Subgroups — C₁₃₇×#34400 #46883786

Order 35072.

1990 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2376×C₁₃₇	C₂	1	4	yes	maximal, complemented
3	#2373×C₁₃₇	C₂	1	4	yes	maximal, complemented
4	#2357×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2353×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2346×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2343×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2337×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2336×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2333×C₁₃₇	C₂	1	2	yes	maximal
11	#2332×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#2320×C₁₃₇	C₂	1	2	yes	maximal, complemented
13	#2318×C₁₃₇	C₂	1	2	yes	maximal, complemented
14	#2283×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#2283×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#529×C₁₃₇	C₄	1	16	yes	complemented
17	C₂×#126×C₁₃₇	C₂²	1	2	yes	—
18	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
28	#391×C₁₃₇	C₂²	1	4	yes	—
29	#390×C₁₃₇	C₂²	1	4	yes	—
30	#389×C₁₃₇	C₂²	1	4	yes	—
31	#389×C₁₃₇	C₂²	1	4	yes	—
32	#388×C₁₃₇	C₂²	1	4	yes	—
33	#388×C₁₃₇	C₂²	1	4	yes	—
34	#388×C₁₃₇	C₂²	1	4	yes	—
35	#388×C₁₃₇	C₂²	1	4	yes	—
36	#388×C₁₃₇	C₂²	1	4	yes	—
37	#388×C₁₃₇	C₂²	1	4	yes	—
38	#387×C₁₃₇	C₂²	1	4	yes	—
39	#387×C₁₃₇	C₂²	1	4	yes	—
40	#387×C₁₃₇	C₂²	1	4	yes	—
41	#387×C₁₃₇	C₂²	1	4	yes	—
42	#387×C₁₃₇	C₂²	1	4	yes	—
43	#387×C₁₃₇	C₂²	1	4	yes	—
44	#386×C₁₃₇	C₂²	1	4	yes	—
45	#386×C₁₃₇	C₂²	1	4	yes	—
46	#385×C₁₃₇	C₂²	1	4	yes	—
47	#385×C₁₃₇	C₂²	1	4	yes	—
48	#383×C₁₃₇	C₂²	1	2	yes	—
49	#383×C₁₃₇	C₂²	1	2	yes	—
50	#383×C₁₃₇	C₂²	1	2	yes	—
51	#382×C₁₃₇	C₂²	1	2	yes	—
52	#382×C₁₃₇	C₂²	1	2	yes	—
53	#382×C₁₃₇	C₂²	1	2	yes	—
54	#381×C₁₃₇	C₂²	1	2	yes	—
55	#381×C₁₃₇	C₂²	1	2	yes	—
56	#381×C₁₃₇	C₂²	1	2	yes	—
57	#380×C₁₃₇	C₂²	1	2	yes	—
58	#380×C₁₃₇	C₂²	1	2	yes	—
59	#380×C₁₃₇	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
71	#376×C₁₃₇	C₂²	1	1	yes	characteristic
72	#376×C₁₃₇	C₂²	1	1	yes	characteristic
73	#376×C₁₃₇	C₂²	1	2	yes	—
74	#376×C₁₃₇	C₂²	1	2	yes	—
75	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
84	#126×C₁₃₇	C₂×C₄	1	16	yes	complemented
85	#125×C₁₃₇	C₂×C₄	1	8	yes	complemented
86	#124×C₁₃₇	C₂×C₄	1	8	yes	—
87	#123×C₁₃₇	C₂×C₄	1	16	yes	complemented
88	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	8	yes	complemented
89	#121×C₁₃₇	C₂×C₄	1	8	yes	—
90	C₄×Q₈×C₁₃₇	C₂×C₄	1	8	yes	complemented
91	C₄×D₄×C₁₃₇	C₂×C₄	1	8	yes	—
92	C₄×D₄×C₁₃₇	C₂×C₄	1	16	yes	complemented
93	#117×C₁₃₇	C₂×C₄	1	16	yes	complemented
94	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₇	C₂×C₄	1	8	yes	complemented
117	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
129	#95×C₁₃₇	C₂³	1	2	yes	—
130	#95×C₁₃₇	C₂³	1	2	yes	—
131	#95×C₁₃₇	C₂³	1	4	yes	—
132	#95×C₁₃₇	C₂³	1	2	yes	—
133	#95×C₁₃₇	C₂³	1	4	yes	—
134	#95×C₁₃₇	C₂³	1	2	yes	—
135	#95×C₁₃₇	C₂³	1	4	yes	—
136	#95×C₁₃₇	C₂³	1	2	yes	—
137	#95×C₁₃₇	C₂³	1	4	yes	—
138	#95×C₁₃₇	C₂³	1	2	yes	—
139	#95×C₁₃₇	C₂³	1	4	yes	—
140	#95×C₁₃₇	C₂³	1	4	yes	—
141	#95×C₁₃₇	C₂³	1	4	yes	—
142	#95×C₁₃₇	C₂³	1	4	yes	—
143	#95×C₁₃₇	C₂³	1	4	yes	—
144	#95×C₁₃₇	C₂³	1	4	yes	—
145	#95×C₁₃₇	C₂³	1	4	yes	—
146	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
148	C₂×Q₈×C₁₃₇	—	4	2	no	—
149	C₂×Q₈×C₁₃₇	C₂²×C₄	1	4	yes	—
150	C₂×D₄×C₁₃₇	—	4	2	no	—
151	C₂×D₄×C₁₃₇	—	4	2	no	—
152	C₂×D₄×C₁₃₇	—	4	2	no	—
