Subgroups — C₁₃₇×#26263 #46875649

Order 35072.

854 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2448×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2055×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2042×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1972×C₁₃₇	C₂	1	1	yes	maximal, characteristic
7	#1972×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	#1971×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1941×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1880×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1771×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₇	C₂²	1	2	yes	—
17	#495×C₁₃₇	—	2	4	no	—
18	#441×C₁₃₇	—	2	4	no	—
19	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
29	#399×C₁₃₇	—	2	2	no	—
30	#397×C₁₃₇	—	2	2	no	—
31	#391×C₁₃₇	C₂²	1	2	yes	—
32	#390×C₁₃₇	C₂²	1	2	yes	—
33	#390×C₁₃₇	C₂²	1	2	yes	—
34	#389×C₁₃₇	C₂²	1	2	yes	—
35	#388×C₁₃₇	—	2	2	no	—
36	#388×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×Q₈×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
44	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
45	C₂×Q₁₆×C₁₃₇	D₄	1	4	yes	—
46	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
47	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
48	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
49	C₂×D₈×C₁₃₇	—	2	2	no	—
50	C₂×D₈×C₁₃₇	—	2	2	no	—
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
56	#124×C₁₃₇	—	2	4	no	—
57	#124×C₁₃₇	—	4	2	no	—
58	C₄×Q₈×C₁₃₇	—	2	4	no	—
59	C₄×Q₈×C₁₃₇	—	4	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₇	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	—	2	2	no	—
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	#106×C₁₃₇	—	2	2	no	—
76	#106×C₁₃₇	—	2	2	no	—
77	C₄⋊C₈×C₁₃₇	—	2	2	no	—
78	#103×C₁₃₇	—	2	4	no	—
79	#103×C₁₃₇	—	4	2	no	—
80	#102×C₁₃₇	—	4	2	no	—
81	#102×C₁₃₇	—	4	2	no	—
82	#97×C₁₃₇	—	2	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	C₄×C₈×C₁₃₇	—	2	2	no	—
85	#95×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	—	2	2	no	—
87	#95×C₁₃₇	—	2	2	no	—
88	#95×C₁₃₇	D₄	1	2	yes	—
89	C₂⁴×C₁₃₇	—	2	2	no	—
90	C₂×Q₈×C₁₃₇	—	2	2	no	—
91	C₂×Q₈×C₁₃₇	—	2	2	no	—
92	C₂×Q₈×C₁₃₇	—	2	2	no	—
93	C₂×Q₈×C₁₃₇	—	2	2	no	—
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	C₂×D₄	1	4	yes	—
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	C₂²×C₄×C₁₃₇	—	2	2	no	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	2	2	no	—
105	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₁₃₇	—	2	8	no	—
111	SD₁₆×C₁₃₇	—	4	8	no	—
112	D₈×C₁₃₇	—	4	4	no	—
113	C₂×C₈×C₁₃₇	—	2	1	no	—
114	C₂×C₈×C₁₃₇	—	2	1	no	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	—	2	1	no	—
118	C₂×C₈×C₁₃₇	—	2	1	no	—
119	C₂×C₈×C₁₃₇	—	2	1	no	—
120	C₂×C₈×C₁₃₇	—	2	1	no	—
121	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃₇	#41	1	2	yes	—
123	C₂×C₈×C₁₃₇	#41	1	2	yes	—
124	C₂×C₈×C₁₃₇	#41	1	2	yes	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	2	no	—
129	C₄⋊C₄×C₁₃₇	—	4	2	no	—
130	C₄⋊C₄×C₁₃₇	—	4	4	no	—
131	C₄⋊C₄×C₁₃₇	—	8	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
133	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
134	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
135	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
