Subgroups — C₁₃₇×#22577 #46871963

Order 35072.

978 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#416×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2347×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2341×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1934×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1926×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1865×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1825×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1807×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1788×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	C₄×#103×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
17	#416×C₁₃₇	C₄	1	8	yes	complemented
18	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
26	#390×C₁₃₇	—	2	2	no	—
27	#390×C₁₃₇	C₂²	1	2	yes	—
28	#389×C₁₃₇	C₂²	1	2	yes	—
29	#388×C₁₃₇	—	2	2	no	—
30	#383×C₁₃₇	—	2	1	no	—
31	#380×C₁₃₇	—	2	1	no	—
32	#380×C₁₃₇	C₂²	1	1	yes	characteristic
33	#380×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#340×C₁₃₇	C₂²	1	2	yes	—
40	#340×C₁₃₇	C₂²	1	2	yes	—
41	#336×C₁₃₇	C₂²	1	2	yes	—
42	C₂×#41×C₁₃₇	—	2	2	no	—
43	C₂×#41×C₁₃₇	—	2	4	no	—
44	C₂×#41×C₁₃₇	—	4	2	no	—
45	C₂×#41×C₁₃₇	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃₇	—	2	1	no	—
48	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃₇	—	2	1	no	—
50	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₇	—	4	2	no	—
52	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₁₃₇	—	2	4	no	—
57	C₄×Q₈×C₁₃₇	—	4	2	no	—
58	#117×C₁₃₇	—	2	2	no	—
59	#117×C₁₃₇	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₇	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃₇	—	2	1	no	—
73	C₂×C₄²×C₁₃₇	—	2	2	no	—
74	C₂×C₄²×C₁₃₇	—	2	2	no	—
75	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
76	#106×C₁₃₇	—	4	2	no	—
77	#103×C₁₃₇	—	2	4	no	—
78	#103×C₁₃₇	C₂×C₄	1	4	yes	—
79	#103×C₁₃₇	C₂×C₄	1	4	yes	—
80	#102×C₁₃₇	—	4	2	no	—
81	#102×C₁₃₇	C₂×C₄	1	4	yes	—
82	#102×C₁₃₇	C₂×C₄	1	4	yes	—
83	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
84	C₄×C₈×C₁₃₇	—	4	2	no	—
85	#95×C₁₃₇	—	2	1	no	—
86	#95×C₁₃₇	—	2	1	no	—
87	#95×C₁₃₇	—	2	2	no	—
88	#95×C₁₃₇	—	2	2	no	—
89	#95×C₁₃₇	D₄	1	1	yes	characteristic
90	#95×C₁₃₇	D₄	1	1	yes	characteristic
91	C₂⁴×C₁₃₇	—	2	1	no	—
92	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
93	#41×C₁₃₇	—	2	8	no	—
94	#41×C₁₃₇	—	4	4	no	—
95	#41×C₁₃₇	—	4	8	no	—
96	C₂×Q₈×C₁₃₇	—	2	1	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₁₃₇	#41	1	4	yes	—
100	C₂×D₄×C₁₃₇	—	2	4	no	—
101	C₂×D₄×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	1	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	4	4	no	—
105	C₂×D₄×C₁₃₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃₇	—	2	1	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	2	2	no	—
109	C₂²×C₄×C₁₃₇	—	2	1	no	—
110	C₂²×C₄×C₁₃₇	—	2	1	no	—
111	C₂²×C₄×C₁₃₇	—	2	4	no	—
112	C₂²×C₄×C₁₃₇	—	2	2	no	—
113	C₂²×C₄×C₁₃₇	—	2	2	no	—
114	C₂²×C₄×C₁₃₇	—	4	4	no	—
115	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
120	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	2	2	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	2	no	—
126	C₂×C₈×C₁₃₇	—	4	4	no	—
127	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₁₃₇	—	2	1	no	—
130	C₄⋊C₄×C₁₃₇	—	2	1	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	2	2	no	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	4	4	no	—
136	C₄⋊C₄×C₁₃₇	—	4	4	no	—
137	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
139	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
140	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
141	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
