Subgroups — C₁₃₇×#26254 #46875640

Order 35072.

1050 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2445×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2054×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2041×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1970×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1970×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1970×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1942×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1879×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₁₃₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₃₇	C₂²	1	2	yes	—
16	C₂×#123×C₁₃₇	—	2	2	no	—
17	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
18	#493×C₁₃₇	—	2	4	no	—
19	C₄×D₈×C₁₃₇	—	2	4	no	—
20	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
30	#394×C₁₃₇	—	2	2	no	—
31	#394×C₁₃₇	—	2	2	no	—
32	#390×C₁₃₇	C₂²	1	2	yes	—
33	#390×C₁₃₇	C₂²	1	2	yes	—
34	#390×C₁₃₇	C₂²	1	2	yes	—
35	#389×C₁₃₇	C₂²	1	2	yes	—
36	#386×C₁₃₇	—	2	2	no	—
37	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	#340×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₇	—	2	2	no	—
42	C₂²×D₄×C₁₃₇	—	2	2	no	—
43	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₇	—	2	2	no	—
46	C₂×D₈×C₁₃₇	—	2	4	no	—
47	C₂×D₈×C₁₃₇	—	2	2	no	—
48	C₂×D₈×C₁₃₇	—	2	2	no	—
49	C₂×D₈×C₁₃₇	—	2	2	no	—
50	C₂×D₈×C₁₃₇	—	2	4	no	—
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂×D₈×C₁₃₇	—	2	2	no	—
53	C₂×D₈×C₁₃₇	—	4	2	no	—
54	C₂×D₈×C₁₃₇	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	#127×C₁₃₇	—	2	4	no	—
60	#127×C₁₃₇	—	4	2	no	—
61	#123×C₁₃₇	—	4	8	no	—
62	C₄×D₄×C₁₃₇	—	2	4	no	—
63	C₄×D₄×C₁₃₇	—	4	2	no	—
64	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
76	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
79	#107×C₁₃₇	—	2	2	no	—
80	#107×C₁₃₇	—	2	2	no	—
81	C₄⋊C₈×C₁₃₇	—	2	2	no	—
82	#102×C₁₃₇	—	2	4	no	—
83	#102×C₁₃₇	—	4	2	no	—
84	#102×C₁₃₇	—	4	2	no	—
85	#102×C₁₃₇	—	4	2	no	—
86	C₄×C₈×C₁₃₇	—	2	2	no	—
87	C₄×C₈×C₁₃₇	—	2	2	no	—
88	C₄×C₈×C₁₃₇	—	2	2	no	—
89	#95×C₁₃₇	—	2	2	no	—
90	#95×C₁₃₇	D₄	1	1	yes	characteristic
91	#95×C₁₃₇	D₄	1	1	yes	characteristic
92	C₂⁴×C₁₃₇	—	2	2	no	—
93	C₂⁴×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	2	2	no	—
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	2	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	4	4	no	—
106	C₂×D₄×C₁₃₇	—	4	4	no	—
107	C₂×D₄×C₁₃₇	—	4	4	no	—
108	C₂×D₄×C₁₃₇	—	4	4	no	—
109	C₂×D₄×C₁₃₇	—	8	2	no	—
110	C₂×D₄×C₁₃₇	—	8	2	no	—
111	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
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	—	4	4	no	—
116	C₂²×C₄×C₁₃₇	—	8	2	no	—
117	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
124	D₈×C₁₃₇	—	2	8	no	—
125	D₈×C₁₃₇	—	4	8	no	—
126	D₈×C₁₃₇	—	4	4	no	—
127	C₂×C₈×C₁₃₇	—	2	1	no	—
128	C₂×C₈×C₁₃₇	—	2	1	no	—
129	C₂×C₈×C₁₃₇	—	2	1	no	—
130	C₂×C₈×C₁₃₇	—	2	1	no	—
131	C₂×C₈×C₁₃₇	—	2	1	no	—
132	C₂×C₈×C₁₃₇	—	2	1	no	—
133	C₂×C₈×C₁₃₇	—	2	1	no	—
134	C₂×C₈×C₁₃₇	—	2	1	no	—
135	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃₇	#41	1	2	yes	—
137	C₂×C₈×C₁₃₇	#41	1	2	yes	—
138	C₂×C₈×C₁₃₇	#41	1	2	yes	—
