Subgroups — C₁₃₇×#22096 #46871482

Order 35072.

726 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3091×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2929×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#1946×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1938×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1922×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1871×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1866×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1855×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1826×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1752×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	#525×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
17	#485×C₁₃₇	C₄	1	2	yes	complemented
18	#484×C₁₃₇	C₄	1	1	yes	characteristic, complemented
19	#483×C₁₃₇	C₄	1	1	yes	characteristic, complemented
20	#482×C₁₃₇	C₄	1	2	yes	complemented
21	#481×C₁₃₇	C₄	1	1	yes	characteristic, complemented
22	#480×C₁₃₇	C₄	1	1	yes	characteristic, complemented
23	#435×C₁₃₇	—	2	1	no	—
24	#435×C₁₃₇	—	2	1	no	—
25	C₈×D₄×C₁₃₇	—	2	1	no	—
26	C₈×D₄×C₁₃₇	—	2	1	no	—
27	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
28	#427×C₁₃₇	C₂²	1	2	yes	—
29	#424×C₁₃₇	—	2	1	no	—
30	#424×C₁₃₇	—	2	1	no	—
31	#424×C₁₃₇	C₂²	1	2	yes	—
32	#424×C₁₃₇	C₂²	1	2	yes	—
33	#424×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
35	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
36	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
37	#416×C₁₃₇	C₂²	1	2	yes	—
38	#408×C₁₃₇	C₂²	1	1	yes	characteristic
39	#407×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
41	#405×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
43	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
44	#341×C₁₃₇	C₂²	1	2	yes	—
45	#339×C₁₃₇	C₂²	1	2	yes	—
46	#339×C₁₃₇	C₂²	1	2	yes	—
47	#339×C₁₃₇	C₂²	1	2	yes	—
48	#336×C₁₃₇	C₂²	1	2	yes	—
49	C₂×#41×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
51	#131×C₁₃₇	—	4	2	no	—
52	C₂×M₁₆×C₁₃₇	—	2	1	no	—
53	C₂×M₁₆×C₁₃₇	—	2	1	no	—
54	C₂×M₁₆×C₁₃₇	—	4	2	no	—
55	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃₇	—	2	1	no	—
59	C₂²×C₈×C₁₃₇	—	2	1	no	—
60	C₂²×C₈×C₁₃₇	—	4	2	no	—
61	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃₇	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
68	#123×C₁₃₇	—	2	1	no	—
69	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
71	#121×C₁₃₇	C₂×C₄	1	1	yes	characteristic
72	#121×C₁₃₇	C₂×C₄	1	1	yes	characteristic
73	#120×C₁₃₇	—	2	1	no	—
74	C₄×D₄×C₁₃₇	—	2	1	no	—
75	C₄×D₄×C₁₃₇	—	2	1	no	—
76	#117×C₁₃₇	—	2	1	no	—
77	#117×C₁₃₇	—	2	1	no	—
78	#117×C₁₃₇	C₂×C₄	1	2	yes	—
79	#117×C₁₃₇	C₂³	1	1	yes	characteristic
80	#117×C₁₃₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
85	C₂×C₄²×C₁₃₇	—	2	1	no	—
86	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
87	#108×C₁₃₇	—	4	2	no	—
88	#107×C₁₃₇	C₂×C₄	1	2	yes	—
89	#107×C₁₃₇	C₂×C₄	1	2	yes	—