142	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
143	C₂²⋊C₄×C₁₃₇	—	8	1	no	—
144	C₂²⋊C₄×C₁₃₇	—	8	1	no	—
145	C₄²×C₁₃₇	—	2	4	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	—	2	2	no	—
148	C₄²×C₁₃₇	—	4	4	no	—
149	C₄²×C₁₃₇	—	8	2	no	—
150	C₂³×C₁₃₇	—	2	2	no	—
151	C₂³×C₁₃₇	—	2	2	no	—
152	C₂³×C₁₃₇	—	2	1	no	—
153	C₂³×C₁₃₇	—	2	1	no	—
154	C₂³×C₁₃₇	—	2	2	no	—
155	C₂³×C₁₃₇	—	4	2	no	—
156	C₂³×C₁₃₇	—	4	2	no	—
157	C₂³×C₁₃₇	—	4	1	no	—
158	C₂³×C₁₃₇	—	4	1	no	—
159	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
160	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₃₇	—	2	2	no	—
162	Q₈×C₁₃₇	—	2	4	no	—
163	Q₈×C₁₃₇	#117	1	4	yes	—
164	D₄×C₁₃₇	—	2	2	no	—
165	D₄×C₁₃₇	—	2	2	no	—
166	D₄×C₁₃₇	—	4	8	no	—
167	D₄×C₁₃₇	—	4	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	2	4	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	2	no	—
173	C₂×C₄×C₁₃₇	—	2	2	no	—
174	C₂×C₄×C₁₃₇	—	2	2	no	—
175	C₂×C₄×C₁₃₇	—	2	4	no	—
176	C₂×C₄×C₁₃₇	—	2	2	no	—
177	C₂×C₄×C₁₃₇	—	2	2	no	—
178	C₂×C₄×C₁₃₇	—	2	2	no	—
179	C₂×C₄×C₁₃₇	—	2	2	no	—
180	C₂×C₄×C₁₃₇	—	2	2	no	—
181	C₂×C₄×C₁₃₇	—	4	8	no	—
182	C₂×C₄×C₁₃₇	—	4	2	no	—
183	C₂×C₄×C₁₃₇	—	4	1	no	—
184	C₂×C₄×C₁₃₇	—	4	1	no	—
185	C₂×C₄×C₁₃₇	—	4	2	no	—
186	C₂×C₄×C₁₃₇	—	4	2	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₃₇	#135	1	4	yes	—
193	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₁₃₇	—	2	2	no	—
198	C₈×C₁₃₇	—	2	2	no	—
199	C₈×C₁₃₇	—	4	2	no	—
200	C₂²×C₁₃₇	—	2	2	no	—
201	C₂²×C₁₃₇	—	2	2	no	—
202	C₂²×C₁₃₇	—	2	2	no	—
203	C₂²×C₁₃₇	—	4	2	no	—
204	C₂²×C₁₃₇	—	4	2	no	—
205	C₂²×C₁₃₇	—	4	2	no	—
206	C₂²×C₁₃₇	—	4	2	no	—
207	C₂²×C₁₃₇	—	4	2	no	—
208	C₂²×C₁₃₇	—	8	2	no	—
209	C₂²×C₁₃₇	—	8	2	no	—
210	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₁₃₇	#546	1	2	yes	—
212	C₂²×C₁₃₇	C₂×#135	1	2	yes	—
213	C₂²×C₁₃₇	#577	1	1	yes	characteristic
214	C₂²×C₁₃₇	#577	1	1	yes	characteristic
215	C₄×C₁₃₇	—	2	2	no	—
216	C₄×C₁₃₇	—	2	4	no	—
217	C₄×C₁₃₇	—	2	4	no	—
218	C₄×C₁₃₇	—	4	2	no	—
219	C₄×C₁₃₇	—	4	2	no	—
220	C₄×C₁₃₇	—	4	2	no	—
221	C₄×C₁₃₇	—	8	2	no	—
222	C₄×C₁₃₇	—	8	2	no	—
223	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
224	C₄×C₁₃₇	#518	1	1	yes	characteristic
225	C₄×C₁₃₇	#551	1	2	yes	—
226	C₂×C₁₃₇	—	4	2	no	—
227	C₂×C₁₃₇	—	8	2	no	—
228	C₂×C₁₃₇	#2342	1	1	yes	characteristic
229	C₂×C₁₃₇	C₄×#135	1	1	yes	characteristic
230	C₂×C₁₃₇	#2952	1	1	yes	characteristic
231	C₂×C₁₃₇	#3301	1	2	yes	—
232	C₂×C₁₃₇	#3304	1	2	yes	—
233	#22577	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₁₃₇	#22577	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×#416	C₂×C₁₃₇	1	1	yes	characteristic
236	#2347	C₂×C₁₃₇	1	1	yes	characteristic, complemented
237	#2341	C₂×C₁₃₇	1	1	yes	characteristic
238	#1934	C₂×C₁₃₇	1	2	yes	complemented
239	#1926	C₂×C₁₃₇	1	2	yes	complemented
240	#1865	C₂×C₁₃₇	1	2	yes	complemented
241	#1825	C₂×C₁₃₇	1	1	yes	characteristic, complemented
242	#1807	C₂×C₁₃₇	1	1	yes	characteristic, complemented
243	#1788	C₂×C₁₃₇	1	1	yes	characteristic
244	C₄×#103	C₂×C₁₃₇	1	2	yes	complemented
245	C₈×C₂²⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
249	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
250	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
251	#416	C₄×C₁₃₇	1	8	yes	complemented
252	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
253	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
254	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
255	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
256	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
260	#390	—	2	2	no	—
261	#390	C₂²×C₁₃₇	1	2	yes	—
262	#389	C₂²×C₁₃₇	1	2	yes	—
263	#388	—	2	2	no	—
264	#383	—	2	1	no	—
265	#380	—	2	1	no	—
266	#380	C₂²×C₁₃₇	1	1	yes	characteristic
