Subgroups — C₁₃₇×#20527 #46869913

Order 35072.

1210 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#407×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2280×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1753×C₁₃₇	C₂	1	4	yes	maximal, complemented
5	#1752×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊C₄×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1750×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
10	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
13	#407×C₁₃₇	C₄	1	8	yes	complemented
14	C₂×C₂²⋊C₈×C₁₃₇	C₄	1	8	yes	complemented
15	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#97×C₁₃₇	C₂²	1	4	yes	complemented
20	C₂×C₄×C₈×C₁₃₇	C₂²	1	4	yes	complemented
21	#381×C₁₃₇	C₄	1	2	yes	—
22	#380×C₁₃₇	C₄	1	2	yes	—
23	#380×C₁₃₇	C₄	1	2	yes	—
24	#379×C₁₃₇	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
26	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
27	#336×C₁₃₇	C₂²	1	4	yes	complemented
28	#336×C₁₃₇	C₂²	1	4	yes	complemented
29	C₂⁵×C₁₃₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₇	—	4	2	no	—
31	C₂³×C₄×C₁₃₇	—	4	2	no	—
32	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₁₃₇	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₃₇	—	4	2	no	—
41	C₂×M₁₆×C₁₃₇	—	4	2	no	—
42	C₂×M₁₆×C₁₃₇	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₁₃₇	—	4	2	no	—
44	C₂²×C₈×C₁₃₇	—	4	2	no	—
45	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	#117×C₁₃₇	—	4	2	no	—
51	#117×C₁₃₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
57	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
58	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
59	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
60	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
61	#97×C₁₃₇	—	4	4	no	—
62	C₄×C₈×C₁₃₇	—	4	4	no	—
63	#95×C₁₃₇	C₂×C₄	1	4	yes	—
64	#95×C₁₃₇	C₂×C₄	1	4	yes	—
65	C₂⁴×C₁₃₇	—	2	4	no	—
66	C₂⁴×C₁₃₇	—	4	2	no	—
67	C₂⁴×C₁₃₇	—	4	2	no	—
68	C₂⁴×C₁₃₇	C₄²	1	4	yes	—
69	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
70	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
71	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₇	—	2	2	no	—
73	C₂²×C₄×C₁₃₇	—	2	2	no	—
74	C₂²×C₄×C₁₃₇	—	2	2	no	—
75	C₂²×C₄×C₁₃₇	—	2	2	no	—
76	C₂²×C₄×C₁₃₇	—	2	2	no	—
77	C₂²×C₄×C₁₃₇	—	2	2	no	—
78	C₂²×C₄×C₁₃₇	—	4	4	no	—
79	C₂²×C₄×C₁₃₇	—	4	4	no	—
80	C₂²×C₄×C₁₃₇	—	4	8	no	—
81	C₂²×C₄×C₁₃₇	—	4	2	no	—
82	C₂²×C₄×C₁₃₇	—	4	2	no	—
83	C₂²×C₄×C₁₃₇	—	4	2	no	—
84	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
85	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
86	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
87	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
88	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₁₃₇	—	4	8	no	—
99	C₂×C₈×C₁₃₇	—	2	4	no	—
100	C₂×C₈×C₁₃₇	—	2	4	no	—
101	C₂×C₈×C₁₃₇	—	2	4	no	—
102	C₂×C₈×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	—	4	4	no	—
104	C₂×C₈×C₁₃₇	—	4	4	no	—
105	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
106	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₁₃₇	C₂²×C₄	1	8	yes	—
108	C₄⋊C₄×C₁₃₇	—	4	4	no	—
109	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
110	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
111	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
112	C₄²×C₁₃₇	—	2	4	no	—
113	C₄²×C₁₃₇	—	2	4	no	—
114	C₂³×C₁₃₇	—	2	2	no	—
115	C₂³×C₁₃₇	—	2	2	no	—
116	C₂³×C₁₃₇	—	2	2	no	—
117	C₂³×C₁₃₇	—	2	2	no	—
118	C₂³×C₁₃₇	—	2	2	no	—
119	C₂³×C₁₃₇	—	2	2	no	—
120	C₂³×C₁₃₇	—	2	2	no	—
121	C₂³×C₁₃₇	—	2	2	no	—
122	C₂³×C₁₃₇	—	2	8	no	—
123	C₂³×C₁₃₇	—	4	4	no	—
124	C₂³×C₁₃₇	—	4	4	no	—