90	#106×C₁₃₇	C₂×C₄	1	2	yes	—
91	#106×C₁₃₇	C₂×C₄	1	2	yes	—
92	C₄⋊C₈×C₁₃₇	—	2	2	no	—
93	C₄⋊C₈×C₁₃₇	—	2	2	no	—
94	C₄⋊C₈×C₁₃₇	—	2	2	no	—
95	C₄⋊C₈×C₁₃₇	—	2	2	no	—
96	C₄⋊C₈×C₁₃₇	—	2	1	no	—
97	C₄⋊C₈×C₁₃₇	—	2	1	no	—
98	#104×C₁₃₇	—	4	2	no	—
99	#103×C₁₃₇	C₂×C₄	1	2	yes	—
100	#103×C₁₃₇	C₂×C₄	1	2	yes	—
101	#102×C₁₃₇	C₂×C₄	1	2	yes	—
102	#102×C₁₃₇	C₂×C₄	1	2	yes	—
103	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
104	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
105	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
106	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
107	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	2	yes	—
110	#97×C₁₃₇	—	2	1	no	—
111	#97×C₁₃₇	—	4	2	no	—
112	C₄×C₈×C₁₃₇	—	2	1	no	—
113	#95×C₁₃₇	—	2	1	no	—
114	C₂⁴×C₁₃₇	#41	1	1	yes	characteristic
115	#41×C₁₃₇	—	2	2	no	—
116	#41×C₁₃₇	—	2	2	no	—
117	C₂×Q₈×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₃₇	—	2	1	no	—
119	C₂×D₄×C₁₃₇	—	2	1	no	—
120	C₂×D₄×C₁₃₇	—	2	1	no	—
121	C₂×D₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₇	—	2	2	no	—
123	C₂²×C₄×C₁₃₇	—	2	2	no	—
124	C₂²×C₄×C₁₃₇	—	2	1	no	—
125	C₂²×C₄×C₁₃₇	—	2	1	no	—
126	C₂²×C₄×C₁₃₇	—	2	1	no	—
127	C₂²×C₄×C₁₃₇	—	2	2	no	—
128	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₇	C₂²×C₄	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	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₁₃₇	—	2	2	no	—
135	M₁₆×C₁₃₇	—	2	2	no	—
136	M₁₆×C₁₃₇	—	2	2	no	—
137	M₁₆×C₁₃₇	—	2	2	no	—
138	M₁₆×C₁₃₇	—	4	2	no	—
139	M₁₆×C₁₃₇	—	4	2	no	—
140	C₂×C₈×C₁₃₇	—	2	2	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	—	2	2	no	—
143	C₂×C₈×C₁₃₇	—	2	2	no	—
144	C₂×C₈×C₁₃₇	—	2	1	no	—
145	C₂×C₈×C₁₃₇	—	2	1	no	—
146	C₂×C₈×C₁₃₇	—	2	2	no	—
147	C₂×C₈×C₁₃₇	—	4	1	no	—
148	C₂×C₈×C₁₃₇	—	4	1	no	—
149	C₂×C₈×C₁₃₇	—	4	1	no	—
150	C₂×C₈×C₁₃₇	—	4	1	no	—
151	C₂×C₈×C₁₃₇	—	4	2	no	—
152	C₂×C₈×C₁₃₇	—	4	2	no	—
153	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₁₃₇	—	2	1	no	—
160	C₄⋊C₄×C₁₃₇	—	2	1	no	—
161	C₄⋊C₄×C₁₃₇	—	2	1	no	—
162	C₄⋊C₄×C₁₃₇	—	2	1	no	—
163	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
164	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
165	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
168	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
169	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
170	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
171	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
172	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
173	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
174	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
175	C₄²×C₁₃₇	—	2	2	no	—
176	C₄²×C₁₃₇	—	2	1	no	—
177	C₄²×C₁₃₇	—	2	2	no	—
178	C₄²×C₁₃₇	—	2	2	no	—
179	C₄²×C₁₃₇	—	2	2	no	—
180	C₂³×C₁₃₇	—	2	2	no	—
181	C₂³×C₁₃₇	—	2	2	no	—
182	C₂³×C₁₃₇	—	2	1	no	—
183	C₂³×C₁₃₇	—	4	1	no	—
184	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₁₃₇	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₃₇	—	2	2	no	—
