Subgroups — C₁₃₇×#18550 #46867936

Order 35072.

1230 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3138×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3113×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#3110×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#1642×C₁₃₇	C₂	1	4	yes	maximal, complemented
6	#1641×C₁₃₇	C₂	1	4	yes	maximal, complemented
7	#1555×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1491×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1490×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₇	—	2	1	no	—
11	#550×C₁₃₇	—	2	2	no	—
12	#550×C₁₃₇	—	2	2	no	—
13	#550×C₁₃₇	—	2	2	no	—
14	#550×C₁₃₇	C₂²	1	4	yes	—
15	#533×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₁₃₇	—	2	1	no	—
17	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#121×C₁₃₇	—	2	2	no	—
19	C₂×#121×C₁₃₇	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃₇	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	#490×C₁₃₇	—	2	2	no	—
24	#486×C₁₃₇	C₂²	1	2	yes	complemented
25	#486×C₁₃₇	C₂²	1	2	yes	complemented
26	#484×C₁₃₇	—	2	1	no	—
27	#483×C₁₃₇	—	2	1	no	—
28	#475×C₁₃₇	C₂²	1	2	yes	complemented
29	#474×C₁₃₇	C₂²	1	2	yes	complemented
30	#462×C₁₃₇	C₂²	1	2	yes	complemented
31	#461×C₁₃₇	C₂²	1	2	yes	complemented
32	#451×C₁₃₇	—	2	1	no	—
33	#450×C₁₃₇	—	2	1	no	—
34	#441×C₁₃₇	—	2	2	no	—
35	#440×C₁₃₇	—	2	2	no	—
36	#432×C₁₃₇	C₂²	1	1	yes	characteristic
37	#432×C₁₃₇	C₂²	1	1	yes	characteristic
38	#418×C₁₃₇	—	2	2	no	—
39	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
40	#331×C₁₃₇	C₂²	1	4	yes	complemented
41	Q₈⋊C₈×C₁₃₇	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₃₇	C₂²	1	4	yes	complemented
43	C₂×#41×C₁₃₇	—	2	4	no	—
44	C₂×#41×C₁₃₇	—	2	4	no	—
45	C₂×#41×C₁₃₇	—	4	8	no	—
46	C₂²×Q₈×C₁₃₇	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃₇	—	2	2	no	—
48	C₂²×D₄×C₁₃₇	—	2	2	no	—
49	C₂²×D₄×C₁₃₇	—	2	1	no	—
50	C₂²×D₄×C₁₃₇	—	2	1	no	—
51	C₂²×D₄×C₁₃₇	D₄	1	2	yes	—
52	C₂²×D₄×C₁₃₇	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃₇	—	2	2	no	—
54	C₂³×C₄×C₁₃₇	—	2	1	no	—
55	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
56	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
57	C₂×M₁₆×C₁₃₇	—	2	1	no	—
58	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
60	#127×C₁₃₇	—	2	4	no	—
61	#127×C₁₃₇	—	2	4	no	—
62	#127×C₁₃₇	—	2	1	no	—
63	#127×C₁₃₇	—	2	1	no	—
64	#127×C₁₃₇	D₄	1	2	yes	—
65	#127×C₁₃₇	C₂³	1	2	yes	—
66	#125×C₁₃₇	—	2	1	no	—
67	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
68	C₂²⋊Q₈×C₁₃₇	—	2	1	no	—
69	#121×C₁₃₇	—	2	4	no	—
70	#121×C₁₃₇	—	2	8	no	—
71	#121×C₁₃₇	—	2	8	no	—
72	#121×C₁₃₇	—	2	4	no	—
73	C₄×Q₈×C₁₃₇	—	2	1	no	—
74	C₄×Q₈×C₁₃₇	—	2	1	no	—
75	C₄×Q₈×C₁₃₇	—	2	1	no	—
