Subgroups — C₁₃₇×#21435 #46870821

Order 35072.

790 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	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#1924×C₁₃₇	C₂	1	2	yes	maximal
3	#1923×C₁₃₇	C₂	1	2	yes	maximal
4	#1917×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#1916×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1749×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1749×C₁₃₇	C₂	1	1	yes	maximal, characteristic
10	#1745×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#97×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#117×C₁₃₇	C₄	1	1	yes	characteristic
13	C₂×#117×C₁₃₇	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₁₃₇	C₄	1	1	yes	characteristic
31	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	#376×C₁₃₇	C₄	1	1	yes	characteristic
34	#376×C₁₃₇	C₄	1	1	yes	characteristic
35	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
37	#336×C₁₃₇	C₂²	1	2	yes	—
38	#336×C₁₃₇	C₂²	1	2	yes	—
39	#336×C₁₃₇	C₂²	1	2	yes	—
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	#336×C₁₃₇	C₂²	1	2	yes	—
42	#336×C₁₃₇	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	#117×C₁₃₇	—	2	4	no	—
51	#117×C₁₃₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₇	—	2	2	no	—
61	C₂×C₄²×C₁₃₇	—	2	2	no	—
62	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₇	—	2	4	no	—
79	C₄⋊C₈×C₁₃₇	—	2	4	no	—
80	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
81	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
82	#97×C₁₃₇	—	2	4	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	2	no	—
85	#97×C₁₃₇	—	2	2	no	—
86	#97×C₁₃₇	—	2	2	no	—
87	C₄×C₈×C₁₃₇	—	2	4	no	—
88	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
89	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
90	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
91	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
92	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
93	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
94	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
95	#95×C₁₃₇	C₂×C₄	1	1	yes	characteristic
96	C₂⁴×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	2	2	no	—
99	C₂²×C₄×C₁₃₇	—	2	2	no	—
100	C₂²×C₄×C₁₃₇	—	2	2	no	—
101	C₂²×C₄×C₁₃₇	—	2	2	no	—
102	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	2	1	no	—
104	C₂²×C₄×C₁₃₇	—	2	1	no	—
105	C₂²×C₄×C₁₃₇	—	4	1	no	—
106	C₂²×C₄×C₁₃₇	—	4	1	no	—
107	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	2	2	no	—
128	C₂×C₈×C₁₃₇	—	2	2	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	—	2	2	no	—
131	C₂×C₈×C₁₃₇	#41	1	4	yes	—
132	C₂×C₈×C₁₃₇	#41	1	4	yes	—
133	C₄⋊C₄×C₁₃₇	—	2	2	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	M₁₆	1	4	yes	—
137	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
138	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
139	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
140	C₂²⋊C₄×C₁₃₇	M₁₆	1	4	yes	—
141	C₄²×C₁₃₇	—	2	2	no	—
142	C₄²×C₁₃₇	—	2	2	no	—
143	C₄²×C₁₃₇	—	2	2	no	—
144	C₄²×C₁₃₇	—	2	2	no	—
145	C₄²×C₁₃₇	—	2	2	no	—
146	C₄²×C₁₃₇	—	2	2	no	—
147	C₄²×C₁₃₇	—	2	2	no	—
148	C₄²×C₁₃₇	—	2	2	no	—
149	C₄²×C₁₃₇	—	2	2	no	—
150	C₄²×C₁₃₇	—	2	2	no	—
151	C₄²×C₁₃₇	—	2	1	no	—
152	C₄²×C₁₃₇	—	2	1	no	—
153	C₄²×C₁₃₇	—	4	1	no	—
154	C₄²×C₁₃₇	—	4	1	no	—
155	C₄²×C₁₃₇	—	4	1	no	—
156	C₄²×C₁₃₇	—	4	1	no	—
157	C₄²×C₁₃₇	#41	1	2	yes	—
158	C₄²×C₁₃₇	#41	1	2	yes	—
159	C₂³×C₁₃₇	—	2	1	no	—
160	C₂³×C₁₃₇	—	2	1	no	—
161	C₂³×C₁₃₇	—	2	1	no	—
162	C₂³×C₁₃₇	—	2	1	no	—
163	C₂³×C₁₃₇	—	2	1	no	—
164	C₂³×C₁₃₇	—	2	1	no	—
165	C₂³×C₁₃₇	C₂×M₁₆	1	2	yes	—
166	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₇	—	2	8	no	—
168	C₂×C₄×C₁₃₇	—	2	1	no	—
