Subgroups — C₁₃₇×#25894 #46875280

Order 35072.

1260 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#491×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#479×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2562×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2036×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2035×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1981×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1955×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1787×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1787×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1763×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃₇	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₃₇	—	2	4	no	—
14	D₄×Q₈×C₁₃₇	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₁₃₇	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	#491×C₁₃₇	—	2	4	no	—
24	#479×C₁₃₇	—	2	4	no	—
25	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
31	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
37	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
38	#400×C₁₃₇	—	2	1	no	—
39	#394×C₁₃₇	—	2	1	no	—
40	#388×C₁₃₇	—	2	2	no	—
41	#380×C₁₃₇	C₂²	1	2	yes	—
42	#380×C₁₃₇	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
44	#340×C₁₃₇	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₇	—	2	4	no	—
46	C₂²×Q₈×C₁₃₇	—	2	4	no	—
47	C₂²×Q₈×C₁₃₇	—	2	2	no	—
48	C₂²×Q₈×C₁₃₇	—	2	4	no	—
49	C₂²×Q₈×C₁₃₇	—	2	4	no	—
50	C₂²×Q₈×C₁₃₇	—	4	2	no	—
51	C₂²×Q₈×C₁₃₇	—	4	2	no	—
52	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃₇	—	2	2	no	—
56	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₁₃₇	—	2	8	no	—
61	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
62	C₄⋊Q₈×C₁₃₇	D₄	1	4	yes	—
63	#125×C₁₃₇	—	2	2	no	—
64	#125×C₁₃₇	—	2	2	no	—
65	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
66	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
67	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
68	C₄×Q₈×C₁₃₇	—	2	2	no	—
69	C₄×Q₈×C₁₃₇	D₄	1	4	yes	—
70	C₄×D₄×C₁₃₇	—	2	8	no	—
71	C₄×D₄×C₁₃₇	—	2	2	no	—
72	C₄×D₄×C₁₃₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃₇	—	2	1	no	—
89	C₂×C₄²×C₁₃₇	—	2	1	no	—
90	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
91	#107×C₁₃₇	—	2	2	no	—
92	#106×C₁₃₇	—	2	2	no	—
93	C₄⋊C₈×C₁₃₇	—	2	2	no	—
94	#103×C₁₃₇	—	2	2	no	—
95	#103×C₁₃₇	—	2	2	no	—
96	#103×C₁₃₇	—	2	4	no	—
97	#103×C₁₃₇	—	2	4	no	—
98	#103×C₁₃₇	—	2	4	no	—
99	#103×C₁₃₇	—	4	2	no	—
100	#103×C₁₃₇	—	4	2	no	—
101	C₂²⋊C₈×C₁₃₇	—	4	2	no	—
102	C₂²⋊C₈×C₁₃₇	—	4	2	no	—
103	#97×C₁₃₇	—	2	2	no	—
104	#95×C₁₃₇	—	2	1	no	—
105	#95×C₁₃₇	—	2	2	no	—
106	#95×C₁₃₇	—	2	2	no	—
107	C₂⁴×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₃₇	—	2	8	no	—
109	C₂×Q₈×C₁₃₇	—	2	1	no	—
110	C₂×Q₈×C₁₃₇	—	2	2	no	—
111	C₂×Q₈×C₁₃₇	—	2	2	no	—
112	C₂×Q₈×C₁₃₇	—	2	2	no	—
113	C₂×Q₈×C₁₃₇	—	2	2	no	—
114	C₂×Q₈×C₁₃₇	—	2	2	no	—
115	C₂×Q₈×C₁₃₇	—	2	2	no	—
116	C₂×Q₈×C₁₃₇	—	4	4	no	—
117	C₂×Q₈×C₁₃₇	—	4	4	no	—
118	C₂×Q₈×C₁₃₇	—	4	8	no	—
119	C₂×Q₈×C₁₃₇	—	4	8	no	—
120	C₂×Q₈×C₁₃₇	—	4	8	no	—
