Subgroups — C₁₃₇×#18855 #46868241

Order 35072.

868 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3502×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#3254×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#3210×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#3112×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1636×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1633×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1626×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1623×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1559×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1497×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1487×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₃₇	—	2	1	no	—
13	Q₈²×C₁₃₇	C₂²	1	2	yes	—
14	#557×C₁₃₇	—	2	1	no	—
15	#557×C₁₃₇	—	2	2	no	—
16	#557×C₁₃₇	—	2	2	no	—
17	#557×C₁₃₇	C₂²	1	2	yes	—
18	#544×C₁₃₇	—	2	2	no	—
19	#544×C₁₃₇	—	2	1	no	—
20	#533×C₁₃₇	—	2	2	no	—
21	#533×C₁₃₇	C₂²	1	1	yes	characteristic
22	#533×C₁₃₇	C₂²	1	1	yes	characteristic
23	#532×C₁₃₇	C₂²	1	1	yes	characteristic
24	#519×C₁₃₇	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
26	#494×C₁₃₇	C₂²	1	1	yes	characteristic
27	#492×C₁₃₇	C₂²	1	1	yes	characteristic
28	#487×C₁₃₇	C₂²	1	1	yes	characteristic
29	#486×C₁₃₇	C₂²	1	1	yes	characteristic
30	#480×C₁₃₇	—	2	1	no	—
31	#477×C₁₃₇	C₂²	1	2	yes	—
32	#477×C₁₃₇	C₂²	1	2	yes	—
33	#474×C₁₃₇	—	2	1	no	—
34	#468×C₁₃₇	—	2	2	no	—
35	#464×C₁₃₇	—	2	2	no	—
36	#461×C₁₃₇	—	2	1	no	—
37	#460×C₁₃₇	C₂²	1	2	yes	—
38	#460×C₁₃₇	C₂²	1	2	yes	—
39	#452×C₁₃₇	—	2	2	no	—
40	#448×C₁₃₇	—	2	1	no	—
41	#440×C₁₃₇	—	2	2	no	—
42	#432×C₁₃₇	C₂²	1	1	yes	characteristic
43	#431×C₁₃₇	C₂²	1	1	yes	characteristic
44	#423×C₁₃₇	C₂²	1	1	yes	characteristic
45	#333×C₁₃₇	C₂²	1	2	yes	—
46	#332×C₁₃₇	C₂²	1	2	yes	—
47	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
50	Q₈⋊C₈×C₁₃₇	C₂²	1	2	yes	—
51	C₂×#41×C₁₃₇	—	2	1	no	—
52	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
56	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
59	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
61	C₄⋊Q₈×C₁₃₇	—	2	4	no	—
62	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
63	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
64	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
69	#127×C₁₃₇	C₂³	1	1	yes	characteristic
70	#125×C₁₃₇	—	2	4	no	—
71	#125×C₁₃₇	—	2	4	no	—
72	#125×C₁₃₇	—	2	2	no	—
73	#125×C₁₃₇	—	2	4	no	—
74	#125×C₁₃₇	—	2	2	no	—
75	#125×C₁₃₇	—	2	1	no	—
76	#125×C₁₃₇	—	2	1	no	—
77	#124×C₁₃₇	—	2	1	no	—
78	C₂²⋊Q₈×C₁₃₇	—	2	4	no	—
