Subgroups — C₁₃₇×#34255 #46883641

Order 35072.

2682 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	C₂×#518×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2357×C₁₃₇	C₂	1	4	yes	maximal, complemented
3	#2354×C₁₃₇	C₂	1	4	yes	maximal, complemented
4	#2342×C₁₃₇	C₂	1	8	yes	maximal, complemented
5	#2319×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#2317×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#2309×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#2293×C₁₃₇	C₂	1	4	yes	maximal, complemented
10	C₂×#390×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	#2274×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
14	#518×C₁₃₇	C₄	1	16	yes	complemented
15	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
17	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₃₇	C₂²	1	8	yes	complemented
22	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
24	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
26	#390×C₁₃₇	C₂²	1	2	yes	—
27	#390×C₁₃₇	C₂²	1	2	yes	—
28	#390×C₁₃₇	C₂²	1	4	yes	—
29	#390×C₁₃₇	C₂²	1	4	yes	—
30	#390×C₁₃₇	C₂²	1	2	yes	—
31	#390×C₁₃₇	C₂²	1	2	yes	—
32	#389×C₁₃₇	C₂²	1	2	yes	complemented
33	#389×C₁₃₇	C₂²	1	4	yes	complemented
34	#389×C₁₃₇	C₂²	1	2	yes	complemented
35	#388×C₁₃₇	C₂²	1	8	yes	complemented
36	#388×C₁₃₇	C₂²	1	8	yes	complemented
37	#388×C₁₃₇	C₂²	1	8	yes	complemented
38	#388×C₁₃₇	C₂²	1	8	yes	complemented
39	#385×C₁₃₇	C₂²	1	4	yes	—
40	#385×C₁₃₇	C₂²	1	4	yes	—
41	#384×C₁₃₇	C₂²	1	2	yes	complemented
42	#382×C₁₃₇	C₂²	1	2	yes	complemented
43	#381×C₁₃₇	C₂²	1	8	yes	complemented
44	#380×C₁₃₇	C₂²	1	8	yes	complemented
45	#379×C₁₃₇	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
47	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
48	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
49	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
50	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
53	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	8	yes	complemented
54	#376×C₁₃₇	C₂²	1	2	yes	complemented
55	C₄³×C₁₃₇	C₂²	1	2	yes	complemented
56	C₂⁵×C₁₃₇	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃₇	—	2	4	no	—
58	C₂²×D₄×C₁₃₇	—	2	4	no	—
59	C₂²×D₄×C₁₃₇	C₂×C₄	1	8	yes	—
60	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃₇	C₂³	1	8	yes	—
65	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₁₃₇	C₂×C₄	1	32	yes	complemented
67	C₄×D₄×C₁₃₇	C₂×C₄	1	32	yes	complemented
68	#117×C₁₃₇	—	2	4	no	—
69	#117×C₁₃₇	—	2	4	no	—
70	#117×C₁₃₇	—	4	16	no	—
71	#117×C₁₃₇	C₂×C₄	1	8	yes	—
72	#117×C₁₃₇	C₂×C₄	1	8	yes	—
73	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₃₇	—	4	8	no	—
85	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	32	yes	—
86	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
95	C₂×C₄²×C₁₃₇	—	2	4	no	—
96	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
101	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃₇	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
106	#95×C₁₃₇	C₂³	1	4	yes	—
107	#95×C₁₃₇	C₂³	1	4	yes	—
108	#95×C₁₃₇	C₂³	1	8	yes	—
109	#95×C₁₃₇	C₂³	1	4	yes	—
110	#95×C₁₃₇	C₂³	1	8	yes	—
111	#95×C₁₃₇	C₂³	1	4	yes	—
112	C₂⁴×C₁₃₇	—	2	4	no	—
113	C₂⁴×C₁₃₇	—	2	4	no	—
114	C₂⁴×C₁₃₇	—	4	4	no	—
115	C₂⁴×C₁₃₇	—	4	4	no	—
116	C₂⁴×C₁₃₇	C₂²×C₄	1	8	yes	—
117	C₂⁴×C₁₃₇	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₁₃₇	—	2	32	no	—
