Subgroups — C₁₃₇×#23527 #46872913

Order 35072.

1336 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2905×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	C₂×#413×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2050×C₁₃₇	C₂	1	8	yes	maximal, complemented
6	C₂×#338×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
8	#575×C₁₃₇	—	2	4	no	—
9	#575×C₁₃₇	—	2	2	no	—
10	#575×C₁₃₇	C₂²	1	4	yes	—
11	C₂×#137×C₁₃₇	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₁₃₇	—	2	2	no	—
13	C₂×#135×C₁₃₇	—	2	2	no	—
14	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
16	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
18	#424×C₁₃₇	—	2	2	no	—
19	#424×C₁₃₇	—	2	2	no	—
20	#423×C₁₃₇	C₂²	1	4	yes	complemented
21	#421×C₁₃₇	—	2	4	no	—
22	#421×C₁₃₇	—	2	4	no	—
23	C₂×#104×C₁₃₇	C₂²	1	8	yes	complemented
24	#413×C₁₃₇	—	2	4	no	—
25	#413×C₁₃₇	C₂²	1	8	yes	complemented
26	C₂×#101×C₁₃₇	—	2	2	no	—
27	C₂×#100×C₁₃₇	—	2	2	no	—
28	#338×C₁₃₇	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₃₇	—	2	2	no	—
30	C₂×#41×C₁₃₇	—	2	2	no	—
31	C₂×#41×C₁₃₇	—	2	2	no	—
32	C₂×#41×C₁₃₇	—	2	2	no	—
33	C₂×#41×C₁₃₇	—	2	2	no	—
34	C₂×#41×C₁₃₇	—	2	2	no	—
35	C₂×#41×C₁₃₇	—	2	2	no	—
36	C₂×#41×C₁₃₇	—	2	2	no	—
37	C₂×#41×C₁₃₇	—	2	2	no	—
38	C₂×#41×C₁₃₇	—	2	2	no	—
39	C₂×#41×C₁₃₇	D₄	1	4	yes	—
40	C₂×#41×C₁₃₇	C₂³	1	4	yes	—
41	C₂²×Q₈×C₁₃₇	D₄	1	2	yes	—
42	C₂²×D₄×C₁₃₇	—	2	2	no	—
43	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
44	C₂³×C₄×C₁₃₇	—	2	2	no	—
45	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
46	#137×C₁₃₇	—	2	8	no	—
47	#137×C₁₃₇	—	2	8	no	—
48	AGL(1,ℤ/8)×C₁₃₇	—	2	8	no	—
49	AGL(1,ℤ/8)×C₁₃₇	—	2	8	no	—
50	#135×C₁₃₇	—	2	8	no	—
51	#135×C₁₃₇	—	2	8	no	—
52	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
54	C₂×D₈×C₁₃₇	—	2	2	no	—
55	C₂×M₁₆×C₁₃₇	—	2	2	no	—
56	C₂×M₁₆×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	—	2	1	no	—
58	C₂×M₁₆×C₁₃₇	—	2	2	no	—
59	C₂×M₁₆×C₁₃₇	—	2	2	no	—
60	C₂×M₁₆×C₁₃₇	—	2	2	no	—
61	C₂×M₁₆×C₁₃₇	—	2	2	no	—
62	C₂×M₁₆×C₁₃₇	—	2	2	no	—
63	C₂×M₁₆×C₁₃₇	—	2	2	no	—
64	C₂×M₁₆×C₁₃₇	—	2	2	no	—
65	C₂×M₁₆×C₁₃₇	D₄	1	2	yes	—
66	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
68	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃₇	—	2	1	no	—
70	C₂²×C₈×C₁₃₇	—	2	2	no	—
71	C₂²×C₈×C₁₃₇	D₄	1	2	yes	—
72	#117×C₁₃₇	—	2	1	no	—
73	#117×C₁₃₇	—	2	1	no	—
74	#117×C₁₃₇	D₄	1	2	yes	—
75	#117×C₁₃₇	D₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
78	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
79	C₄⋊C₈×C₁₃₇	—	2	8	no	—
80	#104×C₁₃₇	—	2	16	no	—
81	#101×C₁₃₇	—	2	8	no	—
82	#100×C₁₃₇	—	2	8	no	—
83	C₂⁴×C₁₃₇	—	2	2	no	—
84	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
85	#41×C₁₃₇	—	2	4	no	—
86	#41×C₁₃₇	—	2	4	no	—
87	#41×C₁₃₇	—	2	4	no	—
88	#41×C₁₃₇	—	2	4	no	—
89	#41×C₁₃₇	—	2	4	no	—
90	#41×C₁₃₇	—	2	4	no	—
91	#41×C₁₃₇	—	2	4	no	—
92	#41×C₁₃₇	—	2	4	no	—
93	#41×C₁₃₇	—	4	2	no	—
94	#41×C₁₃₇	—	4	2	no	—
95	#41×C₁₃₇	—	4	2	no	—
96	#41×C₁₃₇	—	4	2	no	—
97	#41×C₁₃₇	—	4	2	no	—
98	#41×C₁₃₇	—	4	2	no	—
99	#41×C₁₃₇	—	4	2	no	—
100	#41×C₁₃₇	—	4	2	no	—
101	C₂×Q₈×C₁₃₇	—	2	2	no	—