153	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
154	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
155	C₂²×C₄×C₁₃₇	—	4	2	no	—
156	C₂²×C₄×C₁₃₇	—	4	2	no	—
157	C₂²×C₄×C₁₃₇	—	4	4	no	—
158	C₂²×C₄×C₁₃₇	—	4	2	no	—
159	C₂²×C₄×C₁₃₇	—	4	4	no	—
160	C₂²×C₄×C₁₃₇	—	4	4	no	—
161	C₂²×C₄×C₁₃₇	—	4	4	no	—
162	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
163	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
166	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
179	C₄⋊C₄×C₁₃₇	—	4	4	no	—
180	C₄⋊C₄×C₁₃₇	—	4	4	no	—
181	C₄⋊C₄×C₁₃₇	—	4	4	no	—
182	C₄⋊C₄×C₁₃₇	—	4	4	no	—
183	C₄⋊C₄×C₁₃₇	—	4	4	no	—
184	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
185	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
186	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
187	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
188	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
189	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
190	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
191	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
192	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
193	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
194	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
195	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
196	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
197	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
198	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
199	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
200	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
201	C₄²×C₁₃₇	—	4	2	no	—
202	C₄²×C₁₃₇	—	4	2	no	—
203	C₄²×C₁₃₇	—	4	2	no	—
204	C₄²×C₁₃₇	—	4	2	no	—
205	C₄²×C₁₃₇	—	4	4	no	—
206	C₄²×C₁₃₇	—	4	4	no	—
207	C₄²×C₁₃₇	—	4	4	no	—
208	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
209	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
210	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
211	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
212	C₄²×C₁₃₇	C₂²×C₄	1	8	yes	—
213	C₂³×C₁₃₇	—	2	2	no	—
214	C₂³×C₁₃₇	—	2	2	no	—
215	C₂³×C₁₃₇	—	2	2	no	—
216	C₂³×C₁₃₇	—	2	4	no	—
217	C₂³×C₁₃₇	—	2	4	no	—
218	C₂³×C₁₃₇	—	2	2	no	—
219	C₂³×C₁₃₇	—	2	2	no	—
220	C₂³×C₁₃₇	C₂³×C₄	1	4	yes	—
221	C₂³×C₁₃₇	C₂³×C₄	1	2	yes	—
222	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
223	Q₈×C₁₃₇	—	4	4	no	—
224	D₄×C₁₃₇	—	4	4	no	—
225	D₄×C₁₃₇	—	4	8	no	—
226	C₂×C₄×C₁₃₇	—	2	2	no	—
227	C₂×C₄×C₁₃₇	—	2	2	no	—
228	C₂×C₄×C₁₃₇	—	2	2	no	—
229	C₂×C₄×C₁₃₇	—	2	4	no	—
230	C₂×C₄×C₁₃₇	—	2	4	no	—
231	C₂×C₄×C₁₃₇	—	2	2	no	—
232	C₂×C₄×C₁₃₇	—	2	2	no	—
233	C₂×C₄×C₁₃₇	—	2	2	no	—
234	C₂×C₄×C₁₃₇	—	2	2	no	—
235	C₂×C₄×C₁₃₇	—	2	2	no	—
236	C₂×C₄×C₁₃₇	—	2	4	no	—
237	C₂×C₄×C₁₃₇	—	2	4	no	—
238	C₂×C₄×C₁₃₇	—	2	4	no	—
239	C₂×C₄×C₁₃₇	—	2	4	no	—
240	C₂×C₄×C₁₃₇	—	2	4	no	—
241	C₂×C₄×C₁₃₇	—	2	4	no	—
242	C₂×C₄×C₁₃₇	—	2	4	no	—
243	C₂×C₄×C₁₃₇	—	2	4	no	—
244	C₂×C₄×C₁₃₇	—	2	4	no	—
245	C₂×C₄×C₁₃₇	—	2	4	no	—
246	C₂×C₄×C₁₃₇	—	2	4	no	—
247	C₂×C₄×C₁₃₇	—	2	4	no	—
248	C₂×C₄×C₁₃₇	—	4	4	no	—
249	C₂×C₄×C₁₃₇	—	4	8	no	—
250	C₂×C₄×C₁₃₇	—	4	4	no	—
251	C₂×C₄×C₁₃₇	—	4	4	no	—
252	C₂×C₄×C₁₃₇	—	8	8	no	—
253	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
254	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
255	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
256	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