120	C₂×D₄×C₁₃₇	—	2	4	no	—
121	C₂×D₄×C₁₃₇	—	2	4	no	—
122	C₂×D₄×C₁₃₇	—	2	4	no	—
123	C₂×D₄×C₁₃₇	—	2	4	no	—
124	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₃₇	—	2	4	no	—
127	C₂²×C₄×C₁₃₇	—	2	4	no	—
128	C₂²×C₄×C₁₃₇	—	2	4	no	—
129	C₂²×C₄×C₁₃₇	—	4	8	no	—
130	C₂²×C₄×C₁₃₇	—	4	2	no	—
131	C₂²×C₄×C₁₃₇	—	4	8	no	—
132	C₂²×C₄×C₁₃₇	—	4	4	no	—
133	C₂²×C₄×C₁₃₇	C₂²×C₄	1	32	yes	—
134	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
136	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
137	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₁₃₇	—	2	4	no	—
148	C₄⋊C₄×C₁₃₇	—	2	4	no	—
149	C₄⋊C₄×C₁₃₇	—	2	4	no	—
150	C₄⋊C₄×C₁₃₇	—	2	2	no	—
151	C₄⋊C₄×C₁₃₇	—	2	2	no	—
152	C₄⋊C₄×C₁₃₇	—	2	8	no	—
153	C₄⋊C₄×C₁₃₇	—	4	4	no	—
154	C₄⋊C₄×C₁₃₇	—	4	8	no	—
155	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
156	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
157	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
159	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
160	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
161	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
162	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
163	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
164	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
165	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	32	yes	—
166	C₄²×C₁₃₇	—	2	2	no	—
167	C₄²×C₁₃₇	—	2	4	no	—
168	C₄²×C₁₃₇	—	2	2	no	—
169	C₄²×C₁₃₇	—	2	4	no	—
170	C₄²×C₁₃₇	—	2	4	no	—
171	C₄²×C₁₃₇	—	2	8	no	—
172	C₄²×C₁₃₇	—	4	4	no	—
173	C₄²×C₁₃₇	—	4	8	no	—
174	C₄²×C₁₃₇	C₂²×C₄	1	8	yes	—
175	C₄²×C₁₃₇	C₂²×C₄	1	8	yes	—
176	C₂³×C₁₃₇	—	2	2	no	—
177	C₂³×C₁₃₇	—	2	2	no	—
178	C₂³×C₁₃₇	—	2	4	no	—
179	C₂³×C₁₃₇	—	2	4	no	—
180	C₂³×C₁₃₇	—	2	8	no	—
181	C₂³×C₁₃₇	—	2	8	no	—
182	C₂³×C₁₃₇	—	2	16	no	—
183	C₂³×C₁₃₇	—	4	16	no	—
184	C₂³×C₁₃₇	—	8	8	no	—
185	C₂³×C₁₃₇	—	8	4	no	—
186	C₂³×C₁₃₇	—	8	4	no	—
187	C₂³×C₁₃₇	C₂³×C₄	1	8	yes	—
188	C₂³×C₁₃₇	C₂³×C₄	1	2	yes	—
189	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
190	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
191	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
192	D₄×C₁₃₇	—	2	16	no	—
193	D₄×C₁₃₇	—	2	16	no	—
194	C₂×C₄×C₁₃₇	—	2	2	no	—
195	C₂×C₄×C₁₃₇	—	2	4	no	—
196	C₂×C₄×C₁₃₇	—	2	4	no	—
197	C₂×C₄×C₁₃₇	—	2	2	no	—
198	C₂×C₄×C₁₃₇	—	2	4	no	—
199	C₂×C₄×C₁₃₇	—	2	4	no	—
200	C₂×C₄×C₁₃₇	—	2	2	no	—
201	C₂×C₄×C₁₃₇	—	2	4	no	—
202	C₂×C₄×C₁₃₇	—	2	2	no	—
203	C₂×C₄×C₁₃₇	—	2	2	no	—
204	C₂×C₄×C₁₃₇	—	2	4	no	—
205	C₂×C₄×C₁₃₇	—	2	4	no	—
206	C₂×C₄×C₁₃₇	—	2	4	no	—
207	C₂×C₄×C₁₃₇	—	2	8	no	—
208	C₂×C₄×C₁₃₇	—	2	2	no	—
209	C₂×C₄×C₁₃₇	—	2	4	no	—
210	C₂×C₄×C₁₃₇	—	2	4	no	—
211	C₂×C₄×C₁₃₇	—	2	2	no	—
212	C₂×C₄×C₁₃₇	—	4	32	no	—
213	C₂×C₄×C₁₃₇	—	4	8	no	—
214	C₂×C₄×C₁₃₇	—	8	4	no	—
215	C₂×C₄×C₁₃₇	#117	1	16	yes	complemented
216	C₂×C₄×C₁₃₇	C₂³×C₄	1	8	yes	—
217	C₂×C₄×C₁₃₇	C₂³×C₄	1	8	yes	—
218	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
219	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
221	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
222	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
225	C₂²×C₁₃₇	—	2	4	no	—
226	C₂²×C₁₃₇	—	2	4	no	—
227	C₂²×C₁₃₇	—	2	2	no	—
228	C₂²×C₁₃₇	—	2	2	no	—
229	C₂²×C₁₃₇	—	2	8	no	—
230	C₂²×C₁₃₇	—	2	16	no	—
231	C₂²×C₁₃₇	—	4	8	no	—
232	C₂²×C₁₃₇	—	4	4	no	—
233	C₂²×C₁₃₇	—	4	4	no	—
234	C₂²×C₁₃₇	—	8	16	no	—
