Subgroups — C₁₃₇×#20553 #46869939

Order 35072.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2298×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1771×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1771×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1770×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1768×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#1753×C₁₃₇	C₂	1	1	yes	maximal, characteristic
13	#1753×C₁₃₇	C₂	1	1	yes	maximal, characteristic
14	#1752×C₁₃₇	C₂	1	1	yes	maximal, characteristic
15	C₈×C₂²⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
19	#433×C₁₃₇	C₄	1	8	yes	complemented
20	#424×C₁₃₇	C₄	1	8	yes	complemented
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
39	#388×C₁₃₇	C₄	1	2	yes	—
40	#388×C₁₃₇	C₄	1	2	yes	—
41	#387×C₁₃₇	C₄	1	2	yes	—
42	#387×C₁₃₇	C₄	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
47	#376×C₁₃₇	C₂²	1	1	yes	characteristic
48	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
49	#336×C₁₃₇	C₂²	1	1	yes	characteristic
50	#336×C₁₃₇	C₂²	1	1	yes	characteristic
51	#336×C₁₃₇	C₂²	1	1	yes	characteristic
52	#336×C₁₃₇	C₂²	1	1	yes	characteristic
53	#336×C₁₃₇	C₂²	1	1	yes	characteristic
54	#336×C₁₃₇	C₂²	1	1	yes	characteristic
55	#336×C₁₃₇	C₂²	1	1	yes	characteristic
56	#336×C₁₃₇	C₂²	1	1	yes	characteristic
57	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₃₇	—	4	1	no	—
59	C₂×M₁₆×C₁₃₇	—	4	1	no	—
60	C₂×M₁₆×C₁₃₇	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₁₃₇	—	4	1	no	—
62	C₂²×C₈×C₁₃₇	—	4	1	no	—
63	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
64	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
72	#117×C₁₃₇	C₂×C₄	1	4	yes	—
73	#117×C₁₃₇	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
91	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
92	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
93	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
94	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
95	C₄⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
96	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
97	C₂²⋊C₈×C₁₃₇	C₂×C₄	1	4	yes	—
98	#97×C₁₃₇	—	4	1	no	—
99	#97×C₁₃₇	—	4	1	no	—
100	#97×C₁₃₇	—	4	1	no	—
101	#97×C₁₃₇	—	4	1	no	—
102	#97×C₁₃₇	C₂×C₄	1	4	yes	—
103	C₄×C₈×C₁₃₇	—	4	1	no	—
104	C₄×C₈×C₁₃₇	—	4	1	no	—
105	C₄×C₈×C₁₃₇	—	4	1	no	—
106	C₄×C₈×C₁₃₇	—	4	1	no	—
107	C₄×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
108	#95×C₁₃₇	C₂×C₄	1	2	yes	—
109	#95×C₁₃₇	C₂×C₄	1	2	yes	—
110	#95×C₁₃₇	C₂×C₄	1	2	yes	—
111	#95×C₁₃₇	C₂×C₄	1	2	yes	—
112	#95×C₁₃₇	C₂×C₄	1	2	yes	—
113	#95×C₁₃₇	C₂×C₄	1	2	yes	—
114	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	—	2	1	no	—
116	C₂²×C₄×C₁₃₇	—	2	1	no	—
117	C₂²×C₄×C₁₃₇	—	2	1	no	—
118	C₂²×C₄×C₁₃₇	—	2	1	no	—
119	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₁₃₇	—	4	4	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	—	2	1	no	—
136	C₂×C₈×C₁₃₇	—	2	1	no	—
137	C₂×C₈×C₁₃₇	—	2	1	no	—
138	C₂×C₈×C₁₃₇	—	2	1	no	—
139	C₂×C₈×C₁₃₇	—	2	1	no	—
140	C₂×C₈×C₁₃₇	—	2	1	no	—
141	C₂×C₈×C₁₃₇	—	2	1	no	—
142	C₂×C₈×C₁₃₇	—	2	1	no	—
143	C₂×C₈×C₁₃₇	—	2	1	no	—
144	C₂×C₈×C₁₃₇	—	2	1	no	—
145	C₂×C₈×C₁₃₇	—	2	1	no	—
146	C₂×C₈×C₁₃₇	—	2	1	no	—
147	C₂×C₈×C₁₃₇	—	2	1	no	—
148	C₂×C₈×C₁₃₇	—	4	4	no	—
149	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₁₃₇	C₂²×C₄	1	2	yes	—
157	C₄⋊C₄×C₁₃₇	—	2	4	no	—