136	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
137	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
138	C₄²×C₁₃₇	—	2	1	no	—
139	C₄²×C₁₃₇	—	2	1	no	—
140	C₄²×C₁₃₇	—	2	1	no	—
141	C₄²×C₁₃₇	—	2	1	no	—
142	C₄²×C₁₃₇	—	2	1	no	—
143	C₄²×C₁₃₇	—	2	1	no	—
144	C₄²×C₁₃₇	—	4	4	no	—
145	C₂³×C₁₃₇	—	4	2	no	—
146	C₂³×C₁₃₇	—	4	2	no	—
147	C₂³×C₁₃₇	—	4	2	no	—
148	C₂³×C₁₃₇	—	4	2	no	—
149	C₂³×C₁₃₇	—	4	2	no	—
150	C₂³×C₁₃₇	—	4	2	no	—
151	C₂³×C₁₃₇	—	4	2	no	—
152	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₃₇	—	2	4	no	—
154	Q₈×C₁₃₇	—	2	4	no	—
155	Q₈×C₁₃₇	—	4	2	no	—
156	Q₈×C₁₃₇	—	4	2	no	—
157	D₄×C₁₃₇	—	4	2	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	4	2	no	—
160	D₄×C₁₃₇	—	4	2	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	2	no	—
164	C₂×C₄×C₁₃₇	—	2	2	no	—
165	C₂×C₄×C₁₃₇	—	2	4	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	2	2	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	4	2	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	2	no	—
175	C₂×C₄×C₁₃₇	—	4	2	no	—
176	C₂×C₄×C₁₃₇	—	4	2	no	—
177	C₂×C₄×C₁₃₇	—	4	2	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₈×C₁₃₇	—	2	2	no	—
187	C₈×C₁₃₇	—	4	1	no	—
188	C₈×C₁₃₇	—	4	1	no	—
189	C₈×C₁₃₇	#123	1	4	yes	—
190	C₂²×C₁₃₇	—	8	2	no	—
191	C₂²×C₁₃₇	—	8	2	no	—
192	C₂²×C₁₃₇	—	8	2	no	—
193	C₂²×C₁₃₇	—	8	2	no	—
194	C₂²×C₁₃₇	—	8	2	no	—
195	C₂²×C₁₃₇	—	8	2	no	—
196	C₂²×C₁₃₇	—	8	2	no	—
197	C₂²×C₁₃₇	#532	1	1	yes	characteristic
198	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
199	C₂²×C₁₃₇	#550	1	1	yes	characteristic
200	C₂²×C₁₃₇	#575	1	2	yes	—
201	C₂²×C₁₃₇	#577	1	2	yes	—
202	C₄×C₁₃₇	—	4	1	no	—
203	C₄×C₁₃₇	—	4	1	no	—
204	C₄×C₁₃₇	—	4	4	no	—
205	C₄×C₁₃₇	—	4	2	no	—
206	C₄×C₁₃₇	—	4	2	no	—
207	C₄×C₁₃₇	—	8	2	no	—
208	C₄×C₁₃₇	—	8	2	no	—
209	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
210	C₄×C₁₃₇	#540	1	1	yes	characteristic
211	C₄×C₁₃₇	#546	1	1	yes	characteristic
212	C₄×C₁₃₇	#559	1	1	yes	characteristic
213	C₂×C₁₃₇	—	16	2	no	—
214	C₂×C₁₃₇	#2445	1	1	yes	characteristic
215	C₂×C₁₃₇	#3173	1	1	yes	characteristic
216	C₂×C₁₃₇	#3183	1	1	yes	characteristic
217	C₂×C₁₃₇	#3271	1	2	yes	—
218	C₂×C₁₃₇	#3401	1	2	yes	—
219	#26263	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₁₃₇	#26263	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×#495	C₂×C₁₃₇	1	1	yes	characteristic
222	C₂×#441	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#2448	C₂×C₁₃₇	1	2	yes	complemented
224	#2055	C₂×C₁₃₇	1	2	yes	complemented
225	#2042	C₂×C₁₃₇	1	2	yes	complemented
226	#1972	C₂×C₁₃₇	1	1	yes	characteristic
227	#1972	C₂×C₁₃₇	1	1	yes	characteristic
228	#1971	C₂×C₁₃₇	1	1	yes	characteristic, complemented
229	#1941	C₂×C₁₃₇	1	1	yes	characteristic, complemented
230	#1880	C₂×C₁₃₇	1	2	yes	complemented
231	#1771	C₂×C₁₃₇	1	1	yes	characteristic, complemented
232	C₂²×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
233	C₂²×SD₁₆	C₂²×C₁₃₇	1	2	yes	—
234	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
235	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
236	C₂×C₄×Q₈	C₂²×C₁₃₇	1	2	yes	—
237	#495	—	2	4	no	—
238	#441	—	2	4	no	—
239	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
240	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
243	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