235	C₂²×C₁₃₇	C₂×#117	1	4	yes	—
236	C₂²×C₁₃₇	C₂⁴×C₄	1	1	yes	characteristic
237	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
239	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂²×C₁₃₇	#585	1	2	yes	—
241	C₄×C₁₃₇	—	2	8	no	—
242	C₄×C₁₃₇	—	2	8	no	—
243	C₄×C₁₃₇	—	2	4	no	—
244	C₄×C₁₃₇	—	4	4	no	—
245	C₄×C₁₃₇	—	4	2	no	—
246	C₄×C₁₃₇	—	4	2	no	—
247	C₄×C₁₃₇	—	4	4	no	—
248	C₄×C₁₃₇	—	4	2	no	—
249	C₄×C₁₃₇	C₂×#117	1	4	yes	—
250	C₄×C₁₃₇	C₂×#117	1	4	yes	—
251	C₂×C₁₃₇	—	2	4	no	—
252	C₂×C₁₃₇	—	4	8	no	—
253	C₂×C₁₃₇	C₂²×#117	1	1	yes	characteristic
254	C₂×C₁₃₇	C₄×H(5,𝔽₂)	1	2	yes	—
255	C₂×C₁₃₇	#3494	1	2	yes	—
256	C₂×C₁₃₇	#3508	1	1	yes	characteristic
257	C₂×C₁₃₇	#3510	1	1	yes	characteristic
258	#34255	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₁₃₇	#34255	1	1	yes	characteristic, direct product factor, Sylow
260	C₂×#518	C₂×C₁₃₇	1	1	yes	characteristic
261	#2357	C₂×C₁₃₇	1	4	yes	complemented
262	#2354	C₂×C₁₃₇	1	4	yes	complemented
263	#2342	C₂×C₁₃₇	1	8	yes	complemented
264	#2319	C₂×C₁₃₇	1	4	yes	complemented
265	#2317	C₂×C₁₃₇	1	1	yes	characteristic, complemented
266	#2309	C₂×C₁₃₇	1	1	yes	characteristic
267	#2296	C₂×C₁₃₇	1	1	yes	characteristic, complemented
268	#2293	C₂×C₁₃₇	1	4	yes	complemented
269	C₂×#390	C₂×C₁₃₇	1	1	yes	characteristic
270	#2274	C₂×C₁₃₇	1	1	yes	characteristic, complemented
271	C₄×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
273	#518	C₄×C₁₃₇	1	16	yes	complemented
274	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
275	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
276	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
277	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
278	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×#117	C₂²×C₁₃₇	1	8	yes	complemented
281	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
284	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
285	#390	C₂²×C₁₃₇	1	4	yes	—
286	#390	C₂²×C₁₃₇	1	2	yes	—
287	#390	C₂²×C₁₃₇	1	2	yes	—
288	#390	C₂²×C₁₃₇	1	2	yes	—
289	#390	C₂²×C₁₃₇	1	4	yes	—
290	#390	C₂²×C₁₃₇	1	2	yes	—
291	#389	C₂²×C₁₃₇	1	4	yes	complemented
292	#389	C₂²×C₁₃₇	1	2	yes	complemented
293	#389	C₂²×C₁₃₇	1	2	yes	complemented
294	#388	C₂²×C₁₃₇	1	8	yes	complemented
295	#388	C₂²×C₁₃₇	1	8	yes	complemented
296	#388	C₂²×C₁₃₇	1	8	yes	complemented
297	#388	C₂²×C₁₃₇	1	8	yes	complemented
298	#385	C₂²×C₁₃₇	1	4	yes	—
299	#385	C₂²×C₁₃₇	1	4	yes	—
300	#384	C₂²×C₁₃₇	1	2	yes	complemented
301	#382	C₂²×C₁₃₇	1	2	yes	complemented
302	#381	C₂²×C₁₃₇	1	8	yes	complemented
303	#380	C₂²×C₁₃₇	1	8	yes	complemented
304	#379	C₂²×C₁₃₇	1	4	yes	—
305	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
306	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
307	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
308	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
309	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
310	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
312	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	8	yes	complemented
313	#376	C₂²×C₁₃₇	1	2	yes	complemented
314	C₄³	C₂²×C₁₃₇	1	2	yes	complemented
315	C₂⁵	C₂³×C₁₃₇	1	2	yes	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	C₂×C₄×C₁₃₇	1	8	yes	—
319	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃₇	1	8	yes	—
324	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