125	C₂³×C₁₃₇	—	4	16	no	—
126	C₂³×C₁₃₇	C₂×C₄²	1	2	yes	—
127	C₂³×C₁₃₇	C₂×C₄²	1	2	yes	—
128	C₂³×C₁₃₇	C₂×C₄²	1	2	yes	—
129	C₂³×C₁₃₇	#131	1	4	yes	—
130	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₇	—	2	2	no	—
132	C₂×C₄×C₁₃₇	—	2	2	no	—
133	C₂×C₄×C₁₃₇	—	2	2	no	—
134	C₂×C₄×C₁₃₇	—	2	2	no	—
135	C₂×C₄×C₁₃₇	—	2	2	no	—
136	C₂×C₄×C₁₃₇	—	2	4	no	—
137	C₂×C₄×C₁₃₇	—	2	4	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	2	2	no	—
140	C₂×C₄×C₁₃₇	—	2	4	no	—
141	C₂×C₄×C₁₃₇	—	2	2	no	—
142	C₂×C₄×C₁₃₇	—	2	2	no	—
143	C₂×C₄×C₁₃₇	—	2	8	no	—
144	C₂×C₄×C₁₃₇	—	2	8	no	—
145	C₂×C₄×C₁₃₇	—	2	8	no	—
146	C₂×C₄×C₁₃₇	—	4	4	no	—
147	C₂×C₄×C₁₃₇	—	4	4	no	—
148	C₂×C₄×C₁₃₇	—	4	4	no	—
149	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
150	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
155	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
156	C₈×C₁₃₇	—	2	4	no	—
157	C₈×C₁₃₇	—	2	4	no	—
158	C₈×C₁₃₇	—	2	8	no	—
159	C₂²×C₁₃₇	—	2	2	no	—
160	C₂²×C₁₃₇	—	2	8	no	—
161	C₂²×C₁₃₇	—	2	2	no	—
162	C₂²×C₁₃₇	—	2	2	no	—
163	C₂²×C₁₃₇	—	2	2	no	—
164	C₂²×C₁₃₇	—	2	2	no	—
165	C₂²×C₁₃₇	—	2	2	no	—
166	C₂²×C₁₃₇	—	2	2	no	—
167	C₂²×C₁₃₇	—	2	2	no	—
168	C₂²×C₁₃₇	—	4	16	no	—
169	C₂²×C₁₃₇	—	4	4	no	—
170	C₂²×C₁₃₇	—	4	4	no	—
171	C₂²×C₁₃₇	#405	1	4	yes	—
172	C₂²×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
173	C₂²×C₁₃₇	#518	1	2	yes	—
174	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
175	C₂²×C₁₃₇	#568	1	2	yes	—
176	C₄×C₁₃₇	—	2	2	no	—
177	C₄×C₁₃₇	—	2	2	no	—
178	C₄×C₁₃₇	—	2	2	no	—
179	C₄×C₁₃₇	—	4	8	no	—
180	C₄×C₁₃₇	#518	1	1	yes	characteristic
181	C₄×C₁₃₇	#518	1	1	yes	characteristic
182	C₄×C₁₃₇	#518	1	2	yes	—
183	C₂×C₁₃₇	—	2	4	no	—
184	C₂×C₁₃₇	—	4	2	no	—
185	C₂×C₁₃₇	—	4	2	no	—
186	C₂×C₁₃₇	#2273	1	1	yes	characteristic
187	C₂×C₁₃₇	C₂×#405	1	1	yes	characteristic
188	C₂×C₁₃₇	#2873	1	1	yes	characteristic
189	C₂×C₁₃₇	#2976	1	4	yes	—
190	#20527	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₇	#20527	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×#407	C₂×C₁₃₇	1	1	yes	characteristic
193	C₂²×C₂²⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
194	#2280	C₂×C₁₃₇	1	1	yes	characteristic
195	#1753	C₂×C₁₃₇	1	4	yes	complemented
196	#1752	C₂×C₁₃₇	1	2	yes	complemented
197	C₈×C₂²⋊C₄	C₂×C₁₃₇	1	2	yes	complemented
198	#1750	C₂×C₁₃₇	1	4	yes	complemented
199	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
200	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
201	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
204	#407	C₄×C₁₃₇	1	8	yes	complemented
205	C₂×C₂²⋊C₈	C₄×C₁₃₇	1	8	yes	complemented
206	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
207	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
210	C₂×#97	C₂²×C₁₃₇	1	4	yes	complemented
211	C₂×C₄×C₈	C₂²×C₁₃₇	1	4	yes	complemented
212	#381	C₄×C₁₃₇	1	2	yes	—
213	#380	C₄×C₁₃₇	1	2	yes	—
214	#380	C₄×C₁₃₇	1	2	yes	—
215	#379	C₄×C₁₃₇	1	2	yes	—
216	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
218	#336	C₂²×C₁₃₇	1	4	yes	complemented
219	#336	C₂²×C₁₃₇	1	4	yes	complemented
220	C₂⁵	C₂×C₄×C₁₃₇	1	1	yes	characteristic
221	C₂³×C₄	—	4	2	no	—
222	C₂³×C₄	—	4	2	no	—
223	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
226	C₂³×C₄	C₂×C₄×C₁₃₇	1	4	yes	—
227	C₂³×C₄	C₂×C₄×C₁₃₇	1	4	yes	—
228	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
231	C₂×M₁₆	—	4	2	no	—
232	C₂×M₁₆	—	4	2	no	—
233	C₂×M₁₆	C₂×C₄×C₁₃₇	1	8	yes	—
234	C₂²×C₈	—	4	2	no	—
235	C₂²×C₈	—	4	2	no	—
236	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
237	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
238	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