244	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
245	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
246	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
249	#399	—	2	2	no	—
250	#397	—	2	2	no	—
251	#391	C₂²×C₁₃₇	1	2	yes	—
252	#390	C₂²×C₁₃₇	1	2	yes	—
253	#390	C₂²×C₁₃₇	1	2	yes	—
254	#389	C₂²×C₁₃₇	1	2	yes	—
255	#388	—	2	2	no	—
256	#388	—	2	2	no	—
257	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
258	#340	C₂²×C₁₃₇	1	2	yes	—
259	#336	C₂²×C₁₃₇	1	1	yes	characteristic
260	#336	C₂²×C₁₃₇	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
262	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	D₄×C₁₃₇	1	4	yes	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
276	#124	—	2	4	no	—
277	#124	—	4	2	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	4	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
295	#106	—	2	2	no	—
296	#106	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#102	—	4	2	no	—
301	#102	—	4	2	no	—
302	#97	—	2	2	no	—
303	#97	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₁₃₇	1	2	yes	—
309	C₂⁴	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	C₂×D₄×C₁₃₇	1	4	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
330	Q₁₆	—	2	8	no	—
331	SD₁₆	—	4	8	no	—
332	D₈	—	4	4	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
342	C₂×C₈	#41×C₁₃₇	1	2	yes	—
343	C₂×C₈	#41×C₁₃₇	1	2	yes	—
344	C₂×C₈	#41×C₁₃₇	1	2	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	4	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	4	4	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
404	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
405	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	#123×C₁₃₇	1	4	yes	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	#532×C₁₃₇	1	1	yes	characteristic
418	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
419	C₂²	#550×C₁₃₇	1	1	yes	characteristic
420	C₂²	#575×C₁₃₇	1	2	yes	—
421	C₂²	#577×C₁₃₇	1	2	yes	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
430	C₄	#540×C₁₃₇	1	1	yes	characteristic
431	C₄	#546×C₁₃₇	1	1	yes	characteristic
432	C₄	#559×C₁₃₇	1	1	yes	characteristic
433	C₂	—	16	2	no	—
434	C₂	#2445×C₁₃₇	1	1	yes	characteristic
435	C₂	#3173×C₁₃₇	1	1	yes	characteristic
436	C₂	#3183×C₁₃₇	1	1	yes	characteristic
437	C₂	#3271×C₁₃₇	1	2	yes	—
438	C₂	#3401×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂²×D₈×C₁₃₇	C₂²
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×#441×C₁₃₇	C₂	semidirect
3. #2448×C₁₃₇	C₂	semidirect
4. #2055×C₁₃₇	C₂	semidirect
5. #2042×C₁₃₇	C₂	semidirect
8. #1971×C₁₃₇	C₂	semidirect
9. #1941×C₁₃₇	C₂	semidirect
10. #1880×C₁₃₇	C₂	semidirect
11. #1771×C₁₃₇	C₂	semidirect
219. #26263	C₁₃₇	direct (N × H)
220. C₁₃₇	#26263	direct (N × H)
222. C₂×#441	C₂×C₁₃₇	semidirect
223. #2448	C₂×C₁₃₇	semidirect
224. #2055	C₂×C₁₃₇	semidirect
225. #2042	C₂×C₁₃₇	semidirect
228. #1971	C₂×C₁₃₇	semidirect
229. #1941	C₂×C₁₃₇	semidirect
230. #1880	C₂×C₁₃₇	semidirect
231. #1771	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#495×C₁₃₇	2
C₂×#441×C₁₃₇	2
#2448×C₁₃₇	2
#2055×C₁₃₇	2
#2042×C₁₃₇	2
#1972×C₁₃₇	2
#1971×C₁₃₇	2
#1941×C₁₃₇	2
#1880×C₁₃₇	2
#1771×C₁₃₇	2
#26263	137

Subgroups — C137×#26263 #46875649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26263 #46875649