₂×C₁₃₇	1	1	yes	characteristic, complemented
191	#398	C₂×C₁₃₇	1	1	yes	characteristic, complemented
192	#398	C₂×C₁₃₇	1	1	yes	characteristic, complemented
193	#398	C₂×C₁₃₇	1	1	yes	characteristic, complemented
194	#389	C₂×C₁₃₇	1	1	yes	characteristic, complemented
195	#387	C₂×C₁₃₇	1	1	yes	characteristic, complemented
196	#387	C₂×C₁₃₇	1	1	yes	characteristic, complemented
197	#385	C₂×C₁₃₇	1	1	yes	characteristic
198	#385	C₂×C₁₃₇	1	1	yes	characteristic
199	#385	C₂×C₁₃₇	1	1	yes	characteristic
200	#385	C₂×C₁₃₇	1	1	yes	characteristic
201	#380	C₂×C₁₃₇	1	1	yes	characteristic
202	C₄×C₂²⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
203	C₂³×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂³×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
205	C₂³×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
206	#125	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
228	#95	C₂²×C₁₃₇	1	1	yes	characteristic
229	#95	C₂²×C₁₃₇	1	1	yes	characteristic
230	#95	C₂²×C₁₃₇	1	1	yes	characteristic
231	#95	C₂²×C₁₃₇	1	1	yes	characteristic
232	#95	C₂²×C₁₃₇	1	1	yes	characteristic
233	#95	C₂²×C₁₃₇	1	1	yes	characteristic
234	#95	C₂²×C₁₃₇	1	1	yes	characteristic
235	#95	C₂²×C₁₃₇	1	1	yes	characteristic
236	#95	C₂²×C₁₃₇	1	1	yes	characteristic
237	#95	C₂²×C₁₃₇	1	1	yes	characteristic
238	#95	C₂²×C₁₃₇	1	1	yes	characteristic
239	#95	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₂⁴	C₂³×C₁₃₇	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	4	1	no	—
249	C₂²×C₄	—	4	1	no	—
250	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
258	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	4	1	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₂²⋊C₄	—	2	2	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	Q₈×C₁₃₇	1	4	yes	—
282	C₄²	—	2	2	no	—
283	C₄²	—	4	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	C₂×Q₈×C₁₃₇	1	2	yes	—
289	C₂³	#41×C₁₃₇	1	2	yes	—
290	C₂³	#41×C₁₃₇	1	2	yes	—
291	C₂³	C₂⁴×C₁₃₇	1	1	yes	characteristic
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
332	C₂×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
333	C₂×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
334	C₂×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
335	C₂×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
336	C₂×C₄	#41×C₁₃₇	1	2	yes	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	#125×C₁₃₇	1	4	yes	complemented
344	C₂²	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
345	C₂²	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
346	C₂²	C₂×#41×C₁₃₇	1	1	yes	characteristic
347	C₂²	C₂×#41×C₁₃₇	1	1	yes	characteristic
348	C₂²	C₂×#41×C₁₃₇	1	1	yes	characteristic
349	C₂²	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
350	C₂²	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₂	—	2	4	no	—
366	C₂	#525×C₁₃₇	1	1	yes	characteristic
367	C₂	C₂×#125×C₁₃₇	1	1	yes	characteristic
368	C₂	#539×C₁₃₇	1	1	yes	characteristic
369	C₂	#546×C₁₃₇	1	1	yes	characteristic
370	C₂	D₄×Q₈×C₁₃₇	1	1	yes	characteristic
371	C₂	#552×C₁₃₇	1	1	yes	characteristic
372	C₂	#554×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#125×C₁₃₇	C₂	semidirect
3. #400×C₁₃₇	C₂	semidirect
4. #398×C₁₃₇	C₂	semidirect
5. #398×C₁₃₇	C₂	semidirect
6. #398×C₁₃₇	C₂	semidirect
7. #389×C₁₃₇	C₂	semidirect
8. #387×C₁₃₇	C₂	semidirect
9. #387×C₁₃₇	C₂	semidirect
156. C₂²×C₁₃₇	#125	semidirect
186. C₁₃₇	#2473	direct (N × H)
187. #2473	C₁₃₇	direct (N × H)
188. C₂×#125	C₂×C₁₃₇	semidirect
190. #400	C₂×C₁₃₇	semidirect
191. #398	C₂×C₁₃₇	semidirect
192. #398	C₂×C₁₃₇	semidirect
193. #398	C₂×C₁₃₇	semidirect
194. #389	C₂×C₁₃₇	semidirect
195. #387	C₂×C₁₃₇	semidirect
196. #387	C₂×C₁₃₇	semidirect
343. C₂²	#125×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#125×C₁₃₇	2
C₂²×C₄⋊C₄×C₁₃₇	2
#400×C₁₃₇	2
#398×C₁₃₇	2
#389×C₁₃₇	2
#387×C₁₃₇	2
#385×C₁₃₇	2
#380×C₁₃₇	2
C₄×C₂²⋊C₄×C₁₃₇	2
#2473	137

Subgroups — #2473×C137 #31777484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2473×C₁₃₇ #31777484