188	D₄×C₁₃₇	—	2	2	no	—
189	D₄×C₁₃₇	—	4	2	no	—
190	D₄×C₁₃₇	—	4	2	no	—
191	D₄×C₁₃₇	—	4	2	no	—
192	C₂×C₄×C₁₃₇	—	2	2	no	—
193	C₂×C₄×C₁₃₇	—	2	2	no	—
194	C₂×C₄×C₁₃₇	—	2	2	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	—	2	1	no	—
199	C₂×C₄×C₁₃₇	—	2	2	no	—
200	C₂×C₄×C₁₃₇	—	2	2	no	—
201	C₂×C₄×C₁₃₇	—	2	1	no	—
202	C₂×C₄×C₁₃₇	—	2	1	no	—
203	C₂×C₄×C₁₃₇	—	2	1	no	—
204	C₂×C₄×C₁₃₇	—	4	2	no	—
205	C₂×C₄×C₁₃₇	—	4	2	no	—
206	C₂×C₄×C₁₃₇	—	4	1	no	—
207	C₂×C₄×C₁₃₇	—	4	1	no	—
208	C₂×C₄×C₁₃₇	—	4	2	no	—
209	C₂×C₄×C₁₃₇	—	4	2	no	—
210	C₂×C₄×C₁₃₇	—	4	2	no	—
211	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃₇	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
216	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
217	C₈×C₁₃₇	—	2	2	no	—
218	C₈×C₁₃₇	—	2	2	no	—
219	C₈×C₁₃₇	—	2	1	no	—
220	C₈×C₁₃₇	—	2	1	no	—
221	C₈×C₁₃₇	—	2	1	no	—
222	C₈×C₁₃₇	—	2	1	no	—
223	C₈×C₁₃₇	—	4	1	no	—
224	C₈×C₁₃₇	—	4	2	no	—
225	C₈×C₁₃₇	—	4	1	no	—
226	C₂²×C₁₃₇	—	2	1	no	—
227	C₂²×C₁₃₇	—	2	1	no	—
228	C₂²×C₁₃₇	—	2	1	no	—
229	C₂²×C₁₃₇	—	2	1	no	—
230	C₂²×C₁₃₇	—	2	1	no	—
231	C₂²×C₁₃₇	—	2	1	no	—
232	C₂²×C₁₃₇	—	2	1	no	—
233	C₂²×C₁₃₇	—	4	4	no	—
234	C₂²×C₁₃₇	—	4	1	no	—
235	C₂²×C₁₃₇	—	4	1	no	—
236	C₂²×C₁₃₇	—	4	1	no	—
237	C₂²×C₁₃₇	#444	1	2	yes	—
238	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₁₃₇	#539	1	2	yes	—
240	C₄×C₁₃₇	—	2	1	no	—
241	C₄×C₁₃₇	—	2	1	no	—
242	C₄×C₁₃₇	—	4	1	no	—
243	C₄×C₁₃₇	—	4	2	no	—
244	C₄×C₁₃₇	—	4	1	no	—
245	C₄×C₁₃₇	—	4	2	no	—
246	C₄×C₁₃₇	—	4	1	no	—
247	C₄×C₁₃₇	—	8	2	no	—
248	C₄×C₁₃₇	#520	1	2	yes	—
249	C₄×C₁₃₇	#534	1	1	yes	characteristic
250	C₄×C₁₃₇	#536	1	1	yes	characteristic
251	C₂×C₁₃₇	—	2	2	no	—
252	C₂×C₁₃₇	—	2	2	no	—
253	C₂×C₁₃₇	—	4	1	no	—
254	C₂×C₁₃₇	—	8	1	no	—
255	C₂×C₁₃₇	#2322	1	1	yes	characteristic
256	C₂×C₁₃₇	C₂×#444	1	1	yes	characteristic
257	C₂×C₁₃₇	#2955	1	1	yes	characteristic
258	#22096	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₁₃₇	#22096	1	1	yes	characteristic, direct product factor, Sylow
260	#3091	C₂×C₁₃₇	1	1	yes	characteristic
261	#2929	C₂×C₁₃₇	1	1	yes	characteristic
262	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	#1946	C₂×C₁₃₇	1	2	yes	complemented
264	#1938	C₂×C₁₃₇	1	2	yes	complemented
265	#1922	C₂×C₁₃₇	1	2	yes	complemented
266	#1871	C₂×C₁₃₇	1	1	yes	characteristic
267	#1866	C₂×C₁₃₇	1	2	yes	complemented
268	#1855	C₂×C₁₃₇	1	1	yes	characteristic, complemented
269	#1826	C₂×C₁₃₇	1	1	yes	characteristic, complemented
270	#1752	C₂×C₁₃₇	1	1	yes	characteristic, complemented
271	C₂×#131	C₂²×C₁₃₇	1	1	yes	characteristic
272	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
274	#525	C₂²×C₁₃₇	1	1	yes	characteristic
275	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
276	#485	C₄×C₁₃₇	1	2	yes	complemented
277	#484	C₄×C₁₃₇	1	1	yes	characteristic, complemented
278	#483	C₄×C₁₃₇	1	1	yes	characteristic, complemented
279	#482	C₄×C₁₃₇	1	2	yes	complemented