79	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
80	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
81	C₂²⋊Q₈×C₁₃₇	D₄	1	2	yes	—
82	C₂²⋊Q₈×C₁₃₇	D₄	1	2	yes	—
83	#121×C₁₃₇	—	2	1	no	—
84	#121×C₁₃₇	—	2	1	no	—
85	C₄×Q₈×C₁₃₇	—	2	2	no	—
86	C₄×Q₈×C₁₃₇	—	2	2	no	—
87	C₄×Q₈×C₁₃₇	—	2	4	no	—
88	C₄×Q₈×C₁₃₇	—	2	2	no	—
89	C₄×Q₈×C₁₃₇	—	2	2	no	—
90	C₄×Q₈×C₁₃₇	—	2	2	no	—
91	C₄×Q₈×C₁₃₇	—	2	2	no	—
92	C₄×Q₈×C₁₃₇	—	2	1	no	—
93	C₄×Q₈×C₁₃₇	—	2	1	no	—
94	C₄×Q₈×C₁₃₇	—	2	1	no	—
95	C₄×Q₈×C₁₃₇	—	2	1	no	—
96	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
97	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
98	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
99	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
100	C₄×D₄×C₁₃₇	—	2	1	no	—
101	C₄×D₄×C₁₃₇	—	2	1	no	—
102	#117×C₁₃₇	—	2	4	no	—
103	#117×C₁₃₇	—	2	1	no	—
104	#117×C₁₃₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃₇	—	2	1	no	—
108	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
109	#107×C₁₃₇	—	2	2	no	—
110	#107×C₁₃₇	—	2	2	no	—
111	C₄⋊C₈×C₁₃₇	—	2	1	no	—
112	C₄⋊C₈×C₁₃₇	—	2	1	no	—
113	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
115	#103×C₁₃₇	—	2	2	no	—
116	#103×C₁₃₇	—	2	2	no	—
117	#103×C₁₃₇	—	2	2	no	—
118	#102×C₁₃₇	—	2	2	no	—
119	#102×C₁₃₇	—	2	2	no	—
120	#102×C₁₃₇	—	2	2	no	—
121	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
122	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
123	#97×C₁₃₇	—	2	1	no	—
124	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
126	#41×C₁₃₇	—	8	2	no	—
127	C₂×Q₈×C₁₃₇	—	2	4	no	—
128	C₂×Q₈×C₁₃₇	—	2	4	no	—
129	C₂×Q₈×C₁₃₇	—	2	1	no	—
130	C₂×Q₈×C₁₃₇	—	2	1	no	—
131	C₂×Q₈×C₁₃₇	—	2	1	no	—
132	C₂×Q₈×C₁₃₇	—	2	1	no	—
133	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₃₇	—	2	1	no	—
137	C₂×D₄×C₁₃₇	—	2	1	no	—
138	C₂×D₄×C₁₃₇	—	2	1	no	—
139	C₂×D₄×C₁₃₇	—	4	1	no	—
140	C₂²×C₄×C₁₃₇	—	2	1	no	—
141	C₂²×C₄×C₁₃₇	—	2	1	no	—
142	C₂²×C₄×C₁₃₇	—	4	1	no	—
143	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₁₃₇	—	8	2	no	—
147	SD₁₆×C₁₃₇	—	4	4	no	—
148	SD₁₆×C₁₃₇	—	8	2	no	—
149	SD₁₆×C₁₃₇	—	8	2	no	—
150	M₁₆×C₁₃₇	—	8	1	no	—
151	C₂×C₈×C₁₃₇	—	2	1	no	—
152	C₂×C₈×C₁₃₇	—	2	1	no	—
153	C₂×C₈×C₁₃₇	—	2	2	no	—
154	C₂×C₈×C₁₃₇	—	2	2	no	—
155	C₄⋊C₄×C₁₃₇	—	2	4	no	—
156	C₄⋊C₄×C₁₃₇	—	2	4	no	—
157	C₄⋊C₄×C₁₃₇	—	2	4	no	—
158	C₄⋊C₄×C₁₃₇	—	2	4	no	—
159	C₄⋊C₄×C₁₃₇	—	2	4	no	—
160	C₄⋊C₄×C₁₃₇	—	2	2	no	—
161	C₄⋊C₄×C₁₃₇	—	2	1	no	—
162	C₄⋊C₄×C₁₃₇	—	2	1	no	—
163	C₄⋊C₄×C₁₃₇	—	2	1	no	—
164	C₄⋊C₄×C₁₃₇	—	2	2	no	—
165	C₄⋊C₄×C₁₃₇	—	2	2	no	—
166	C₄⋊C₄×C₁₃₇	—	2	1	no	—
167	C₄⋊C₄×C₁₃₇	—	2	2	no	—
168	C₄⋊C₄×C₁₃₇	—	2	2	no	—