325	C₄×D₄	C₂×C₄×C₁₃₇	1	32	yes	complemented
326	C₄×D₄	C₂×C₄×C₁₃₇	1	32	yes	complemented
327	#117	—	2	4	no	—
328	#117	—	2	4	no	—
329	#117	—	4	16	no	—
330	#117	C₂×C₄×C₁₃₇	1	8	yes	—
331	#117	C₂×C₄×C₁₃₇	1	8	yes	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
343	C₂×C₂²⋊C₄	—	4	8	no	—
344	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	32	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
357	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
358	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
361	C₂×C₄²	C₂³×C₁₃₇	1	8	yes	—
362	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
363	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
364	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
365	#95	C₂³×C₁₃₇	1	4	yes	—
366	#95	C₂³×C₁₃₇	1	4	yes	—
367	#95	C₂³×C₁₃₇	1	8	yes	—
368	#95	C₂³×C₁₃₇	1	4	yes	—
369	#95	C₂³×C₁₃₇	1	8	yes	—
370	#95	C₂³×C₁₃₇	1	4	yes	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	2	4	no	—
373	C₂⁴	—	4	4	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	C₂²×C₄×C₁₃₇	1	8	yes	—
376	C₂⁴	C₂⁴×C₁₃₇	1	4	yes	—
377	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
378	C₂×D₄	—	2	32	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
384	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	8	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	C₂²×C₄×C₁₃₇	1	32	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
394	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
395	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	8	no	—
414	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
415	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	16	no	—
419	C₂²⋊C₄	—	4	8	no	—
420	C₂²⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
424	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	32	yes	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	4	no	—
430	C₄²	—	2	8	no	—
431	C₄²	—	4	4	no	—
432	C₄²	—	4	8	no	—
433	C₄²	C₂²×C₄×C₁₃₇	1	8	yes	—
434	C₄²	C₂²×C₄×C₁₃₇	1	8	yes	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	16	no	—
442	C₂³	—	4	16	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	4	no	—
445	C₂³	—	8	4	no	—
446	C₂³	C₂³×C₄×C₁₃₇	1	8	yes	—
447	C₂³	C₂³×C₄×C₁₃₇	1	2	yes	—
448	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
449	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
450	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
451	D₄	—	2	16	no	—
452	D₄	—	2	16	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	32	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	#117×C₁₃₇	1	16	yes	complemented
475	C₂×C₄	C₂³×C₄×C₁₃₇	1	8	yes	—
476	C₂×C₄	C₂³×C₄×C₁₃₇	1	8	yes	—
477	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
479	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
480	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
481	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
482	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
483	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	16	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	8	16	no	—
494	C₂²	C₂×#117×C₁₃₇	1	4	yes	—
495	C₂²	C₂⁴×C₄×C₁₃₇	1	1	yes	characteristic
496	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
497	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
498	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
499	C₂²	#585×C₁₃₇	1	2	yes	—