139	C₄⋊C₄×C₁₃₇	—	2	2	no	—
140	C₄⋊C₄×C₁₃₇	—	2	2	no	—
141	C₄⋊C₄×C₁₃₇	—	2	2	no	—
142	C₄⋊C₄×C₁₃₇	—	2	2	no	—
143	C₄⋊C₄×C₁₃₇	—	2	2	no	—
144	C₄⋊C₄×C₁₃₇	—	4	4	no	—
145	C₄⋊C₄×C₁₃₇	D₈	1	4	yes	complemented
146	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
147	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
148	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
149	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
150	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
151	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
152	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
153	C₄²×C₁₃₇	—	2	1	no	—
154	C₄²×C₁₃₇	—	2	1	no	—
155	C₄²×C₁₃₇	—	2	1	no	—
156	C₄²×C₁₃₇	—	2	1	no	—
157	C₄²×C₁₃₇	—	2	1	no	—
158	C₄²×C₁₃₇	—	2	1	no	—
159	C₂³×C₁₃₇	—	2	4	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	—	4	2	no	—
163	C₂³×C₁₃₇	—	4	2	no	—
164	C₂³×C₁₃₇	—	4	2	no	—
165	C₂³×C₁₃₇	—	4	2	no	—
166	C₂³×C₁₃₇	—	4	2	no	—
167	C₂³×C₁₃₇	—	4	2	no	—
168	C₂³×C₁₃₇	—	4	2	no	—
169	C₂³×C₁₃₇	—	4	2	no	—
170	C₂³×C₁₃₇	—	4	2	no	—
171	C₂³×C₁₃₇	—	4	2	no	—
172	C₂³×C₁₃₇	—	4	2	no	—
173	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₁₃₇	—	2	4	no	—
175	D₄×C₁₃₇	—	2	4	no	—
176	D₄×C₁₃₇	—	4	2	no	—
177	D₄×C₁₃₇	—	4	2	no	—
178	D₄×C₁₃₇	—	4	2	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	D₄×C₁₃₇	—	4	2	no	—
181	D₄×C₁₃₇	—	4	2	no	—
182	D₄×C₁₃₇	—	8	8	no	—
183	D₄×C₁₃₇	—	8	8	no	—
184	C₂×C₄×C₁₃₇	—	2	1	no	—
185	C₂×C₄×C₁₃₇	—	2	1	no	—
186	C₂×C₄×C₁₃₇	—	2	1	no	—
187	C₂×C₄×C₁₃₇	—	2	1	no	—
188	C₂×C₄×C₁₃₇	—	2	1	no	—
189	C₂×C₄×C₁₃₇	—	2	1	no	—
190	C₂×C₄×C₁₃₇	—	2	1	no	—
191	C₂×C₄×C₁₃₇	—	2	1	no	—
192	C₂×C₄×C₁₃₇	—	2	1	no	—
193	C₂×C₄×C₁₃₇	—	2	1	no	—
194	C₂×C₄×C₁₃₇	—	2	1	no	—
195	C₂×C₄×C₁₃₇	—	2	1	no	—
196	C₂×C₄×C₁₃₇	—	2	1	no	—
197	C₂×C₄×C₁₃₇	—	2	1	no	—
198	C₂×C₄×C₁₃₇	—	4	2	no	—
199	C₂×C₄×C₁₃₇	—	4	2	no	—
200	C₂×C₄×C₁₃₇	—	4	2	no	—
201	C₂×C₄×C₁₃₇	—	4	2	no	—
202	C₂×C₄×C₁₃₇	—	4	2	no	—
203	C₂×C₄×C₁₃₇	—	4	2	no	—
204	C₂×C₄×C₁₃₇	—	8	8	no	—
205	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
206	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
208	C₂×C₄×C₁₃₇	#135	1	2	yes	—
209	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
215	C₈×C₁₃₇	—	2	2	no	—
216	C₈×C₁₃₇	—	4	1	no	—
217	C₈×C₁₃₇	—	4	1	no	—
218	C₈×C₁₃₇	#123	1	4	yes	complemented
219	C₂²×C₁₃₇	—	4	4	no	—
220	C₂²×C₁₃₇	—	4	4	no	—
221	C₂²×C₁₃₇	—	4	4	no	—
222	C₂²×C₁₃₇	—	8	2	no	—
223	C₂²×C₁₃₇	—	8	2	no	—
224	C₂²×C₁₃₇	—	8	2	no	—
225	C₂²×C₁₃₇	—	8	2	no	—
226	C₂²×C₁₃₇	—	8	2	no	—
227	C₂²×C₁₃₇	—	8	2	no	—
228	C₂²×C₁₃₇	—	8	2	no	—
229	C₂²×C₁₃₇	—	8	2	no	—
230	C₂²×C₁₃₇	—	8	2	no	—
231	C₂²×C₁₃₇	—	8	2	no	—
232	C₂²×C₁₃₇	—	8	2	no	—
233	C₂²×C₁₃₇	#532	1	1	yes	characteristic
234	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
235	C₂²×C₁₃₇	#550	1	1	yes	characteristic
236	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
237	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
238	C₂²×C₁₃₇	#576	1	1	yes	characteristic
239	C₂²×C₁₃₇	#576	1	1	yes	characteristic
240	C₄×C₁₃₇	—	2	2	no	—
241	C₄×C₁₃₇	—	2	2	no	—
242	C₄×C₁₃₇	—	2	2	no	—
243	C₄×C₁₃₇	—	2	2	no	—
244	C₄×C₁₃₇	—	4	1	no	—
245	C₄×C₁₃₇	—	4	1	no	—