102	C₂×Q₈×C₁₃₇	—	2	2	no	—
103	C₂×Q₈×C₁₃₇	—	2	2	no	—
104	C₂×Q₈×C₁₃₇	—	2	2	no	—
105	C₂×Q₈×C₁₃₇	—	2	2	no	—
106	C₂×Q₈×C₁₃₇	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₁₃₇	—	2	4	no	—
108	C₂×D₄×C₁₃₇	—	2	4	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	2	2	no	—
111	C₂×D₄×C₁₃₇	—	2	2	no	—
112	C₂×D₄×C₁₃₇	—	2	2	no	—
113	C₂×D₄×C₁₃₇	—	2	2	no	—
114	C₂×D₄×C₁₃₇	—	4	2	no	—
115	C₂×D₄×C₁₃₇	—	4	2	no	—
116	C₂×D₄×C₁₃₇	—	4	2	no	—
117	C₂×D₄×C₁₃₇	—	4	2	no	—
118	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₃₇	—	2	2	no	—
120	C₂²×C₄×C₁₃₇	—	2	2	no	—
121	C₂²×C₄×C₁₃₇	—	2	4	no	—
122	C₂²×C₄×C₁₃₇	—	2	4	no	—
123	C₂²×C₄×C₁₃₇	—	4	2	no	—
124	C₂²×C₄×C₁₃₇	—	4	2	no	—
125	C₂²×C₄×C₁₃₇	—	4	2	no	—
126	C₂²×C₄×C₁₃₇	—	4	2	no	—
127	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
135	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
136	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₃₇	—	2	8	no	—
138	SD₁₆×C₁₃₇	—	2	16	no	—
139	D₈×C₁₃₇	—	2	8	no	—
140	M₁₆×C₁₃₇	—	2	4	no	—
141	M₁₆×C₁₃₇	—	2	4	no	—
142	M₁₆×C₁₃₇	—	2	4	no	—
143	M₁₆×C₁₃₇	—	2	4	no	—
144	M₁₆×C₁₃₇	—	2	4	no	—
145	M₁₆×C₁₃₇	—	4	1	no	—
146	M₁₆×C₁₃₇	—	4	1	no	—
147	M₁₆×C₁₃₇	—	4	2	no	—
148	M₁₆×C₁₃₇	—	4	2	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	4	no	—
153	C₂×C₈×C₁₃₇	—	4	2	no	—
154	C₂×C₈×C₁₃₇	—	4	2	no	—
155	C₂×C₈×C₁₃₇	—	4	2	no	—
156	C₂×C₈×C₁₃₇	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₁₃₇	—	2	2	no	—
158	C₄⋊C₄×C₁₃₇	—	2	2	no	—
159	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
160	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
161	C₄²×C₁₃₇	—	2	2	no	—
162	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
163	C₂³×C₁₃₇	—	2	4	no	—
164	C₂³×C₁₃₇	—	4	2	no	—
165	C₂³×C₁₃₇	—	4	2	no	—
166	C₂³×C₁₃₇	—	8	1	no	—
167	C₂³×C₁₃₇	—	8	4	no	—
168	C₂³×C₁₃₇	#121	1	1	yes	characteristic
169	C₂³×C₁₃₇	#121	1	1	yes	characteristic
170	C₂³×C₁₃₇	#123	1	2	yes	—
171	C₂³×C₁₃₇	#123	1	2	yes	—
172	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
173	Q₈×C₁₃₇	—	2	4	no	—
174	Q₈×C₁₃₇	—	2	4	no	—
175	Q₈×C₁₃₇	—	4	2	no	—
176	Q₈×C₁₃₇	—	4	2	no	—
177	D₄×C₁₃₇	—	2	4	no	—
178	D₄×C₁₃₇	—	2	4	no	—
179	D₄×C₁₃₇	—	4	4	no	—
180	D₄×C₁₃₇	—	4	4	no	—
181	D₄×C₁₃₇	—	4	4	no	—
182	D₄×C₁₃₇	—	4	4	no	—
183	D₄×C₁₃₇	—	4	2	no	—
184	D₄×C₁₃₇	—	4	2	no	—
185	C₂×C₄×C₁₃₇	—	2	4	no	—
186	C₂×C₄×C₁₃₇	—	2	4	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	4	no	—
190	C₂×C₄×C₁₃₇	—	4	4	no	—
191	C₂×C₄×C₁₃₇	—	4	4	no	—
192	C₂×C₄×C₁₃₇	—	4	4	no	—
193	C₂×C₄×C₁₃₇	—	8	2	no	—
194	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	#120	1	2	yes	—
197	C₂×C₄×C₁₃₇	#121	1	2	yes	—
198	C₂×C₄×C₁₃₇	#121	1	2	yes	—
199	C₂×C₄×C₁₃₇	#121	1	2	yes	—
200	C₂×C₄×C₁₃₇	#121	1	2	yes	—
201	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃₇	#123	1	2	yes	—
204	C₂×C₄×C₁₃₇	#123	1	2	yes	—
205	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	#124	1	2	yes	—
207	C₂×C₄×C₁₃₇	#124	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
212	C₈×C₁₃₇	—	2	4	no	—
213	C₈×C₁₃₇	—	4	2	no	—
214	C₈×C₁₃₇	—	4	4	no	—
215	C₂²×C₁₃₇	—	4	1	no	—
216	C₂²×C₁₃₇	—	4	2	no	—