158	C₄⋊C₄×C₁₃₇	—	4	2	no	—
159	C₄⋊C₄×C₁₃₇	C₄²	1	4	yes	—
160	C₄⋊C₄×C₁₃₇	C₄²	1	4	yes	—
161	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
162	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
163	C₂²⋊C₄×C₁₃₇	C₄²	1	4	yes	—
164	C₂²⋊C₄×C₁₃₇	C₄²	1	4	yes	—
165	C₄²×C₁₃₇	—	2	4	no	—
166	C₄²×C₁₃₇	—	2	1	no	—
167	C₄²×C₁₃₇	—	2	1	no	—
168	C₄²×C₁₃₇	—	2	1	no	—
169	C₄²×C₁₃₇	—	2	1	no	—
170	C₄²×C₁₃₇	—	2	1	no	—
171	C₄²×C₁₃₇	—	2	1	no	—
172	C₄²×C₁₃₇	—	2	1	no	—
173	C₄²×C₁₃₇	—	2	1	no	—
174	C₄²×C₁₃₇	—	4	2	no	—
175	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
176	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
177	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
178	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
179	C₂³×C₁₃₇	—	2	1	no	—
180	C₂³×C₁₃₇	—	2	1	no	—
181	C₂³×C₁₃₇	—	2	2	no	—
182	C₂³×C₁₃₇	—	2	2	no	—
183	C₂³×C₁₃₇	C₂×C₄²	1	2	yes	—
184	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃₇	—	2	2	no	—
186	C₂×C₄×C₁₃₇	—	2	1	no	—
187	C₂×C₄×C₁₃₇	—	2	1	no	—
188	C₂×C₄×C₁₃₇	—	2	2	no	—
189	C₂×C₄×C₁₃₇	—	2	2	no	—
190	C₂×C₄×C₁₃₇	—	2	2	no	—
191	C₂×C₄×C₁₃₇	—	2	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	2	no	—
196	C₂×C₄×C₁₃₇	—	2	2	no	—
197	C₂×C₄×C₁₃₇	—	2	2	no	—
198	C₂×C₄×C₁₃₇	—	2	2	no	—
199	C₂×C₄×C₁₃₇	—	2	2	no	—
200	C₂×C₄×C₁₃₇	—	2	2	no	—
201	C₂×C₄×C₁₃₇	—	2	2	no	—
202	C₂×C₄×C₁₃₇	—	2	2	no	—
203	C₂×C₄×C₁₃₇	—	2	2	no	—
204	C₂×C₄×C₁₃₇	—	2	2	no	—
205	C₂×C₄×C₁₃₇	—	2	2	no	—
206	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
207	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
208	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
209	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
210	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
211	C₂×C₄×C₁₃₇	#131	1	4	yes	—
212	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
218	C₈×C₁₃₇	—	2	2	no	—
219	C₈×C₁₃₇	—	2	2	no	—
220	C₈×C₁₃₇	—	2	2	no	—
221	C₈×C₁₃₇	—	2	2	no	—
222	C₈×C₁₃₇	—	2	2	no	—
223	C₈×C₁₃₇	—	2	2	no	—
224	C₈×C₁₃₇	—	2	2	no	—
225	C₈×C₁₃₇	—	2	2	no	—
226	C₂²×C₁₃₇	—	2	2	no	—
227	C₂²×C₁₃₇	—	2	2	no	—
228	C₂²×C₁₃₇	—	2	2	no	—
229	C₂²×C₁₃₇	—	4	2	no	—
230	C₂²×C₁₃₇	—	4	2	no	—
231	C₂²×C₁₃₇	C₂²×C₄²	1	1	yes	characteristic
232	C₂²×C₁₃₇	#520	1	1	yes	characteristic
233	C₂²×C₁₃₇	#520	1	1	yes	characteristic
234	C₂²×C₁₃₇	C₂×#131	1	2	yes	—
235	C₂²×C₁₃₇	#568	1	2	yes	—
236	C₄×C₁₃₇	—	2	2	no	—
237	C₄×C₁₃₇	—	2	2	no	—
238	C₄×C₁₃₇	—	2	2	no	—
239	C₄×C₁₃₇	—	2	2	no	—
240	C₄×C₁₃₇	—	2	4	no	—
241	C₄×C₁₃₇	—	2	2	no	—
242	C₄×C₁₃₇	—	4	2	no	—
243	C₄×C₁₃₇	—	4	2	no	—
244	C₄×C₁₃₇	—	4	2	no	—
245	C₄×C₁₃₇	#518	1	1	yes	characteristic
246	C₄×C₁₃₇	#519	1	1	yes	characteristic
247	C₄×C₁₃₇	#520	1	1	yes	characteristic
248	C₄×C₁₃₇	#520	1	1	yes	characteristic
249	C₂×C₁₃₇	—	4	2	no	—
250	C₂×C₁₃₇	#2274	1	1	yes	characteristic
251	C₂×C₁₃₇	C₄×#131	1	1	yes	characteristic
252	C₂×C₁₃₇	#2875	1	1	yes	characteristic
253	C₂×C₁₃₇	#2992	1	2	yes	—
254	C₂×C₁₃₇	#2993	1	2	yes	—
255	#20553	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₃₇	#20553	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#433	C₂×C₁₃₇	1	1	yes	characteristic
258	C₂×#424	C₂×C₁₃₇	1	1	yes	characteristic
259	#2298	C₂×C₁₃₇	1	1	yes	characteristic
260	#1771	C₂×C₁₃₇	1	1	yes	characteristic, complemented
261	#1771	C₂×C₁₃₇	1	1	yes	characteristic, complemented
262	#1770	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