76	C₄×Q₈×C₁₃₇	—	2	1	no	—
77	C₄×Q₈×C₁₃₇	D₄	1	2	yes	—
78	C₄×Q₈×C₁₃₇	C₂³	1	2	yes	—
79	C₄×D₄×C₁₃₇	—	2	4	no	—
80	C₄×D₄×C₁₃₇	—	2	4	no	—
81	C₄×D₄×C₁₃₇	—	2	1	no	—
82	C₄×D₄×C₁₃₇	—	2	1	no	—
83	C₄×D₄×C₁₃₇	D₄	1	2	yes	—
84	C₄×D₄×C₁₃₇	C₂³	1	2	yes	—
85	#117×C₁₃₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₃₇	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
91	C₂×C₄²×C₁₃₇	—	2	1	no	—
92	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
93	#107×C₁₃₇	—	2	2	no	—
94	#106×C₁₃₇	—	2	2	no	—
95	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
96	C₄⋊C₈×C₁₃₇	C₂³	1	2	yes	—
97	#103×C₁₃₇	—	2	2	no	—
98	#103×C₁₃₇	—	2	2	no	—
99	#103×C₁₃₇	—	2	2	no	—
100	#102×C₁₃₇	—	2	4	no	—
101	#102×C₁₃₇	—	2	4	no	—
102	#102×C₁₃₇	—	2	2	no	—
103	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
104	C₂²⋊C₈×C₁₃₇	—	2	1	no	—
105	#97×C₁₃₇	—	2	1	no	—
106	#97×C₁₃₇	—	2	1	no	—
107	#97×C₁₃₇	—	2	1	no	—
108	C₄×C₈×C₁₃₇	C₂³	1	2	yes	—
109	C₂⁴×C₁₃₇	—	2	2	no	—
110	C₂⁴×C₁₃₇	—	2	1	no	—
111	#41×C₁₃₇	—	4	16	no	—
112	#41×C₁₃₇	—	4	8	no	—
113	#41×C₁₃₇	—	4	8	no	—
114	C₂×Q₈×C₁₃₇	—	2	4	no	—
115	C₂×Q₈×C₁₃₇	—	2	1	no	—
116	C₂×Q₈×C₁₃₇	—	2	1	no	—
117	C₂×Q₈×C₁₃₇	—	2	1	no	—
118	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₁₃₇	—	2	8	no	—
120	C₂×D₄×C₁₃₇	—	2	8	no	—
121	C₂×D₄×C₁₃₇	—	2	1	no	—
122	C₂×D₄×C₁₃₇	—	2	2	no	—
123	C₂×D₄×C₁₃₇	—	2	2	no	—
124	C₂×D₄×C₁₃₇	—	2	2	no	—
125	C₂×D₄×C₁₃₇	—	2	2	no	—
126	C₂×D₄×C₁₃₇	—	2	2	no	—
127	C₂×D₄×C₁₃₇	—	4	2	no	—
128	C₂×D₄×C₁₃₇	—	4	4	no	—
129	C₂×D₄×C₁₃₇	—	4	8	no	—
130	C₂×D₄×C₁₃₇	—	4	4	no	—
131	C₂×D₄×C₁₃₇	—	4	4	no	—
132	C₂×D₄×C₁₃₇	—	8	4	no	—
133	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃₇	—	2	1	no	—
136	C₂²×C₄×C₁₃₇	—	2	8	no	—
137	C₂²×C₄×C₁₃₇	—	2	1	no	—
138	C₂²×C₄×C₁₃₇	—	2	1	no	—
139	C₂²×C₄×C₁₃₇	—	2	2	no	—
140	C₂²×C₄×C₁₃₇	—	2	2	no	—
141	C₂²×C₄×C₁₃₇	—	4	8	no	—
142	C₂²×C₄×C₁₃₇	—	4	4	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	—	4	4	no	—
147	SD₁₆×C₁₃₇	—	4	4	no	—
148	M₁₆×C₁₃₇	—	4	2	no	—
149	C₂×C₈×C₁₃₇	—	2	2	no	—
150	C₂×C₈×C₁₃₇	—	2	2	no	—
151	C₂×C₈×C₁₃₇	—	2	2	no	—
152	C₄⋊C₄×C₁₃₇	—	2	2	no	—
153	C₄⋊C₄×C₁₃₇	—	2	1	no	—
154	C₄⋊C₄×C₁₃₇	—	2	1	no	—
155	C₄⋊C₄×C₁₃₇	—	2	2	no	—
156	C₄⋊C₄×C₁₃₇	—	2	1	no	—
157	C₄⋊C₄×C₁₃₇	—	2	1	no	—
158	C₄⋊C₄×C₁₃₇	—	2	1	no	—
159	C₄⋊C₄×C₁₃₇	—	2	1	no	—
160	C₄⋊C₄×C₁₃₇	—	4	1	no	—
161	C₄⋊C₄×C₁₃₇	—	4	1	no	—
162	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
166	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
167	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
168	C₄²×C₁₃₇	—	2	2	no	—
169	C₄²×C₁₃₇	—	2	2	no	—
170	C₄²×C₁₃₇	—	4	1	no	—
171	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃₇	C₂⁴	1	1	yes	characteristic
175	C₂³×C₁₃₇	—	2	2	no	—
176	C₂³×C₁₃₇	—	2	4	no	—