217	C₂²×C₁₃₇	—	4	1	no	—
218	C₂²×C₁₃₇	—	4	1	no	—
219	C₂²×C₁₃₇	—	4	2	no	—
220	C₂²×C₁₃₇	—	4	4	no	—
221	C₂²×C₁₃₇	—	8	4	no	—
222	C₂²×C₁₃₇	—	8	4	no	—
223	C₂²×C₁₃₇	—	8	4	no	—
224	C₂²×C₁₃₇	#394	1	1	yes	characteristic
225	C₂²×C₁₃₇	#394	1	2	yes	—
226	C₂²×C₁₃₇	#394	1	1	yes	characteristic
227	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
228	C₂²×C₁₃₇	C₂×#123	1	2	yes	—
229	C₄×C₁₃₇	—	4	4	no	—
230	C₄×C₁₃₇	—	4	4	no	—
231	C₄×C₁₃₇	#394	1	1	yes	characteristic
232	C₄×C₁₃₇	#394	1	2	yes	—
233	C₄×C₁₃₇	#394	1	1	yes	characteristic
234	C₄×C₁₃₇	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₃₇	C₂×#121	1	2	yes	—
236	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
237	C₂×C₁₃₇	—	2	1	no	—
238	C₂×C₁₃₇	—	2	1	no	—
239	C₂×C₁₃₇	—	2	2	no	—
240	C₂×C₁₃₇	—	2	2	no	—
241	C₂×C₁₃₇	—	2	1	no	—
242	C₂×C₁₃₇	—	8	4	no	—
243	C₂×C₁₃₇	C₂×#394	1	1	yes	characteristic
244	#23527	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₁₃₇	#23527	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#575	C₂×C₁₃₇	1	1	yes	characteristic
247	#2905	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	C₂×#421	C₂×C₁₃₇	1	2	yes	complemented
249	C₂×#413	C₂×C₁₃₇	1	2	yes	complemented
250	#2050	C₂×C₁₃₇	1	8	yes	complemented
251	C₂×#338	C₂×C₁₃₇	1	1	yes	characteristic, complemented
252	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
253	#575	—	2	4	no	—
254	#575	—	2	2	no	—
255	#575	C₂²×C₁₃₇	1	4	yes	—
256	C₂×#137	—	2	2	no	—
257	C₂×AGL(1,ℤ/8)	—	2	2	no	—
258	C₂×#135	—	2	2	no	—
259	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
261	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
263	#424	—	2	2	no	—
264	#424	—	2	2	no	—
265	#423	C₂²×C₁₃₇	1	4	yes	complemented
266	#421	—	2	4	no	—
267	#421	—	2	4	no	—
268	C₂×#104	C₂²×C₁₃₇	1	8	yes	complemented
269	#413	—	2	4	no	—
270	#413	C₂²×C₁₃₇	1	8	yes	complemented
271	C₂×#101	—	2	2	no	—
272	C₂×#100	—	2	2	no	—
273	#338	C₂²×C₁₃₇	1	4	yes	complemented
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	D₄×C₁₃₇	1	4	yes	—
285	C₂×#41	C₂³×C₁₃₇	1	4	yes	—
286	C₂²×Q₈	D₄×C₁₃₇	1	2	yes	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
291	#137	—	2	8	no	—
292	#137	—	2	8	no	—
293	AGL(1,ℤ/8)	—	2	8	no	—
294	AGL(1,ℤ/8)	—	2	8	no	—
295	#135	—	2	8	no	—
296	#135	—	2	8	no	—
297	C₂×Q₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	D₄×C₁₃₇	1	2	yes	—
311	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
312	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
313	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	D₄×C₁₃₇	1	2	yes	—
317	#117	—	2	1	no	—
318	#117	—	2	1	no	—
319	#117	D₄×C₁₃₇	1	2	yes	—
320	#117	D₄×C₁₃₇	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
324	C₄⋊C₈	—	2	8	no	—
325	#104	—	2	16	no	—
326	#101	—	2	8	no	—
327	#100	—	2	8	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	2	no	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₂×D₄×C₁₃₇	1	4	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
378	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
379	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