257	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
258	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
259	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
260	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
261	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
262	C₂²×C₁₃₇	—	2	2	no	—
263	C₂²×C₁₃₇	—	2	2	no	—
264	C₂²×C₁₃₇	—	2	2	no	—
265	C₂²×C₁₃₇	—	2	4	no	—
266	C₂²×C₁₃₇	—	2	4	no	—
267	C₂²×C₁₃₇	—	2	4	no	—
268	C₂²×C₁₃₇	—	4	4	no	—
269	C₂²×C₁₃₇	—	4	4	no	—
270	C₂²×C₁₃₇	—	4	4	no	—
271	C₂²×C₁₃₇	C₂⁴×C₄	1	1	yes	characteristic
272	C₂²×C₁₃₇	#585	1	2	yes	—
273	C₂²×C₁₃₇	#585	1	2	yes	—
274	C₂²×C₁₃₇	#585	1	2	yes	—
275	C₄×C₁₃₇	—	2	2	no	—
276	C₄×C₁₃₇	—	2	2	no	—
277	C₄×C₁₃₇	—	2	2	no	—
278	C₄×C₁₃₇	—	2	4	no	—
279	C₄×C₁₃₇	—	2	2	no	—
280	C₄×C₁₃₇	—	2	2	no	—
281	C₄×C₁₃₇	—	2	2	no	—
282	C₄×C₁₃₇	—	2	4	no	—
283	C₄×C₁₃₇	—	2	4	no	—
284	C₄×C₁₃₇	—	4	4	no	—
285	C₄×C₁₃₇	—	4	4	no	—
286	C₄×C₁₃₇	—	4	4	no	—
287	C₄×C₁₃₇	—	4	4	no	—
288	C₂×C₁₃₇	—	4	2	no	—
289	C₂×C₁₃₇	—	4	4	no	—
290	C₂×C₁₃₇	#3428	1	1	yes	characteristic
291	C₂×C₁₃₇	#3428	1	1	yes	characteristic
292	C₂×C₁₃₇	#3428	1	1	yes	characteristic
293	C₂×C₁₃₇	#3566	1	4	yes	—
294	#34400	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₁₃₇	#34400	1	1	yes	characteristic, direct product factor, Sylow
296	C₂×#529	C₂×C₁₃₇	1	1	yes	characteristic
297	#2376	C₂×C₁₃₇	1	4	yes	complemented
298	#2373	C₂×C₁₃₇	1	4	yes	complemented
299	#2357	C₂×C₁₃₇	1	2	yes	complemented
300	#2353	C₂×C₁₃₇	1	2	yes	complemented
301	#2346	C₂×C₁₃₇	1	2	yes	complemented
302	#2343	C₂×C₁₃₇	1	2	yes	complemented
303	#2337	C₂×C₁₃₇	1	2	yes	complemented
304	#2336	C₂×C₁₃₇	1	2	yes	complemented
305	#2333	C₂×C₁₃₇	1	2	yes	—
306	#2332	C₂×C₁₃₇	1	2	yes	complemented
307	#2320	C₂×C₁₃₇	1	2	yes	complemented
308	#2318	C₂×C₁₃₇	1	2	yes	complemented
309	#2283	C₂×C₁₃₇	1	1	yes	characteristic, complemented
310	#2283	C₂×C₁₃₇	1	1	yes	characteristic, complemented
311	#529	C₄×C₁₃₇	1	16	yes	complemented
312	C₂×#126	C₂²×C₁₃₇	1	2	yes	—
313	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
314	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
315	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
316	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
317	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
321	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
322	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
323	#391	C₂²×C₁₃₇	1	4	yes	—
324	#390	C₂²×C₁₃₇	1	4	yes	—
325	#389	C₂²×C₁₃₇	1	4	yes	—
326	#389	C₂²×C₁₃₇	1	4	yes	—
327	#388	C₂²×C₁₃₇	1	4	yes	—
328	#388	C₂²×C₁₃₇	1	4	yes	—
329	#388	C₂²×C₁₃₇	1	4	yes	—
330	#388	C₂²×C₁₃₇	1	4	yes	—
331	#388	C₂²×C₁₃₇	1	4	yes	—
332	#388	C₂²×C₁₃₇	1	4	yes	—
333	#387	C₂²×C₁₃₇	1	4	yes	—
334	#387	C₂²×C₁₃₇	1	4	yes	—
335	#387	C₂²×C₁₃₇	1	4	yes	—
336	#387	C₂²×C₁₃₇	1	4	yes	—
337	#387	C₂²×C₁₃₇	1	4	yes	—
338	#387	C₂²×C₁₃₇	1	4	yes	—
339	#386	C₂²×C₁₃₇	1	4	yes	—
340	#386	C₂²×C₁₃₇	1	4	yes	—
341	#385	C₂²×C₁₃₇	1	4	yes	—
342	#385	C₂²×C₁₃₇	1	4	yes	—
343	#383	C₂²×C₁₃₇	1	2	yes	—
344	#383	C₂²×C₁₃₇	1	2	yes	—
345	#383	C₂²×C₁₃₇	1	2	yes	—
346	#382	C₂²×C₁₃₇	1	2	yes	—
347	#382	C₂²×C₁₃₇	1	2	yes	—
348	#382	C₂²×C₁₃₇	1	2	yes	—
349	#381	C₂²×C₁₃₇	1	2	yes	—
350	#381	C₂²×C₁₃₇	1	2	yes	—
351	#381	C₂²×C₁₃₇	1	2	yes	—
352	#380	C₂²×C₁₃₇	1	2	yes	—
353	#380	C₂²×C₁₃₇	1	2	yes	—
354	#380	C₂²×C₁₃₇	1	2	yes	—
355	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