169	C₄⋊C₄×C₁₃₇	—	2	1	no	—
170	C₄⋊C₄×C₁₃₇	—	2	1	no	—
171	C₄⋊C₄×C₁₃₇	—	2	1	no	—
172	C₄⋊C₄×C₁₃₇	—	2	2	no	—
173	C₄⋊C₄×C₁₃₇	—	2	1	no	—
174	C₄⋊C₄×C₁₃₇	—	2	1	no	—
175	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
179	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
180	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
181	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
182	C₄²×C₁₃₇	—	2	4	no	—
183	C₄²×C₁₃₇	—	2	4	no	—
184	C₄²×C₁₃₇	—	2	2	no	—
185	C₄²×C₁₃₇	—	2	2	no	—
186	C₄²×C₁₃₇	—	2	2	no	—
187	C₄²×C₁₃₇	—	2	2	no	—
188	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
192	C₂³×C₁₃₇	—	4	1	no	—
193	C₂³×C₁₃₇	#120	1	1	yes	characteristic
194	Q₈×C₁₃₇	—	2	4	no	—
195	Q₈×C₁₃₇	—	2	2	no	—
196	Q₈×C₁₃₇	—	2	2	no	—
197	Q₈×C₁₃₇	—	2	2	no	—
198	Q₈×C₁₃₇	—	4	2	no	—
199	Q₈×C₁₃₇	—	4	2	no	—
200	Q₈×C₁₃₇	—	4	1	no	—
201	Q₈×C₁₃₇	—	4	1	no	—
202	Q₈×C₁₃₇	—	8	1	no	—
203	Q₈×C₁₃₇	—	8	4	no	—
204	Q₈×C₁₃₇	#137	1	4	yes	—
205	D₄×C₁₃₇	—	4	2	no	—
206	D₄×C₁₃₇	—	4	2	no	—
207	D₄×C₁₃₇	—	4	1	no	—
208	D₄×C₁₃₇	—	4	1	no	—
209	D₄×C₁₃₇	—	8	2	no	—
210	C₂×C₄×C₁₃₇	—	2	4	no	—
211	C₂×C₄×C₁₃₇	—	2	2	no	—
212	C₂×C₄×C₁₃₇	—	2	2	no	—
213	C₂×C₄×C₁₃₇	—	2	1	no	—
214	C₂×C₄×C₁₃₇	—	2	1	no	—
215	C₂×C₄×C₁₃₇	—	2	2	no	—
216	C₂×C₄×C₁₃₇	—	2	2	no	—
217	C₂×C₄×C₁₃₇	—	2	2	no	—
218	C₂×C₄×C₁₃₇	—	2	2	no	—
219	C₂×C₄×C₁₃₇	—	2	2	no	—
220	C₂×C₄×C₁₃₇	—	4	1	no	—
221	C₂×C₄×C₁₃₇	—	4	1	no	—
222	C₂×C₄×C₁₃₇	—	8	2	no	—
223	C₂×C₄×C₁₃₇	—	8	1	no	—
224	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₁₃₇	—	4	1	no	—
231	C₈×C₁₃₇	—	4	1	no	—
232	C₈×C₁₃₇	—	4	2	no	—
233	C₈×C₁₃₇	—	4	2	no	—
234	C₂²×C₁₃₇	—	2	1	no	—
235	C₂²×C₁₃₇	—	2	1	no	—
236	C₂²×C₁₃₇	—	2	1	no	—
237	C₂²×C₁₃₇	—	8	1	no	—
238	C₂²×C₁₃₇	—	8	1	no	—
239	C₂²×C₁₃₇	—	8	1	no	—
240	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
241	C₄×C₁₃₇	—	2	4	no	—
242	C₄×C₁₃₇	—	2	1	no	—
243	C₄×C₁₃₇	—	2	1	no	—
244	C₄×C₁₃₇	—	2	1	no	—
245	C₄×C₁₃₇	—	2	1	no	—
246	C₄×C₁₃₇	—	4	2	no	—
247	C₄×C₁₃₇	—	4	2	no	—
248	C₄×C₁₃₇	—	4	2	no	—
249	C₄×C₁₃₇	—	4	2	no	—
250	C₄×C₁₃₇	—	4	2	no	—
251	C₄×C₁₃₇	—	8	1	no	—
252	C₄×C₁₃₇	C₂×#137	1	2	yes	—
253	C₄×C₁₃₇	#577	1	1	yes	characteristic
254	C₄×C₁₃₇	#578	1	1	yes	characteristic
255	C₂×C₁₃₇	—	4	1	no	—
256	C₂×C₁₃₇	—	16	1	no	—
257	C₂×C₁₃₇	#3004	1	1	yes	characteristic
258	C₂×C₁₃₇	#3013	1	1	yes	characteristic
259	C₂×C₁₃₇	#3021	1	1	yes	characteristic
260	#18855	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₁₃₇	#18855	1	1	yes	characteristic, direct product factor, Sylow
262	#3502	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	#3254	C₂×C₁₃₇	1	1	yes	characteristic