169	C₂×C₄×C₁₃₇	—	2	1	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	1	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	1	no	—
174	C₂×C₄×C₁₃₇	—	2	1	no	—
175	C₂×C₄×C₁₃₇	—	2	1	no	—
176	C₂×C₄×C₁₃₇	—	2	1	no	—
177	C₂×C₄×C₁₃₇	—	2	1	no	—
178	C₂×C₄×C₁₃₇	—	2	1	no	—
179	C₂×C₄×C₁₃₇	—	2	1	no	—
180	C₂×C₄×C₁₃₇	—	2	1	no	—
181	C₂×C₄×C₁₃₇	—	2	1	no	—
182	C₂×C₄×C₁₃₇	—	2	1	no	—
183	C₂×C₄×C₁₃₇	—	2	1	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	—	2	1	no	—
199	C₂×C₄×C₁₃₇	—	2	1	no	—
200	C₂×C₄×C₁₃₇	—	4	4	no	—
201	C₂×C₄×C₁₃₇	—	4	2	no	—
202	C₂×C₄×C₁₃₇	—	4	2	no	—
203	C₂×C₄×C₁₃₇	#117	1	2	yes	—
204	C₂×C₄×C₁₃₇	#117	1	2	yes	—
205	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
206	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
208	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
209	C₂×C₄×C₁₃₇	C₂×M₁₆	1	2	yes	—
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	2	yes	—
213	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
214	C₈×C₁₃₇	—	2	4	no	—
215	C₈×C₁₃₇	—	2	4	no	—
216	C₈×C₁₃₇	—	4	2	no	—
217	C₈×C₁₃₇	—	4	2	no	—
218	C₂²×C₁₃₇	—	2	2	no	—
219	C₂²×C₁₃₇	—	2	2	no	—
220	C₂²×C₁₃₇	—	2	2	no	—
221	C₂²×C₁₃₇	—	4	1	no	—
222	C₂²×C₁₃₇	—	4	1	no	—
223	C₂²×C₁₃₇	—	4	1	no	—
224	C₂²×C₁₃₇	—	4	1	no	—
225	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
226	C₂²×C₁₃₇	C₄×#41	1	1	yes	characteristic
227	C₂²×C₁₃₇	C₄×#41	1	1	yes	characteristic
228	C₂²×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
229	C₂²×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
230	C₂²×C₁₃₇	#568	1	1	yes	characteristic
231	C₂²×C₁₃₇	#568	1	1	yes	characteristic
232	C₄×C₁₃₇	—	2	2	no	—
233	C₄×C₁₃₇	—	2	2	no	—
234	C₄×C₁₃₇	—	2	2	no	—
235	C₄×C₁₃₇	—	2	2	no	—
236	C₄×C₁₃₇	—	2	2	no	—
237	C₄×C₁₃₇	—	2	2	no	—
238	C₄×C₁₃₇	—	2	2	no	—
239	C₄×C₁₃₇	—	4	1	no	—
240	C₄×C₁₃₇	—	4	1	no	—
241	C₄×C₁₃₇	—	4	1	no	—
242	C₄×C₁₃₇	—	4	1	no	—
243	C₄×C₁₃₇	—	4	1	no	—
244	C₄×C₁₃₇	—	4	1	no	—
245	C₄×C₁₃₇	#529	1	2	yes	—
246	C₄×C₁₃₇	#529	1	2	yes	—
247	C₂×C₁₃₇	—	4	2	no	—
248	C₂×C₁₃₇	#2298	1	1	yes	characteristic
249	C₂×C₁₃₇	#2920	1	1	yes	characteristic
250	C₂×C₁₃₇	#2921	1	1	yes	characteristic
251	C₂×C₁₃₇	#2970	1	1	yes	characteristic
252	C₂×C₁₃₇	#2970	1	1	yes	characteristic
253	C₂×C₁₃₇	#2970	1	1	yes	characteristic
254	C₂×C₁₃₇	#2971	1	1	yes	characteristic
255	#21435	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₁₃₇	#21435	1	1	yes	characteristic, direct product factor, Sylow
257	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic
258	#1924	C₂×C₁₃₇	1	2	yes	—
259	#1923	C₂×C₁₃₇	1	2	yes	—
260	#1917	C₂×C₁₃₇	1	2	yes	complemented
261	#1916	C₂×C₁₃₇	1	2	yes	complemented
262	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
264	#1749	C₂×C₁₃₇	1	1	yes	characteristic
265	#1749	C₂×C₁₃₇	1	1	yes	characteristic
266	#1745	C₂×C₁₃₇	1	1	yes	characteristic, complemented
267	C₄×#97	C₂×C₁₃₇	1	1	yes	characteristic, complemented
268	C₂×#117	C₄×C₁₃₇	1	1	yes	characteristic
269	C₂×#117	C₄×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
272	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
273	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
275	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
276	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
277	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
278	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
281	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
284	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	C₄×C₁₃₇	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
289	#376	C₄×C₁₃₇	1	1	yes	characteristic
290	#376	C₄×C₁₃₇	1	1	yes	characteristic
291	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
292	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
293	#336	C₂²×C₁₃₇	1	2	yes	—