177	C₂³×C₁₃₇	—	4	4	no	—
178	C₂³×C₁₃₇	—	4	2	no	—
179	C₂³×C₁₃₇	—	4	2	no	—
180	C₂³×C₁₃₇	—	4	4	no	—
181	C₂³×C₁₃₇	—	4	4	no	—
182	C₂³×C₁₃₇	—	4	2	no	—
183	C₂³×C₁₃₇	#120	1	1	yes	characteristic
184	Q₈×C₁₃₇	—	2	4	no	—
185	Q₈×C₁₃₇	—	2	2	no	—
186	Q₈×C₁₃₇	—	4	2	no	—
187	Q₈×C₁₃₇	—	4	2	no	—
188	Q₈×C₁₃₇	AGL(1,ℤ/8)	1	4	yes	—
189	D₄×C₁₃₇	—	2	2	no	—
190	D₄×C₁₃₇	—	2	2	no	—
191	D₄×C₁₃₇	—	4	4	no	—
192	D₄×C₁₃₇	—	4	2	no	—
193	D₄×C₁₃₇	—	4	4	no	—
194	D₄×C₁₃₇	—	4	16	no	—
195	D₄×C₁₃₇	—	4	4	no	—
196	D₄×C₁₃₇	—	4	4	no	—
197	D₄×C₁₃₇	—	4	4	no	—
198	D₄×C₁₃₇	—	8	2	no	—
199	D₄×C₁₃₇	—	8	8	no	—
200	C₂×C₄×C₁₃₇	—	2	4	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	—	2	2	no	—
207	C₂×C₄×C₁₃₇	—	4	16	no	—
208	C₂×C₄×C₁₃₇	—	4	4	no	—
209	C₂×C₄×C₁₃₇	—	4	2	no	—
210	C₂×C₄×C₁₃₇	—	4	2	no	—
211	C₂×C₄×C₁₃₇	—	4	4	no	—
212	C₂×C₄×C₁₃₇	—	4	1	no	—
213	C₂×C₄×C₁₃₇	—	4	1	no	—
214	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₃₇	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
220	C₈×C₁₃₇	—	4	2	no	—
221	C₈×C₁₃₇	—	4	2	no	—
222	C₈×C₁₃₇	—	4	2	no	—
223	C₂²×C₁₃₇	—	2	1	no	—
224	C₂²×C₁₃₇	—	2	1	no	—
225	C₂²×C₁₃₇	—	4	4	no	—
226	C₂²×C₁₃₇	—	4	2	no	—
227	C₂²×C₁₃₇	—	4	2	no	—
228	C₂²×C₁₃₇	—	4	4	no	—
229	C₂²×C₁₃₇	—	4	4	no	—
230	C₂²×C₁₃₇	—	4	2	no	—
231	C₂²×C₁₃₇	—	8	8	no	—
232	C₂²×C₁₃₇	—	8	4	no	—
233	C₂²×C₁₃₇	#455	1	2	yes	—
234	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
235	C₄×C₁₃₇	—	2	4	no	—
236	C₄×C₁₃₇	—	2	1	no	—
237	C₄×C₁₃₇	—	2	1	no	—
238	C₄×C₁₃₇	—	2	1	no	—
239	C₄×C₁₃₇	—	2	1	no	—
240	C₄×C₁₃₇	—	4	2	no	—
241	C₄×C₁₃₇	—	4	2	no	—
242	C₄×C₁₃₇	—	8	1	no	—
243	C₄×C₁₃₇	—	8	1	no	—
244	C₄×C₁₃₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
245	C₄×C₁₃₇	#575	1	2	yes	—
246	C₂×C₁₃₇	—	2	2	no	—
247	C₂×C₁₃₇	—	8	2	no	—
248	C₂×C₁₃₇	—	8	4	no	—
249	C₂×C₁₃₇	#3003	1	1	yes	characteristic
250	C₂×C₁₃₇	#3005	1	1	yes	characteristic
251	C₂×C₁₃₇	C₂×#455	1	1	yes	characteristic
252	#18550	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₁₃₇	#18550	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#550	C₂×C₁₃₇	1	1	yes	characteristic
255	#3138	C₂×C₁₃₇	1	1	yes	characteristic, complemented
256	#3113	C₂×C₁₃₇	1	1	yes	characteristic, complemented
257	#3110	C₂×C₁₃₇	1	1	yes	characteristic, complemented
258	#1642	C₂×C₁₃₇	1	4	yes	complemented
259	#1641	C₂×C₁₃₇	1	4	yes	complemented
260	#1555	C₂×C₁₃₇	1	1	yes	characteristic, complemented
261	#1491	C₂×C₁₃₇	1	1	yes	characteristic, complemented
262	#1490	C₂×C₁₃₇	1	1	yes	characteristic, complemented
263	C₂²×#41	—	2	1	no	—
264	#550	—	2	2	no	—
265	#550	—	2	2	no	—
266	#550	—	2	2	no	—
267	#550	C₂²×C₁₃₇	1	4	yes	—
268	#533	C₂²×C₁₃₇	1	1	yes	characteristic
269	C₂×#127	—	2	1	no	—