121	C₂×Q₈×C₁₃₇	—	4	8	no	—
122	C₂×Q₈×C₁₃₇	C₂×D₄	1	4	yes	—
123	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂×Q₈×C₁₃₇	#41	1	4	yes	—
125	C₂×D₄×C₁₃₇	—	2	4	no	—
126	C₂×D₄×C₁₃₇	—	2	2	no	—
127	C₂²×C₄×C₁₃₇	—	2	1	no	—
128	C₂²×C₄×C₁₃₇	—	2	8	no	—
129	C₂²×C₄×C₁₃₇	—	2	1	no	—
130	C₂²×C₄×C₁₃₇	—	2	2	no	—
131	C₂²×C₄×C₁₃₇	—	2	2	no	—
132	C₂²×C₄×C₁₃₇	—	2	2	no	—
133	C₂²×C₄×C₁₃₇	—	2	2	no	—
134	C₂²×C₄×C₁₃₇	—	2	2	no	—
135	C₂²×C₄×C₁₃₇	—	2	2	no	—
136	C₂²×C₄×C₁₃₇	—	2	2	no	—
137	C₂²×C₄×C₁₃₇	—	2	2	no	—
138	C₂²×C₄×C₁₃₇	—	2	1	no	—
139	C₂²×C₄×C₁₃₇	—	2	1	no	—
140	C₂²×C₄×C₁₃₇	—	4	4	no	—
141	C₂²×C₄×C₁₃₇	—	4	4	no	—
142	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₁₃₇	—	2	2	no	—
147	C₂×C₈×C₁₃₇	—	2	1	no	—
148	C₂×C₈×C₁₃₇	—	2	1	no	—
149	C₂×C₈×C₁₃₇	—	2	2	no	—
150	C₂×C₈×C₁₃₇	—	2	2	no	—
151	C₂×C₈×C₁₃₇	—	2	2	no	—
152	C₂×C₈×C₁₃₇	—	2	2	no	—
153	C₄⋊C₄×C₁₃₇	—	2	8	no	—
154	C₄⋊C₄×C₁₃₇	—	2	4	no	—
155	C₄⋊C₄×C₁₃₇	—	2	4	no	—
156	C₄⋊C₄×C₁₃₇	—	2	4	no	—
157	C₄⋊C₄×C₁₃₇	—	2	2	no	—
158	C₄⋊C₄×C₁₃₇	—	2	1	no	—
159	C₄⋊C₄×C₁₃₇	—	2	1	no	—
160	C₄⋊C₄×C₁₃₇	—	2	1	no	—
161	C₄⋊C₄×C₁₃₇	—	2	1	no	—
162	C₄⋊C₄×C₁₃₇	—	2	1	no	—
163	C₄⋊C₄×C₁₃₇	—	2	2	no	—
164	C₄⋊C₄×C₁₃₇	—	2	2	no	—
165	C₄⋊C₄×C₁₃₇	—	4	2	no	—
166	C₄⋊C₄×C₁₃₇	—	4	2	no	—
167	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
169	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
170	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
171	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
172	C₄²×C₁₃₇	—	2	4	no	—
173	C₄²×C₁₃₇	—	8	1	no	—
174	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
176	C₂³×C₁₃₇	—	2	2	no	—
177	C₂³×C₁₃₇	—	2	2	no	—
178	C₂³×C₁₃₇	—	2	2	no	—
179	C₂³×C₁₃₇	—	2	2	no	—
180	C₂³×C₁₃₇	—	2	2	no	—
181	C₂³×C₁₃₇	—	2	2	no	—
182	C₂³×C₁₃₇	#137	1	4	yes	—
183	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃₇	—	2	2	no	—
185	Q₈×C₁₃₇	—	2	4	no	—
186	Q₈×C₁₃₇	—	2	4	no	—
187	Q₈×C₁₃₇	—	2	4	no	—
188	Q₈×C₁₃₇	—	4	16	no	—
189	Q₈×C₁₃₇	—	4	2	no	—
190	Q₈×C₁₃₇	—	4	2	no	—
191	Q₈×C₁₃₇	#124	1	4	yes	—
192	D₄×C₁₃₇	—	2	8	no	—
193	C₂×C₄×C₁₃₇	—	2	2	no	—
194	C₂×C₄×C₁₃₇	—	2	4	no	—
195	C₂×C₄×C₁₃₇	—	2	2	no	—
196	C₂×C₄×C₁₃₇	—	2	1	no	—
197	C₂×C₄×C₁₃₇	—	2	1	no	—
198	C₂×C₄×C₁₃₇	—	2	2	no	—
199	C₂×C₄×C₁₃₇	—	2	4	no	—
200	C₂×C₄×C₁₃₇	—	2	2	no	—
201	C₂×C₄×C₁₃₇	—	2	2	no	—
202	C₂×C₄×C₁₃₇	—	2	2	no	—
203	C₂×C₄×C₁₃₇	—	4	16	no	—
204	C₂×C₄×C₁₃₇	—	4	2	no	—
205	C₂×C₄×C₁₃₇	—	4	2	no	—
206	C₂×C₄×C₁₃₇	—	4	1	no	—
207	C₂×C₄×C₁₃₇	—	4	1	no	—
208	C₂×C₄×C₁₃₇	—	4	2	no	—
209	C₂×C₄×C₁₃₇	—	4	2	no	—
210	C₂×C₄×C₁₃₇	—	4	2	no	—
211	C₂×C₄×C₁₃₇	—	4	2	no	—
212	C₂×C₄×C₁₃₇	—	4	1	no	—
213	C₂×C₄×C₁₃₇	—	4	1	no	—
214	C₂×C₄×C₁₃₇	—	4	2	no	—
215	C₂×C₄×C₁₃₇	—	4	2	no	—
216	C₂×C₄×C₁₃₇	—	4	2	no	—
217	C₂×C₄×C₁₃₇	—	4	2	no	—
218	C₂×C₄×C₁₃₇	—	4	1	no	—
219	C₂×C₄×C₁₃₇	—	4	1	no	—
220	C₂×C₄×C₁₃₇	#120	1	2	yes	—
221	C₂×C₄×C₁₃₇	#120	1	2	yes	—
222	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₁₃₇	—	4	1	no	—
227	C₈×C₁₃₇	—	4	1	no	—
228	C₈×C₁₃₇	—	4	2	no	—
229	C₂²×C₁₃₇	—	2	4	no	—
230	C₂²×C₁₃₇	—	2	4	no	—
231	C₂²×C₁₃₇	—	2	4	no	—
232	C₂²×C₁₃₇	—	4	2	no	—
233	C₂²×C₁₃₇	—	4	2	no	—
234	C₂²×C₁₃₇	—	4	2	no	—