294	#336	C₂²×C₁₃₇	1	2	yes	—
295	#336	C₂²×C₁₃₇	1	2	yes	—
296	#336	C₂²×C₁₃₇	1	2	yes	—
297	#336	C₂²×C₁₃₇	1	2	yes	—
298	#336	C₂²×C₁₃₇	1	2	yes	—
299	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
300	C₂³×C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
306	#117	—	2	4	no	—
307	#117	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
321	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
322	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
334	C₄⋊C₈	—	2	4	no	—
335	C₄⋊C₈	—	2	4	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	2	4	no	—
338	#97	—	2	4	no	—
339	#97	—	2	2	no	—
340	#97	—	2	2	no	—
341	#97	—	2	2	no	—
342	#97	—	2	2	no	—
343	C₄×C₈	—	2	4	no	—
344	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
345	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
346	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
347	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
348	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
349	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
350	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
351	#95	C₂×C₄×C₁₃₇	1	1	yes	characteristic
352	C₂⁴	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	#41×C₁₃₇	1	4	yes	—
388	C₂×C₈	#41×C₁₃₇	1	4	yes	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	M₁₆×C₁₃₇	1	4	yes	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	M₁₆×C₁₃₇	1	4	yes	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₄²	—	4	1	no	—
412	C₄²	—	4	1	no	—
413	C₄²	#41×C₁₃₇	1	2	yes	—
414	C₄²	#41×C₁₃₇	1	2	yes	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	C₂×M₁₆×C₁₃₇	1	2	yes	—
422	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	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	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	#117×C₁₃₇	1	2	yes	—
460	C₂×C₄	#117×C₁₃₇	1	2	yes	—
461	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
462	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
463	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
464	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
465	C₂×C₄	C₂×M₁₆×C₁₃₇	1	2	yes	—
466	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
469	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
470	C₈	—	2	4	no	—
471	C₈	—	2	4	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
482	C₂²	C₄×#41×C₁₃₇	1	1	yes	characteristic
483	C₂²	C₄×#41×C₁₃₇	1	1	yes	characteristic
484	C₂²	C₂²×M₁₆×C₁₃₇	1	1	yes	characteristic
485	C₂²	C₂²×M₁₆×C₁₃₇	1	1	yes	characteristic
486	C₂²	#568×C₁₃₇	1	1	yes	characteristic
487	C₂²	#568×C₁₃₇	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	#529×C₁₃₇	1	2	yes	—
502	C₄	#529×C₁₃₇	1	2	yes	—
503	C₂	—	4	2	no	—
504	C₂	#2298×C₁₃₇	1	1	yes	characteristic
505	C₂	#2920×C₁₃₇	1	1	yes	characteristic
506	C₂	#2921×C₁₃₇	1	1	yes	characteristic
507	C₂	#2970×C₁₃₇	1	1	yes	characteristic
508	C₂	#2970×C₁₃₇	1	1	yes	characteristic
509	C₂	#2970×C₁₃₇	1	1	yes	characteristic
510	C₂	#2971×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #1917×C₁₃₇	C₂	semidirect
5. #1916×C₁₃₇	C₂	semidirect
6. #1767×C₁₃₇	C₂	semidirect
7. #1767×C₁₃₇	C₂	semidirect
10. #1745×C₁₃₇	C₂	semidirect
11. C₄×#97×C₁₃₇	C₂	semidirect
255. #21435	C₁₃₇	direct (N × H)
256. C₁₃₇	#21435	direct (N × H)
260. #1917	C₂×C₁₃₇	semidirect
261. #1916	C₂×C₁₃₇	semidirect
262. #1767	C₂×C₁₃₇	semidirect
263. #1767	C₂×C₁₃₇	semidirect
266. #1745	C₂×C₁₃₇	semidirect
267. C₄×#97	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×#117×C₁₃₇	2
#1924×C₁₃₇	2
#1923×C₁₃₇	2
#1917×C₁₃₇	2
#1916×C₁₃₇	2
#1767×C₁₃₇	2
#1749×C₁₃₇	2
#1745×C₁₃₇	2
C₄×#97×C₁₃₇	2
#21435	137

Subgroups — C137×#21435 #46870821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#21435 #46870821