357	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	—
359	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
364	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
365	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
366	#376	C₂²×C₁₃₇	1	2	yes	—
367	#376	C₂²×C₁₃₇	1	1	yes	characteristic
368	#376	C₂²×C₁₃₇	1	1	yes	characteristic
369	#376	C₂²×C₁₃₇	1	2	yes	—
370	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
371	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
373	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
375	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
376	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
379	#126	C₂×C₄×C₁₃₇	1	16	yes	complemented
380	#125	C₂×C₄×C₁₃₇	1	8	yes	complemented
381	#124	C₂×C₄×C₁₃₇	1	8	yes	—
382	#123	C₂×C₄×C₁₃₇	1	16	yes	complemented
383	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	8	yes	complemented
384	#121	C₂×C₄×C₁₃₇	1	8	yes	—
385	C₄×Q₈	C₂×C₄×C₁₃₇	1	8	yes	complemented
386	C₄×D₄	C₂×C₄×C₁₃₇	1	8	yes	—
387	C₄×D₄	C₂×C₄×C₁₃₇	1	16	yes	complemented
388	#117	C₂×C₄×C₁₃₇	1	16	yes	complemented
389	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
411	C₂×C₄²	C₂×C₄×C₁₃₇	1	8	yes	complemented
412	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
414	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
415	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
416	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
417	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
424	#95	C₂³×C₁₃₇	1	2	yes	—
425	#95	C₂³×C₁₃₇	1	2	yes	—
426	#95	C₂³×C₁₃₇	1	4	yes	—
427	#95	C₂³×C₁₃₇	1	2	yes	—
428	#95	C₂³×C₁₃₇	1	4	yes	—
429	#95	C₂³×C₁₃₇	1	2	yes	—
430	#95	C₂³×C₁₃₇	1	4	yes	—
431	#95	C₂³×C₁₃₇	1	2	yes	—
432	#95	C₂³×C₁₃₇	1	4	yes	—
433	#95	C₂³×C₁₃₇	1	2	yes	—
434	#95	C₂³×C₁₃₇	1	4	yes	—
435	#95	C₂³×C₁₃₇	1	4	yes	—
436	#95	C₂³×C₁₃₇	1	4	yes	—
437	#95	C₂³×C₁₃₇	1	4	yes	—
438	#95	C₂³×C₁₃₇	1	4	yes	—
439	#95	C₂³×C₁₃₇	1	4	yes	—
440	#95	C₂³×C₁₃₇	1	4	yes	—
441	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
442	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	C₂²×C₄×C₁₃₇	1	4	yes	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
449	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
458	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
459	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
460	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
461	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
480	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
481	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
482	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
483	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
484	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	4	no	—
491	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
492	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
493	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
494	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
495	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
496	C₄²	—	4	2	no	—
497	C₄²	—	4	2	no	—
498	C₄²	—	4	2	no	—
499	C₄²	—	4	2	no	—
500	C₄²	—	4	4	no	—
501	C₄²	—	4	4	no	—
502	C₄²	—	4	4	no	—
503	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
504	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
505	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