280	#481	C₄×C₁₃₇	1	1	yes	characteristic, complemented
281	#480	C₄×C₁₃₇	1	1	yes	characteristic, complemented
282	#435	—	2	1	no	—
283	#435	—	2	1	no	—
284	C₈×D₄	—	2	1	no	—
285	C₈×D₄	—	2	1	no	—
286	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
287	#427	C₂²×C₁₃₇	1	2	yes	—
288	#424	—	2	1	no	—
289	#424	—	2	1	no	—
290	#424	C₂²×C₁₃₇	1	2	yes	—
291	#424	C₂²×C₁₃₇	1	2	yes	—
292	#424	C₂²×C₁₃₇	1	1	yes	characteristic
293	C₂×C₄⋊C₈	—	2	1	no	—
294	C₂×C₄⋊C₈	—	2	1	no	—
295	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
296	#416	C₂²×C₁₃₇	1	2	yes	—
297	#408	C₂²×C₁₃₇	1	1	yes	characteristic
298	#407	C₂²×C₁₃₇	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
300	#405	C₂²×C₁₃₇	1	1	yes	characteristic
301	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
303	#341	C₂²×C₁₃₇	1	2	yes	—
304	#339	C₂²×C₁₃₇	1	2	yes	—
305	#339	C₂²×C₁₃₇	1	2	yes	—
306	#339	C₂²×C₁₃₇	1	2	yes	—
307	#336	C₂²×C₁₃₇	1	2	yes	—
308	C₂×#41	C₂³×C₁₃₇	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
310	#131	—	4	2	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	4	2	no	—
314	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
315	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
316	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	4	2	no	—
320	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
322	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
323	C₂²×C₈	D₄×C₁₃₇	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
325	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
327	#123	—	2	1	no	—
328	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
330	#121	C₂×C₄×C₁₃₇	1	1	yes	characteristic
331	#121	C₂×C₄×C₁₃₇	1	1	yes	characteristic
332	#120	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	C₂×C₄×C₁₃₇	1	2	yes	—
338	#117	C₂³×C₁₃₇	1	2	yes	—
339	#117	C₂³×C₁₃₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
346	#108	—	4	2	no	—
347	#107	C₂×C₄×C₁₃₇	1	2	yes	—
348	#107	C₂×C₄×C₁₃₇	1	2	yes	—
349	#106	C₂×C₄×C₁₃₇	1	2	yes	—
350	#106	C₂×C₄×C₁₃₇	1	2	yes	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	2	1	no	—
357	#104	—	4	2	no	—
358	#103	C₂×C₄×C₁₃₇	1	2	yes	—
359	#103	C₂×C₄×C₁₃₇	1	2	yes	—
360	#102	C₂×C₄×C₁₃₇	1	2	yes	—
361	#102	C₂×C₄×C₁₃₇	1	2	yes	—
362	C₂²⋊C₈	—	2	1	no	—
363	C₂²⋊C₈	—	2	1	no	—
364	C₂²⋊C₈	—	2	1	no	—
365	C₂²⋊C₈	—	2	1	no	—
366	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
367	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	1	yes	characteristic
368	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	2	yes	—
369	#97	—	2	1	no	—
370	#97	—	4	2	no	—
371	C₄×C₈	—	2	1	no	—
372	#95	—	2	1	no	—
373	C₂⁴	#41×C₁₃₇	1	1	yes	characteristic
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	C₂×Q₈	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
391	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
393	M₁₆	—	2	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	4	2	no	—