246	C₄×C₁₃₇	—	8	2	no	—
247	C₄×C₁₃₇	—	8	2	no	—
248	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
249	C₄×C₁₃₇	#540	1	1	yes	characteristic
250	C₄×C₁₃₇	#546	1	1	yes	characteristic
251	C₄×C₁₃₇	#559	1	1	yes	characteristic
252	C₂×C₁₃₇	—	8	4	no	—
253	C₂×C₁₃₇	—	16	2	no	—
254	C₂×C₁₃₇	#2445	1	1	yes	characteristic
255	C₂×C₁₃₇	#3169	1	1	yes	characteristic
256	C₂×C₁₃₇	#3176	1	1	yes	characteristic
257	C₂×C₁₃₇	D₄×D₈	1	1	yes	characteristic
258	C₂×C₁₃₇	#3280	1	1	yes	characteristic
259	C₂×C₁₃₇	#3391	1	1	yes	characteristic
260	C₂×C₁₃₇	#3396	1	1	yes	characteristic
261	#26254	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₁₃₇	#26254	1	1	yes	characteristic, direct product factor, Sylow
263	C₂×#493	C₂×C₁₃₇	1	1	yes	characteristic
264	C₂×C₄×D₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
265	#2445	C₂×C₁₃₇	1	2	yes	complemented
266	#2054	C₂×C₁₃₇	1	2	yes	complemented
267	#2041	C₂×C₁₃₇	1	2	yes	complemented
268	#1970	C₂×C₁₃₇	1	1	yes	characteristic, complemented
269	#1970	C₂×C₁₃₇	1	1	yes	characteristic, complemented
270	#1970	C₂×C₁₃₇	1	1	yes	characteristic, complemented
271	#1942	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	#1879	C₂×C₁₃₇	1	2	yes	complemented
273	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
274	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
275	C₂²×D₈	C₂²×C₁₃₇	1	2	yes	—
276	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
277	C₂×#127	C₂²×C₁₃₇	1	2	yes	—
278	C₂×#123	—	2	2	no	—
279	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
280	#493	—	2	4	no	—
281	C₄×D₈	—	2	4	no	—
282	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₂×#107	C₂²×C₁₃₇	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
285	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
286	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
287	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
288	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
289	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
292	#394	—	2	2	no	—
293	#394	—	2	2	no	—
294	#390	C₂²×C₁₃₇	1	2	yes	—
295	#390	C₂²×C₁₃₇	1	2	yes	—
296	#390	C₂²×C₁₃₇	1	2	yes	—
297	#389	C₂²×C₁₃₇	1	2	yes	—
298	#386	—	2	2	no	—
299	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
300	#340	C₂²×C₁₃₇	1	2	yes	—
301	#336	C₂²×C₁₃₇	1	1	yes	characteristic
302	#336	C₂²×C₁₃₇	1	1	yes	characteristic
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
306	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
307	C₂³×C₄	—	2	2	no	—
308	C₂×D₈	—	2	4	no	—
309	C₂×D₈	—	2	2	no	—
310	C₂×D₈	—	2	2	no	—
311	C₂×D₈	—	2	2	no	—
312	C₂×D₈	—	2	4	no	—
313	C₂×D₈	—	2	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	4	2	no	—
316	C₂×D₈	D₄×C₁₃₇	1	4	yes	—
317	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
321	#127	—	2	4	no	—
322	#127	—	4	2	no	—
323	#123	—	4	8	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	4	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	#102	—	2	4	no	—
345	#102	—	4	2	no	—
346	#102	—	4	2	no	—
347	#102	—	4	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	D₄×C₁₃₇	1	1	yes	characteristic
353	#95	D₄×C₁₃₇	1	1	yes	characteristic