270	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
271	C₂×#121	—	2	2	no	—
272	C₂×#121	—	2	1	no	—
273	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
274	C₂×C₄×D₄	—	2	1	no	—
275	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
276	#490	—	2	2	no	—
277	#486	C₂²×C₁₃₇	1	2	yes	complemented
278	#486	C₂²×C₁₃₇	1	2	yes	complemented
279	#484	—	2	1	no	—
280	#483	—	2	1	no	—
281	#475	C₂²×C₁₃₇	1	2	yes	complemented
282	#474	C₂²×C₁₃₇	1	2	yes	complemented
283	#462	C₂²×C₁₃₇	1	2	yes	complemented
284	#461	C₂²×C₁₃₇	1	2	yes	complemented
285	#451	—	2	1	no	—
286	#450	—	2	1	no	—
287	#441	—	2	2	no	—
288	#440	—	2	2	no	—
289	#432	C₂²×C₁₃₇	1	1	yes	characteristic
290	#432	C₂²×C₁₃₇	1	1	yes	characteristic
291	#418	—	2	2	no	—
292	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
293	#331	C₂²×C₁₃₇	1	4	yes	complemented
294	Q₈⋊C₈	C₂²×C₁₃₇	1	4	yes	complemented
295	D₄⋊C₈	C₂²×C₁₃₇	1	4	yes	complemented
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	4	8	no	—
299	C₂²×Q₈	D₄×C₁₃₇	1	1	yes	characteristic
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	D₄×C₁₃₇	1	1	yes	characteristic
305	C₂²×D₄	D₄×C₁₃₇	1	2	yes	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
312	C₄⋊Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
313	#127	—	2	4	no	—
314	#127	—	2	4	no	—
315	#127	—	2	1	no	—
316	#127	—	2	1	no	—
317	#127	D₄×C₁₃₇	1	2	yes	—
318	#127	C₂³×C₁₃₇	1	2	yes	—
319	#125	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	#121	—	2	4	no	—
323	#121	—	2	8	no	—
324	#121	—	2	8	no	—
325	#121	—	2	4	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	D₄×C₁₃₇	1	2	yes	—
331	C₄×Q₈	C₂³×C₁₃₇	1	2	yes	—
332	C₄×D₄	—	2	4	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	D₄×C₁₃₇	1	2	yes	—
337	C₄×D₄	C₂³×C₁₃₇	1	2	yes	—
338	#117	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	D₄×C₁₃₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
346	#107	—	2	2	no	—
347	#106	—	2	2	no	—
348	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
349	C₄⋊C₈	C₂³×C₁₃₇	1	2	yes	—
350	#103	—	2	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#102	—	2	4	no	—
354	#102	—	2	4	no	—
355	#102	—	2	2	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	2	1	no	—
358	#97	—	2	1	no	—
359	#97	—	2	1	no	—
360	#97	—	2	1	no	—
361	C₄×C₈	C₂³×C₁₃₇	1	2	yes	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	1	no	—
364	#41	—	4	16	no	—
365	#41	—	4	8	no	—
366	#41	—	4	8	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	8	4	no	—
386	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
387	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	8	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
399	Q₁₆	—	4	4	no	—
400	SD₁₆	—	4	4	no	—