264	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
265	#1768	C₂×C₁₃₇	1	1	yes	characteristic, complemented
266	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
267	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
268	#1753	C₂×C₁₃₇	1	1	yes	characteristic
269	#1753	C₂×C₁₃₇	1	1	yes	characteristic
270	#1752	C₂×C₁₃₇	1	1	yes	characteristic
271	C₈×C₂²⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic
272	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
274	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
275	#433	C₄×C₁₃₇	1	8	yes	complemented
276	#424	C₄×C₁₃₇	1	8	yes	complemented
277	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
285	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
286	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
287	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
289	C₂×#97	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	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
295	#388	C₄×C₁₃₇	1	2	yes	—
296	#388	C₄×C₁₃₇	1	2	yes	—
297	#387	C₄×C₁₃₇	1	2	yes	—
298	#387	C₄×C₁₃₇	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
303	#376	C₂²×C₁₃₇	1	1	yes	characteristic
304	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
305	#336	C₂²×C₁₃₇	1	1	yes	characteristic
306	#336	C₂²×C₁₃₇	1	1	yes	characteristic
307	#336	C₂²×C₁₃₇	1	1	yes	characteristic
308	#336	C₂²×C₁₃₇	1	1	yes	characteristic
309	#336	C₂²×C₁₃₇	1	1	yes	characteristic
310	#336	C₂²×C₁₃₇	1	1	yes	characteristic
311	#336	C₂²×C₁₃₇	1	1	yes	characteristic
312	#336	C₂²×C₁₃₇	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₂×M₁₆	—	4	1	no	—
315	C₂×M₁₆	—	4	1	no	—
316	C₂×M₁₆	C₂×C₄×C₁₃₇	1	4	yes	—
317	C₂²×C₈	—	4	1	no	—
318	C₂²×C₈	—	4	1	no	—
319	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
320	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
328	#117	C₂×C₄×C₁₃₇	1	4	yes	—
329	#117	C₂×C₄×C₁₃₇	1	4	yes	—
330	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
331	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
332	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
339	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
340	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
346	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
347	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
348	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
349	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
350	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
351	C₄⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
352	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
353	C₂²⋊C₈	C₂×C₄×C₁₃₇	1	4	yes	—
354	#97	—	4	1	no	—
355	#97	—	4	1	no	—
356	#97	—	4	1	no	—
357	#97	—	4	1	no	—
358	#97	C₂×C₄×C₁₃₇	1	4	yes	—
359	C₄×C₈	—	4	1	no	—
360	C₄×C₈	—	4	1	no	—
361	C₄×C₈	—	4	1	no	—
362	C₄×C₈	—	4	1	no	—
363	C₄×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
364	#95	C₂×C₄×C₁₃₇	1	2	yes	—
365	#95	C₂×C₄×C₁₃₇	1	2	yes	—
366	#95	C₂×C₄×C₁₃₇	1	2	yes	—
367	#95	C₂×C₄×C₁₃₇	1	2	yes	—
368	#95	C₂×C₄×C₁₃₇	1	2	yes	—
369	#95	C₂×C₄×C₁₃₇	1	2	yes	—
370	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	1	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	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	4	4	no	—
405	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
406	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