264	#3210	C₂×C₁₃₇	1	1	yes	characteristic
265	#3112	C₂×C₁₃₇	1	1	yes	characteristic
266	#1636	C₂×C₁₃₇	1	2	yes	complemented
267	#1633	C₂×C₁₃₇	1	2	yes	complemented
268	#1626	C₂×C₁₃₇	1	2	yes	complemented
269	#1623	C₂×C₁₃₇	1	2	yes	complemented
270	#1559	C₂×C₁₃₇	1	1	yes	characteristic, complemented
271	#1497	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	#1487	C₂×C₁₃₇	1	1	yes	characteristic, complemented
273	Q₈²	—	2	1	no	—
274	Q₈²	C₂²×C₁₃₇	1	2	yes	—
275	#557	—	2	1	no	—
276	#557	—	2	2	no	—
277	#557	—	2	2	no	—
278	#557	C₂²×C₁₃₇	1	2	yes	—
279	#544	—	2	2	no	—
280	#544	—	2	1	no	—
281	#533	—	2	2	no	—
282	#533	C₂²×C₁₃₇	1	1	yes	characteristic
283	#533	C₂²×C₁₃₇	1	1	yes	characteristic
284	#532	C₂²×C₁₃₇	1	1	yes	characteristic
285	#519	—	2	1	no	—
286	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
287	#494	C₂²×C₁₃₇	1	1	yes	characteristic
288	#492	C₂²×C₁₃₇	1	1	yes	characteristic
289	#487	C₂²×C₁₃₇	1	1	yes	characteristic
290	#486	C₂²×C₁₃₇	1	1	yes	characteristic
291	#480	—	2	1	no	—
292	#477	C₂²×C₁₃₇	1	2	yes	—
293	#477	C₂²×C₁₃₇	1	2	yes	—
294	#474	—	2	1	no	—
295	#468	—	2	2	no	—
296	#464	—	2	2	no	—
297	#461	—	2	1	no	—
298	#460	C₂²×C₁₃₇	1	2	yes	—
299	#460	C₂²×C₁₃₇	1	2	yes	—
300	#452	—	2	2	no	—
301	#448	—	2	1	no	—
302	#440	—	2	2	no	—
303	#432	C₂²×C₁₃₇	1	1	yes	characteristic
304	#431	C₂²×C₁₃₇	1	1	yes	characteristic
305	#423	C₂²×C₁₃₇	1	1	yes	characteristic
306	#333	C₂²×C₁₃₇	1	2	yes	—
307	#332	C₂²×C₁₃₇	1	2	yes	—
308	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
309	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
310	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
311	Q₈⋊C₈	C₂²×C₁₃₇	1	2	yes	—
312	C₂×#41	—	2	1	no	—
313	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
314	C₂×Q₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₄⋊Q₈	—	2	4	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	4	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
326	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
327	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
330	#127	C₂³×C₁₃₇	1	1	yes	characteristic
331	#125	—	2	4	no	—
332	#125	—	2	4	no	—
333	#125	—	2	2	no	—
334	#125	—	2	4	no	—
335	#125	—	2	2	no	—
336	#125	—	2	1	no	—
337	#125	—	2	1	no	—
338	#124	—	2	1	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	D₄×C₁₃₇	1	2	yes	—
343	C₂²⋊Q₈	D₄×C₁₃₇	1	2	yes	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
358	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
359	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
360	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	#117	—	2	4	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