500	C₄	—	2	8	no	—
501	C₄	—	2	8	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	C₂×#117×C₁₃₇	1	4	yes	—
509	C₄	C₂×#117×C₁₃₇	1	4	yes	—
510	C₂	—	2	4	no	—
511	C₂	—	4	8	no	—
512	C₂	C₂²×#117×C₁₃₇	1	1	yes	characteristic
513	C₂	C₄×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
514	C₂	#3494×C₁₃₇	1	2	yes	—
515	C₂	#3508×C₁₃₇	1	1	yes	characteristic
516	C₂	#3510×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₇
Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂³×D₄×C₁₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2357×C₁₃₇	C₂	semidirect
3. #2354×C₁₃₇	C₂	semidirect
4. #2342×C₁₃₇	C₂	semidirect
5. #2319×C₁₃₇	C₂	semidirect
6. #2317×C₁₃₇	C₂	semidirect
8. #2296×C₁₃₇	C₂	semidirect
9. #2293×C₁₃₇	C₂	semidirect
11. #2274×C₁₃₇	C₂	semidirect
12. C₄×#117×C₁₃₇	C₂	semidirect
14. #518×C₁₃₇	C₄	semidirect
21. C₂×#117×C₁₃₇	C₂²	semidirect
32. #389×C₁₃₇	C₂²	semidirect
33. #389×C₁₃₇	C₂²	semidirect
34. #389×C₁₃₇	C₂²	semidirect
35. #388×C₁₃₇	C₂²	semidirect
36. #388×C₁₃₇	C₂²	semidirect
37. #388×C₁₃₇	C₂²	semidirect
38. #388×C₁₃₇	C₂²	semidirect
41. #384×C₁₃₇	C₂²	semidirect
42. #382×C₁₃₇	C₂²	semidirect
43. #381×C₁₃₇	C₂²	semidirect
44. #380×C₁₃₇	C₂²	semidirect
46. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
47. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
48. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
49. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
50. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
53. C₄×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
54. #376×C₁₃₇	C₂²	semidirect
55. C₄³×C₁₃₇	C₂²	semidirect
66. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
67. C₄×D₄×C₁₃₇	C₂×C₄	semidirect
215. C₂×C₄×C₁₃₇	#117	semidirect
258. #34255	C₁₃₇	direct (N × H)
259. C₁₃₇	#34255	direct (N × H)
261. #2357	C₂×C₁₃₇	semidirect
262. #2354	C₂×C₁₃₇	semidirect
263. #2342	C₂×C₁₃₇	semidirect
264. #2319	C₂×C₁₃₇	semidirect
265. #2317	C₂×C₁₃₇	semidirect
267. #2296	C₂×C₁₃₇	semidirect
268. #2293	C₂×C₁₃₇	semidirect
270. #2274	C₂×C₁₃₇	semidirect
271. C₄×#117	C₂×C₁₃₇	semidirect
273. #518	C₄×C₁₃₇	semidirect
280. C₂×#117	C₂²×C₁₃₇	semidirect
291. #389	C₂²×C₁₃₇	semidirect
292. #389	C₂²×C₁₃₇	semidirect
293. #389	C₂²×C₁₃₇	semidirect
294. #388	C₂²×C₁₃₇	semidirect
295. #388	C₂²×C₁₃₇	semidirect
296. #388	C₂²×C₁₃₇	semidirect
297. #388	C₂²×C₁₃₇	semidirect
300. #384	C₂²×C₁₃₇	semidirect
301. #382	C₂²×C₁₃₇	semidirect
302. #381	C₂²×C₁₃₇	semidirect
303. #380	C₂²×C₁₃₇	semidirect
305. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
306. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
307. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
308. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
309. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
312. C₄×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
313. #376	C₂²×C₁₃₇	semidirect
314. C₄³	C₂²×C₁₃₇	semidirect
325. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
326. C₄×D₄	C₂×C₄×C₁₃₇	semidirect
474. C₂×C₄	#117×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₁₃₇	2
#2357×C₁₃₇	2
#2354×C₁₃₇	2
#2342×C₁₃₇	2
#2319×C₁₃₇	2
#2317×C₁₃₇	2
#2309×C₁₃₇	2
#2296×C₁₃₇	2
#2293×C₁₃₇	2
C₂×#390×C₁₃₇	2
#2274×C₁₃₇	2
C₄×#117×C₁₃₇	2
#34255	137

Subgroups — C137×#34255 #46883641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34255 #46883641