267	#380	C₂²×C₁₃₇	1	1	yes	characteristic
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
270	C₄×C₂²⋊C₄	—	2	1	no	—
271	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
272	#340	C₂²×C₁₃₇	1	2	yes	—
273	#340	C₂²×C₁₃₇	1	2	yes	—
274	#340	C₂²×C₁₃₇	1	2	yes	—
275	#336	C₂²×C₁₃₇	1	2	yes	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	4	2	no	—
279	C₂×#41	C₂×C₄×C₁₃₇	1	4	yes	—
280	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₂²×C₈	—	4	2	no	—
286	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
287	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	4	2	no	—
292	#117	—	2	2	no	—
293	#117	C₂×C₄×C₁₃₇	1	4	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	D₄×C₁₃₇	1	2	yes	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
310	#106	—	4	2	no	—
311	#103	—	2	4	no	—
312	#103	C₂×C₄×C₁₃₇	1	4	yes	—
313	#103	C₂×C₄×C₁₃₇	1	4	yes	—
314	#102	—	4	2	no	—
315	#102	C₂×C₄×C₁₃₇	1	4	yes	—
316	#102	C₂×C₄×C₁₃₇	1	4	yes	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₄×C₈	—	4	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	1	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	D₄×C₁₃₇	1	1	yes	characteristic
324	#95	D₄×C₁₃₇	1	1	yes	characteristic
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	#41	—	2	8	no	—
328	#41	—	4	4	no	—
329	#41	—	4	8	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂²×C₄×C₁₃₇	1	2	yes	—
333	C₂×Q₈	#41×C₁₃₇	1	4	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₁₃₇	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
353	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
362	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
372	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₂²⋊C₄	—	8	1	no	—
378	C₂²⋊C₄	—	8	1	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	4	no	—
383	C₄²	—	8	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	4	no	—
397	Q₈	#117×C₁₃₇	1	4	yes	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	4	8	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
426	C₂×C₄	#135×C₁₃₇	1	4	yes	—
427	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
429	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
445	C₂²	#546×C₁₃₇	1	2	yes	—
446	C₂²	C₂×#135×C₁₃₇	1	2	yes	—
447	C₂²	#577×C₁₃₇	1	1	yes	characteristic
448	C₂²	#577×C₁₃₇	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
458	C₄	#518×C₁₃₇	1	1	yes	characteristic
459	C₄	#551×C₁₃₇	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	8	2	no	—
462	C₂	#2342×C₁₃₇	1	1	yes	characteristic
463	C₂	C₄×#135×C₁₃₇	1	1	yes	characteristic
464	C₂	#2952×C₁₃₇	1	1	yes	characteristic
465	C₂	#3301×C₁₃₇	1	2	yes	—
466	C₂	#3304×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×#41×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄×C₂²⋊C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2347×C₁₃₇	C₂	semidirect
4. #1934×C₁₃₇	C₂	semidirect
5. #1926×C₁₃₇	C₂	semidirect
6. #1865×C₁₃₇	C₂	semidirect
7. #1825×C₁₃₇	C₂	semidirect
8. #1807×C₁₃₇	C₂	semidirect
10. C₄×#103×C₁₃₇	C₂	semidirect
11. C₈×C₂²⋊C₄×C₁₃₇	C₂	semidirect
17. #416×C₁₃₇	C₄	semidirect
233. #22577	C₁₃₇	direct (N × H)
234. C₁₃₇	#22577	direct (N × H)
236. #2347	C₂×C₁₃₇	semidirect
238. #1934	C₂×C₁₃₇	semidirect
239. #1926	C₂×C₁₃₇	semidirect
240. #1865	C₂×C₁₃₇	semidirect
241. #1825	C₂×C₁₃₇	semidirect
242. #1807	C₂×C₁₃₇	semidirect
244. C₄×#103	C₂×C₁₃₇	semidirect
245. C₈×C₂²⋊C₄	C₂×C₁₃₇	semidirect
251. #416	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×#416×C₁₃₇	2
#2347×C₁₃₇	2
#2341×C₁₃₇	2
#1934×C₁₃₇	2
#1926×C₁₃₇	2
#1865×C₁₃₇	2
#1825×C₁₃₇	2
#1807×C₁₃₇	2
#1788×C₁₃₇	2
C₄×#103×C₁₃₇	2
C₈×C₂²⋊C₄×C₁₃₇	2
#22577	137

Subgroups — C137×#22577 #46871963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22577 #46871963