380	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
382	Q₁₆	—	2	8	no	—
383	SD₁₆	—	2	16	no	—
384	D₈	—	2	8	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	4	no	—
390	M₁₆	—	4	1	no	—
391	M₁₆	—	4	1	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	4	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	—	4	2	no	—
401	C₂×C₈	C₂×D₄×C₁₃₇	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
408	C₂³	—	2	4	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	8	4	no	—
413	C₂³	#121×C₁₃₇	1	1	yes	characteristic
414	C₂³	#121×C₁₃₇	1	1	yes	characteristic
415	C₂³	#123×C₁₃₇	1	2	yes	—
416	C₂³	#123×C₁₃₇	1	2	yes	—
417	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
440	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
441	C₂×C₄	#120×C₁₃₇	1	2	yes	—
442	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
443	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
444	C₂×C₄	#121×C₁₃₇	1	2	yes	—
445	C₂×C₄	#121×C₁₃₇	1	2	yes	—
446	C₂×C₄	#121×C₁₃₇	1	2	yes	—
447	C₂×C₄	#121×C₁₃₇	1	2	yes	—
448	C₂×C₄	#123×C₁₃₇	1	2	yes	—
449	C₂×C₄	#123×C₁₃₇	1	2	yes	—
450	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
451	C₂×C₄	#124×C₁₃₇	1	2	yes	—
452	C₂×C₄	#124×C₁₃₇	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	4	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	8	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	4	no	—
469	C₂²	#394×C₁₃₇	1	1	yes	characteristic
470	C₂²	#394×C₁₃₇	1	2	yes	—
471	C₂²	#394×C₁₃₇	1	1	yes	characteristic
472	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
473	C₂²	C₂×#123×C₁₃₇	1	2	yes	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	#394×C₁₃₇	1	1	yes	characteristic
477	C₄	#394×C₁₃₇	1	2	yes	—
478	C₄	#394×C₁₃₇	1	1	yes	characteristic
479	C₄	C₂×#120×C₁₃₇	1	1	yes	characteristic
480	C₄	C₂×#121×C₁₃₇	1	2	yes	—
481	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	2	no	—
485	C₂	—	2	2	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	4	no	—
488	C₂	C₂×#394×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₇	C₂×#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂×C₁₃₇	C₂×#394
prime radical	C₂×#575×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₇ ◁ C₂³×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2905×C₁₃₇	C₂	semidirect
3. C₂×#421×C₁₃₇	C₂	semidirect
4. C₂×#413×C₁₃₇	C₂	semidirect
5. #2050×C₁₃₇	C₂	semidirect
6. C₂×#338×C₁₃₇	C₂	semidirect
20. #423×C₁₃₇	C₂²	semidirect
23. C₂×#104×C₁₃₇	C₂²	semidirect
25. #413×C₁₃₇	C₂²	semidirect
28. #338×C₁₃₇	C₂²	semidirect
244. #23527	C₁₃₇	direct (N × H)
245. C₁₃₇	#23527	direct (N × H)
247. #2905	C₂×C₁₃₇	semidirect
248. C₂×#421	C₂×C₁₃₇	semidirect
249. C₂×#413	C₂×C₁₃₇	semidirect
250. #2050	C₂×C₁₃₇	semidirect
251. C₂×#338	C₂×C₁₃₇	semidirect
265. #423	C₂²×C₁₃₇	semidirect
268. C₂×#104	C₂²×C₁₃₇	semidirect
270. #413	C₂²×C₁₃₇	semidirect
273. #338	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×#575×C₁₃₇	2
#2905×C₁₃₇	2
C₂×#421×C₁₃₇	2
C₂×#413×C₁₃₇	2
#2050×C₁₃₇	2
C₂×#338×C₁₃₇	2
#23527	137

Subgroups — C137×#23527 #46872913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#23527 #46872913