401	M₁₆	—	4	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
416	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
427	C₄²	C₂⁴×C₁₃₇	1	1	yes	characteristic
428	C₂³	—	2	2	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	#120×C₁₃₇	1	1	yes	characteristic
437	Q₈	—	2	4	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	AGL(1,ℤ/8)×C₁₃₇	1	4	yes	—
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	16	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	8	no	—
453	C₂×C₄	—	2	4	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	—	4	16	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
468	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
469	C₂×C₄	#120×C₁₃₇	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
473	C₈	—	4	2	no	—
474	C₈	—	4	2	no	—
475	C₈	—	4	2	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	8	no	—
485	C₂²	—	8	4	no	—
486	C₂²	#455×C₁₃₇	1	2	yes	—
487	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	C₂×AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
498	C₄	#575×C₁₃₇	1	2	yes	—
499	C₂	—	2	2	no	—
500	C₂	—	8	2	no	—
501	C₂	—	8	4	no	—
502	C₂	#3003×C₁₃₇	1	1	yes	characteristic
503	C₂	#3005×C₁₃₇	1	1	yes	characteristic
504	C₂	C₂×#455×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₇
prime radical	C₂×#550×C₁₃₇	C₂
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
2. #3138×C₁₃₇	C₂	semidirect
3. #3113×C₁₃₇	C₂	semidirect
4. #3110×C₁₃₇	C₂	semidirect
5. #1642×C₁₃₇	C₂	semidirect
6. #1641×C₁₃₇	C₂	semidirect
7. #1555×C₁₃₇	C₂	semidirect
8. #1491×C₁₃₇	C₂	semidirect
9. #1490×C₁₃₇	C₂	semidirect
24. #486×C₁₃₇	C₂²	semidirect
25. #486×C₁₃₇	C₂²	semidirect
28. #475×C₁₃₇	C₂²	semidirect
29. #474×C₁₃₇	C₂²	semidirect
30. #462×C₁₃₇	C₂²	semidirect
31. #461×C₁₃₇	C₂²	semidirect
40. #331×C₁₃₇	C₂²	semidirect
41. Q₈⋊C₈×C₁₃₇	C₂²	semidirect
42. D₄⋊C₈×C₁₃₇	C₂²	semidirect
252. #18550	C₁₃₇	direct (N × H)
253. C₁₃₇	#18550	direct (N × H)
255. #3138	C₂×C₁₃₇	semidirect
256. #3113	C₂×C₁₃₇	semidirect
257. #3110	C₂×C₁₃₇	semidirect
258. #1642	C₂×C₁₃₇	semidirect
259. #1641	C₂×C₁₃₇	semidirect
260. #1555	C₂×C₁₃₇	semidirect
261. #1491	C₂×C₁₃₇	semidirect
262. #1490	C₂×C₁₃₇	semidirect
277. #486	C₂²×C₁₃₇	semidirect
278. #486	C₂²×C₁₃₇	semidirect
281. #475	C₂²×C₁₃₇	semidirect
282. #474	C₂²×C₁₃₇	semidirect
283. #462	C₂²×C₁₃₇	semidirect
284. #461	C₂²×C₁₃₇	semidirect
293. #331	C₂²×C₁₃₇	semidirect
294. Q₈⋊C₈	C₂²×C₁₃₇	semidirect
295. D₄⋊C₈	C₂²×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₃₇	2
#3138×C₁₃₇	2
#3113×C₁₃₇	2
#3110×C₁₃₇	2
#1642×C₁₃₇	2
#1641×C₁₃₇	2
#1555×C₁₃₇	2
#1491×C₁₃₇	2
#1490×C₁₃₇	2
#18550	137

Subgroups — C137×#18550 #46867936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#18550 #46867936