398	M₁₆	—	4	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	4	1	no	—
407	C₂×C₈	—	4	1	no	—
408	C₂×C₈	—	4	1	no	—
409	C₂×C₈	—	4	1	no	—
410	C₂×C₈	—	4	2	no	—
411	C₂×C₈	—	4	2	no	—
412	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
413	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
414	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
417	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
423	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
424	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
425	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	4	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
444	C₂³	C₄×D₄×C₁₃₇	1	1	yes	characteristic
445	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	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	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
471	C₂×C₄	C₄×D₄×C₁₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
474	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
475	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	4	1	no	—
483	C₈	—	4	2	no	—
484	C₈	—	4	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	#444×C₁₃₇	1	2	yes	—
497	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
498	C₂²	#539×C₁₃₇	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	8	2	no	—
507	C₄	#520×C₁₃₇	1	2	yes	—
508	C₄	#534×C₁₃₇	1	1	yes	characteristic
509	C₄	#536×C₁₃₇	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	#2322×C₁₃₇	1	1	yes	characteristic
515	C₂	C₂×#444×C₁₃₇	1	1	yes	characteristic
516	C₂	#2955×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₄×D₄
prime radical	#525×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₇ ◁ C₂³×C₈×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#424×C₁₃₇	C₂	semidirect
4. #1946×C₁₃₇	C₂	semidirect
5. #1938×C₁₃₇	C₂	semidirect
6. #1922×C₁₃₇	C₂	semidirect
8. #1866×C₁₃₇	C₂	semidirect
9. #1855×C₁₃₇	C₂	semidirect
10. #1826×C₁₃₇	C₂	semidirect
11. #1752×C₁₃₇	C₂	semidirect
17. #485×C₁₃₇	C₄	semidirect
18. #484×C₁₃₇	C₄	semidirect
19. #483×C₁₃₇	C₄	semidirect
20. #482×C₁₃₇	C₄	semidirect
21. #481×C₁₃₇	C₄	semidirect
22. #480×C₁₃₇	C₄	semidirect
258. #22096	C₁₃₇	direct (N × H)
259. C₁₃₇	#22096	direct (N × H)
262. C₂×#424	C₂×C₁₃₇	semidirect
263. #1946	C₂×C₁₃₇	semidirect
264. #1938	C₂×C₁₃₇	semidirect
265. #1922	C₂×C₁₃₇	semidirect
267. #1866	C₂×C₁₃₇	semidirect
268. #1855	C₂×C₁₃₇	semidirect
269. #1826	C₂×C₁₃₇	semidirect
270. #1752	C₂×C₁₃₇	semidirect
276. #485	C₄×C₁₃₇	semidirect
277. #484	C₄×C₁₃₇	semidirect
278. #483	C₄×C₁₃₇	semidirect
279. #482	C₄×C₁₃₇	semidirect
280. #481	C₄×C₁₃₇	semidirect
281. #480	C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3091×C₁₃₇	2
#2929×C₁₃₇	2
C₂×#424×C₁₃₇	2
#1946×C₁₃₇	2
#1938×C₁₃₇	2
#1922×C₁₃₇	2
#1871×C₁₃₇	2
#1866×C₁₃₇	2
#1855×C₁₃₇	2
#1826×C₁₃₇	2
#1752×C₁₃₇	2
#22096	137

Subgroups — C137×#22096 #46871482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22096 #46871482