370	#107	—	2	2	no	—
371	#107	—	2	2	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
375	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	2	2	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	#97	—	2	1	no	—
385	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
386	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
387	#41	—	8	2	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
395	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
396	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
407	Q₁₆	—	8	2	no	—
408	SD₁₆	—	4	4	no	—
409	SD₁₆	—	8	2	no	—
410	SD₁₆	—	8	2	no	—
411	M₁₆	—	8	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	4	1	no	—
442	C₂²⋊C₄	—	4	1	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	4	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
452	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
453	C₂³	—	4	1	no	—
454	C₂³	#120×C₁₃₇	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	1	no	—
462	Q₈	—	4	1	no	—
463	Q₈	—	8	1	no	—
464	Q₈	—	8	4	no	—
465	Q₈	#137×C₁₃₇	1	4	yes	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
486	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
487	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
491	C₈	—	4	1	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	8	1	no	—
513	C₄	C₂×#137×C₁₃₇	1	2	yes	—
514	C₄	#577×C₁₃₇	1	1	yes	characteristic
515	C₄	#578×C₁₃₇	1	1	yes	characteristic
516	C₂	—	4	1	no	—
517	C₂	—	16	1	no	—
518	C₂	#3004×C₁₃₇	1	1	yes	characteristic
519	C₂	#3013×C₁₃₇	1	1	yes	characteristic
520	C₂	#3021×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	#532×C₁₃₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3502×C₁₃₇	C₂	semidirect
5. #1636×C₁₃₇	C₂	semidirect
6. #1633×C₁₃₇	C₂	semidirect
7. #1626×C₁₃₇	C₂	semidirect
8. #1623×C₁₃₇	C₂	semidirect
9. #1559×C₁₃₇	C₂	semidirect
10. #1497×C₁₃₇	C₂	semidirect
11. #1487×C₁₃₇	C₂	semidirect
260. #18855	C₁₃₇	direct (N × H)
261. C₁₃₇	#18855	direct (N × H)
262. #3502	C₂×C₁₃₇	semidirect
266. #1636	C₂×C₁₃₇	semidirect
267. #1633	C₂×C₁₃₇	semidirect
268. #1626	C₂×C₁₃₇	semidirect
269. #1623	C₂×C₁₃₇	semidirect
270. #1559	C₂×C₁₃₇	semidirect
271. #1497	C₂×C₁₃₇	semidirect
272. #1487	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3502×C₁₃₇	2
#3254×C₁₃₇	2
#3210×C₁₃₇	2
#3112×C₁₃₇	2
#1636×C₁₃₇	2
#1633×C₁₃₇	2
#1626×C₁₃₇	2
#1623×C₁₃₇	2
#1559×C₁₃₇	2
#1497×C₁₃₇	2
#1487×C₁₃₇	2
#18855	137

Subgroups — C137×#18855 #46868241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#18855 #46868241