240	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
241	#117	—	4	2	no	—
242	#117	—	4	2	no	—
243	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
247	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
248	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
249	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
250	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
251	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
252	#97	—	4	4	no	—
253	C₄×C₈	—	4	4	no	—
254	#95	C₂×C₄×C₁₃₇	1	4	yes	—
255	#95	C₂×C₄×C₁₃₇	1	4	yes	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	4	2	no	—
258	C₂⁴	—	4	2	no	—
259	C₂⁴	C₄²×C₁₃₇	1	4	yes	—
260	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
261	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
262	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
276	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
277	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
289	M₁₆	—	4	8	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	4	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
297	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
298	C₂×C₈	C₂²×C₄×C₁₃₇	1	8	yes	—
299	C₄⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	2	8	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	4	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	16	no	—
317	C₂³	C₂×C₄²×C₁₃₇	1	2	yes	—
318	C₂³	C₂×C₄²×C₁₃₇	1	2	yes	—
319	C₂³	C₂×C₄²×C₁₃₇	1	2	yes	—
320	C₂³	#131×C₁₃₇	1	4	yes	—
321	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
341	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
342	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
343	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
346	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
347	C₈	—	2	4	no	—
348	C₈	—	2	4	no	—
349	C₈	—	2	8	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	16	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	#405×C₁₃₇	1	4	yes	—
363	C₂²	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
364	C₂²	#518×C₁₃₇	1	2	yes	—
365	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
366	C₂²	#568×C₁₃₇	1	2	yes	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	4	8	no	—
371	C₄	#518×C₁₃₇	1	1	yes	characteristic
372	C₄	#518×C₁₃₇	1	1	yes	characteristic
373	C₄	#518×C₁₃₇	1	2	yes	—
374	C₂	—	2	4	no	—
375	C₂	—	4	2	no	—
376	C₂	—	4	2	no	—
377	C₂	#2273×C₁₃₇	1	1	yes	characteristic
378	C₂	C₂×#405×C₁₃₇	1	1	yes	characteristic
379	C₂	#2873×C₁₃₇	1	1	yes	characteristic
380	C₂	#2976×C₁₃₇	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂³×C₄
prime radical	C₂⁵×C₁₃₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1753×C₁₃₇	C₂	semidirect
5. #1752×C₁₃₇	C₂	semidirect
6. C₈×C₂²⋊C₄×C₁₃₇	C₂	semidirect
7. #1750×C₁₃₇	C₂	semidirect
13. #407×C₁₃₇	C₄	semidirect
14. C₂×C₂²⋊C₈×C₁₃₇	C₄	semidirect
19. C₂×#97×C₁₃₇	C₂²	semidirect
20. C₂×C₄×C₈×C₁₃₇	C₂²	semidirect
27. #336×C₁₃₇	C₂²	semidirect
28. #336×C₁₃₇	C₂²	semidirect
190. #20527	C₁₃₇	direct (N × H)
191. C₁₃₇	#20527	direct (N × H)
195. #1753	C₂×C₁₃₇	semidirect
196. #1752	C₂×C₁₃₇	semidirect
197. C₈×C₂²⋊C₄	C₂×C₁₃₇	semidirect
198. #1750	C₂×C₁₃₇	semidirect
204. #407	C₄×C₁₃₇	semidirect
205. C₂×C₂²⋊C₈	C₄×C₁₃₇	semidirect
210. C₂×#97	C₂²×C₁₃₇	semidirect
211. C₂×C₄×C₈	C₂²×C₁₃₇	semidirect
218. #336	C₂²×C₁₃₇	semidirect
219. #336	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#407×C₁₃₇	2
C₂²×C₂²⋊C₈×C₁₃₇	2
#2280×C₁₃₇	2
#1753×C₁₃₇	2
#1752×C₁₃₇	2
C₈×C₂²⋊C₄×C₁₃₇	2
#1750×C₁₃₇	2
#20527	137

Subgroups — C137×#20527 #46869913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20527 #46869913