235	C₂²×C₁₃₇	—	4	2	no	—
236	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
237	C₂²×C₁₃₇	#546	1	2	yes	—
238	C₂²×C₁₃₇	C₂×#137	1	2	yes	—
239	C₂²×C₁₃₇	#577	1	1	yes	characteristic
240	C₂²×C₁₃₇	#578	1	1	yes	characteristic
241	C₄×C₁₃₇	—	2	4	no	—
242	C₄×C₁₃₇	—	2	2	no	—
243	C₄×C₁₃₇	—	2	2	no	—
244	C₄×C₁₃₇	—	4	2	no	—
245	C₄×C₁₃₇	—	4	4	no	—
246	C₄×C₁₃₇	—	4	2	no	—
247	C₄×C₁₃₇	—	8	1	no	—
248	C₄×C₁₃₇	—	8	1	no	—
249	C₄×C₁₃₇	—	8	2	no	—
250	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
251	C₄×C₁₃₇	#535	1	1	yes	characteristic
252	C₄×C₁₃₇	#546	1	2	yes	—
253	C₂×C₁₃₇	—	4	4	no	—
254	C₂×C₁₃₇	#2435	1	1	yes	characteristic
255	C₂×C₁₃₇	#3004	1	1	yes	characteristic
256	C₂×C₁₃₇	#3013	1	1	yes	characteristic
257	C₂×C₁₃₇	#3312	1	2	yes	—
258	C₂×C₁₃₇	#3320	1	2	yes	—
259	#25894	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₁₃₇	#25894	1	1	yes	characteristic, direct product factor, Sylow
261	C₂×D₄×Q₈	C₂×C₁₃₇	1	1	yes	characteristic
262	C₂×#491	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	C₂×#479	C₂×C₁₃₇	1	1	yes	characteristic, complemented
264	#2562	C₂×C₁₃₇	1	1	yes	characteristic
265	#2036	C₂×C₁₃₇	1	2	yes	complemented
266	#2035	C₂×C₁₃₇	1	2	yes	complemented
267	#1981	C₂×C₁₃₇	1	1	yes	characteristic, complemented
268	#1955	C₂×C₁₃₇	1	1	yes	characteristic
269	#1787	C₂×C₁₃₇	1	2	yes	complemented
270	#1787	C₂×C₁₃₇	1	2	yes	complemented
271	#1763	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	C₂³×Q₈	C₂²×C₁₃₇	1	2	yes	—
273	D₄×Q₈	—	2	4	no	—
274	D₄×Q₈	—	2	4	no	—
275	C₂×C₄⋊Q₈	—	2	1	no	—
276	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
277	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
278	C₂×C₂²⋊Q₈	—	2	2	no	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
280	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₂×C₄×D₄	—	2	1	no	—
282	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
283	#491	—	2	4	no	—
284	#479	—	2	4	no	—
285	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
286	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
291	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
292	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
293	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
294	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
297	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
298	#400	—	2	1	no	—
299	#394	—	2	1	no	—
300	#388	—	2	2	no	—
301	#380	C₂²×C₁₃₇	1	2	yes	—
302	#380	C₂²×C₁₃₇	1	2	yes	—
303	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
304	#340	C₂²×C₁₃₇	1	2	yes	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	—	2	4	no	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	4	no	—
309	C₂²×Q₈	—	2	4	no	—
310	C₂²×Q₈	—	4	2	no	—
311	C₂²×Q₈	—	4	2	no	—
312	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
313	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
317	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
318	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	8	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	D₄×C₁₃₇	1	4	yes	—
323	#125	—	2	2	no	—