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	8	2	no	—
372	C₂×D₄	—	8	2	no	—
373	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
386	D₈	—	2	8	no	—
387	D₈	—	4	8	no	—
388	D₈	—	4	4	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
398	C₂×C₈	#41×C₁₃₇	1	2	yes	—
399	C₂×C₈	#41×C₁₃₇	1	2	yes	—
400	C₂×C₈	#41×C₁₃₇	1	2	yes	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₄⋊C₄	D₈×C₁₃₇	1	4	yes	complemented
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	8	8	no	—
445	D₄	—	8	8	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	8	8	no	—
467	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
468	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
469	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
470	C₂×C₄	#135×C₁₃₇	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
476	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	1	no	—
480	C₈	#123×C₁₃₇	1	4	yes	complemented
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	#532×C₁₃₇	1	1	yes	characteristic
496	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
497	C₂²	#550×C₁₃₇	1	1	yes	characteristic
498	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
499	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
500	C₂²	#576×C₁₃₇	1	1	yes	characteristic
501	C₂²	#576×C₁₃₇	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	2	no	—
510	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
511	C₄	#540×C₁₃₇	1	1	yes	characteristic
512	C₄	#546×C₁₃₇	1	1	yes	characteristic
513	C₄	#559×C₁₃₇	1	1	yes	characteristic
514	C₂	—	8	4	no	—
515	C₂	—	16	2	no	—
516	C₂	#2445×C₁₃₇	1	1	yes	characteristic
517	C₂	#3169×C₁₃₇	1	1	yes	characteristic
518	C₂	#3176×C₁₃₇	1	1	yes	characteristic
519	C₂	D₄×D₈×C₁₃₇	1	1	yes	characteristic
520	C₂	#3280×C₁₃₇	1	1	yes	characteristic
521	C₂	#3391×C₁₃₇	1	1	yes	characteristic
522	C₂	#3396×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#493×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄×C₄⋊C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₁₃₇	C₂	semidirect
3. #2445×C₁₃₇	C₂	semidirect
4. #2054×C₁₃₇	C₂	semidirect
5. #2041×C₁₃₇	C₂	semidirect
6. #1970×C₁₃₇	C₂	semidirect
7. #1970×C₁₃₇	C₂	semidirect
8. #1970×C₁₃₇	C₂	semidirect
9. #1942×C₁₃₇	C₂	semidirect
10. #1879×C₁₃₇	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₃₇	C₂	semidirect
145. C₄⋊C₄×C₁₃₇	D₈	semidirect
218. C₈×C₁₃₇	#123	semidirect
261. #26254	C₁₃₇	direct (N × H)
262. C₁₃₇	#26254	direct (N × H)
264. C₂×C₄×D₈	C₂×C₁₃₇	semidirect
265. #2445	C₂×C₁₃₇	semidirect
266. #2054	C₂×C₁₃₇	semidirect
267. #2041	C₂×C₁₃₇	semidirect
268. #1970	C₂×C₁₃₇	semidirect
269. #1970	C₂×C₁₃₇	semidirect
270. #1970	C₂×C₁₃₇	semidirect
271. #1942	C₂×C₁₃₇	semidirect
272. #1879	C₂×C₁₃₇	semidirect
273. C₈×C₄⋊C₄	C₂×C₁₃₇	semidirect
407. C₄⋊C₄	D₈×C₁₃₇	semidirect
480. C₈	#123×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493×C₁₃₇	2
C₂×C₄×D₈×C₁₃₇	2
#2445×C₁₃₇	2
#2054×C₁₃₇	2
#2041×C₁₃₇	2
#1970×C₁₃₇	2
#1942×C₁₃₇	2
#1879×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
#26254	137

Subgroups — C137×#26254 #46875640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26254 #46875640