506	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
507	C₄²	C₂²×C₄×C₁₃₇	1	8	yes	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	C₂³×C₄×C₁₃₇	1	4	yes	—
516	C₂³	C₂³×C₄×C₁₃₇	1	2	yes	—
517	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
518	Q₈	—	4	4	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	8	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	8	8	no	—
548	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
549	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
550	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
551	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
552	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
553	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
554	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
555	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
556	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	C₂⁴×C₄×C₁₃₇	1	1	yes	characteristic
567	C₂²	#585×C₁₃₇	1	2	yes	—
568	C₂²	#585×C₁₃₇	1	2	yes	—
569	C₂²	#585×C₁₃₇	1	2	yes	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	4	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	4	no	—
578	C₄	—	2	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	4	no	—
585	C₂	#3428×C₁₃₇	1	1	yes	characteristic
586	C₂	#3428×C₁₃₇	1	1	yes	characteristic
587	C₂	#3428×C₁₃₇	1	1	yes	characteristic
588	C₂	#3566×C₁₃₇	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₇
Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂×#121×C₁₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2376×C₁₃₇	C₂	semidirect
3. #2373×C₁₃₇	C₂	semidirect
4. #2357×C₁₃₇	C₂	semidirect
5. #2353×C₁₃₇	C₂	semidirect
6. #2346×C₁₃₇	C₂	semidirect
7. #2343×C₁₃₇	C₂	semidirect
8. #2337×C₁₃₇	C₂	semidirect
9. #2336×C₁₃₇	C₂	semidirect
11. #2332×C₁₃₇	C₂	semidirect
12. #2320×C₁₃₇	C₂	semidirect
13. #2318×C₁₃₇	C₂	semidirect
14. #2283×C₁₃₇	C₂	semidirect
15. #2283×C₁₃₇	C₂	semidirect
16. #529×C₁₃₇	C₄	semidirect
84. #126×C₁₃₇	C₂×C₄	semidirect
85. #125×C₁₃₇	C₂×C₄	semidirect
87. #123×C₁₃₇	C₂×C₄	semidirect
88. C₂²⋊Q₈×C₁₃₇	C₂×C₄	semidirect
90. C₄×Q₈×C₁₃₇	C₂×C₄	semidirect
92. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
93. #117×C₁₃₇	C₂×C₄	semidirect
116. C₂×C₄²×C₁₃₇	C₂×C₄	semidirect
294. #34400	C₁₃₇	direct (N × H)
295. C₁₃₇	#34400	direct (N × H)
297. #2376	C₂×C₁₃₇	semidirect
298. #2373	C₂×C₁₃₇	semidirect
299. #2357	C₂×C₁₃₇	semidirect
300. #2353	C₂×C₁₃₇	semidirect
301. #2346	C₂×C₁₃₇	semidirect
302. #2343	C₂×C₁₃₇	semidirect
303. #2337	C₂×C₁₃₇	semidirect
304. #2336	C₂×C₁₃₇	semidirect
306. #2332	C₂×C₁₃₇	semidirect
307. #2320	C₂×C₁₃₇	semidirect
308. #2318	C₂×C₁₃₇	semidirect
309. #2283	C₂×C₁₃₇	semidirect
310. #2283	C₂×C₁₃₇	semidirect
311. #529	C₄×C₁₃₇	semidirect
379. #126	C₂×C₄×C₁₃₇	semidirect
380. #125	C₂×C₄×C₁₃₇	semidirect
382. #123	C₂×C₄×C₁₃₇	semidirect
383. C₂²⋊Q₈	C₂×C₄×C₁₃₇	semidirect
385. C₄×Q₈	C₂×C₄×C₁₃₇	semidirect
387. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
388. #117	C₂×C₄×C₁₃₇	semidirect
411. C₂×C₄²	C₂×C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₇	2
#2376×C₁₃₇	2
#2373×C₁₃₇	2
#2357×C₁₃₇	2
#2353×C₁₃₇	2
#2346×C₁₃₇	2
#2343×C₁₃₇	2
#2337×C₁₃₇	2
#2336×C₁₃₇	2
#2333×C₁₃₇	2
#2332×C₁₃₇	2
#2320×C₁₃₇	2
#2318×C₁₃₇	2
#2283×C₁₃₇	2
#34400	137

Subgroups — C137×#34400 #46883786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34400 #46883786