407	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
408	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
409	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
410	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
411	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
412	C₂×C₈	C₂²×C₄×C₁₃₇	1	2	yes	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₄²×C₁₃₇	1	4	yes	—
416	C₄⋊C₄	C₄²×C₁₃₇	1	4	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	C₄²×C₁₃₇	1	4	yes	—
420	C₂²⋊C₄	C₄²×C₁₃₇	1	4	yes	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	4	2	no	—
431	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
432	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
433	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
434	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂×C₄²×C₁₃₇	1	2	yes	—
440	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
463	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
464	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
465	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
466	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
467	C₂×C₄	#131×C₁₃₇	1	4	yes	—
468	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
469	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
470	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
471	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
472	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
473	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂²×C₄²×C₁₃₇	1	1	yes	characteristic
488	C₂²	#520×C₁₃₇	1	1	yes	characteristic
489	C₂²	#520×C₁₃₇	1	1	yes	characteristic
490	C₂²	C₂×#131×C₁₃₇	1	2	yes	—
491	C₂²	#568×C₁₃₇	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	#518×C₁₃₇	1	1	yes	characteristic
502	C₄	#519×C₁₃₇	1	1	yes	characteristic
503	C₄	#520×C₁₃₇	1	1	yes	characteristic
504	C₄	#520×C₁₃₇	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	#2274×C₁₃₇	1	1	yes	characteristic
507	C₂	C₄×#131×C₁₃₇	1	1	yes	characteristic
508	C₂	#2875×C₁₃₇	1	1	yes	characteristic
509	C₂	#2992×C₁₃₇	1	2	yes	—
510	C₂	#2993×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂³×C₄
prime radical	C₂⁴×C₁₃₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1771×C₁₃₇	C₂	semidirect
5. #1771×C₁₃₇	C₂	semidirect
6. #1770×C₁₃₇	C₂	semidirect
7. C₈×C₄⋊C₄×C₁₃₇	C₂	semidirect
8. #1768×C₁₃₇	C₂	semidirect
9. #1768×C₁₃₇	C₂	semidirect
10. #1767×C₁₃₇	C₂	semidirect
11. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
19. #433×C₁₃₇	C₄	semidirect
20. #424×C₁₃₇	C₄	semidirect
255. #20553	C₁₃₇	direct (N × H)
256. C₁₃₇	#20553	direct (N × H)
260. #1771	C₂×C₁₃₇	semidirect
261. #1771	C₂×C₁₃₇	semidirect
262. #1770	C₂×C₁₃₇	semidirect
263. C₈×C₄⋊C₄	C₂×C₁₃₇	semidirect
264. #1768	C₂×C₁₃₇	semidirect
265. #1768	C₂×C₁₃₇	semidirect
266. #1767	C₂×C₁₃₇	semidirect
267. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
275. #433	C₄×C₁₃₇	semidirect
276. #424	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×#433×C₁₃₇	2
C₂×#424×C₁₃₇	2
#2298×C₁₃₇	2
#1771×C₁₃₇	2
#1770×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
#1768×C₁₃₇	2
#1767×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#1753×C₁₃₇	2
#1752×C₁₃₇	2
C₈×C₂²⋊C₄×C₁₃₇	2
#20553	137

Subgroups — C137×#20553 #46869939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#20553 #46869939