324	#125	—	2	2	no	—
325	C₂²⋊Q₈	—	2	16	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₁₃₇	1	4	yes	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
351	#107	—	2	2	no	—
352	#106	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	#103	—	2	2	no	—
355	#103	—	2	2	no	—
356	#103	—	2	4	no	—
357	#103	—	2	4	no	—
358	#103	—	2	4	no	—
359	#103	—	4	2	no	—
360	#103	—	4	2	no	—
361	C₂²⋊C₈	—	4	2	no	—
362	C₂²⋊C₈	—	4	2	no	—
363	#97	—	2	2	no	—
364	#95	—	2	1	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	C₂⁴	C₂×D₄×C₁₃₇	1	2	yes	—
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	—	4	8	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	8	no	—
381	C₂×Q₈	—	4	8	no	—
382	C₂×Q₈	C₂×D₄×C₁₃₇	1	4	yes	—
383	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
384	C₂×Q₈	#41×C₁₃₇	1	4	yes	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	8	2	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	8	1	no	—
434	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
435	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	#137×C₁₃₇	1	4	yes	—
443	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	16	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	#124×C₁₃₇	1	4	yes	—
452	D₄	—	2	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	#120×C₁₃₇	1	2	yes	—
481	C₂×C₄	#120×C₁₃₇	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
485	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
486	C₈	—	4	1	no	—
487	C₈	—	4	1	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
497	C₂²	#546×C₁₃₇	1	2	yes	—
498	C₂²	C₂×#137×C₁₃₇	1	2	yes	—
499	C₂²	#577×C₁₃₇	1	1	yes	characteristic
500	C₂²	#578×C₁₃₇	1	1	yes	characteristic
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	1	no	—
510	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
511	C₄	#535×C₁₃₇	1	1	yes	characteristic
512	C₄	#546×C₁₃₇	1	2	yes	—
513	C₂	—	4	4	no	—
514	C₂	#2435×C₁₃₇	1	1	yes	characteristic
515	C₂	#3004×C₁₃₇	1	1	yes	characteristic
516	C₂	#3013×C₁₃₇	1	1	yes	characteristic
517	C₂	#3312×C₁₃₇	1	2	yes	—
518	C₂	#3320×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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₂×C₄×D₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#491×C₁₃₇	C₂	semidirect
3. C₂×#479×C₁₃₇	C₂	semidirect
5. #2036×C₁₃₇	C₂	semidirect
6. #2035×C₁₃₇	C₂	semidirect
7. #1981×C₁₃₇	C₂	semidirect
9. #1787×C₁₃₇	C₂	semidirect
10. #1787×C₁₃₇	C₂	semidirect
11. #1763×C₁₃₇	C₂	semidirect
259. #25894	C₁₃₇	direct (N × H)
260. C₁₃₇	#25894	direct (N × H)
262. C₂×#491	C₂×C₁₃₇	semidirect
263. C₂×#479	C₂×C₁₃₇	semidirect
265. #2036	C₂×C₁₃₇	semidirect
266. #2035	C₂×C₁₃₇	semidirect
267. #1981	C₂×C₁₃₇	semidirect
269. #1787	C₂×C₁₃₇	semidirect
270. #1787	C₂×C₁₃₇	semidirect
271. #1763	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×D₄×Q₈×C₁₃₇	2
C₂×#491×C₁₃₇	2
C₂×#479×C₁₃₇	2
#2562×C₁₃₇	2
#2036×C₁₃₇	2
#2035×C₁₃₇	2
#1981×C₁₃₇	2
#1955×C₁₃₇	2
#1787×C₁₃₇	2
#1763×C₁₃₇	2
#25894	137

Subgroups — C137×#25894 #46875280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#25894 #46875280