Subgroups — C₁₃₇×#28661 #46878047

Order 35072.

854 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#501×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#490×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2858×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#125×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2067×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2065×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1993×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1961×C₁₃₇	C₂	1	1	yes	maximal, characteristic
9	#1926×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1925×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1767×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₇	—	2	1	no	—
16	C₂×#124×C₁₃₇	—	2	1	no	—
17	#501×C₁₃₇	—	2	4	no	—
18	#490×C₁₃₇	—	2	4	no	—
19	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
20	C₂×#106×C₁₃₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#102×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	#390×C₁₃₇	—	2	1	no	—
29	#390×C₁₃₇	—	2	1	no	—
30	#390×C₁₃₇	C₂²	1	2	yes	—
31	#390×C₁₃₇	C₂²	1	2	yes	—
32	#389×C₁₃₇	C₂²	1	1	yes	characteristic
33	#389×C₁₃₇	C₂²	1	1	yes	characteristic
34	#387×C₁₃₇	—	2	1	no	—
35	#387×C₁₃₇	—	2	1	no	—
36	#382×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₃₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
42	#340×C₁₃₇	C₂²	1	2	yes	—
43	#340×C₁₃₇	C₂²	1	2	yes	—
44	#336×C₁₃₇	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₇	—	2	1	no	—
46	C₂²×D₄×C₁₃₇	—	2	1	no	—
47	C₂²×D₄×C₁₃₇	—	2	1	no	—
48	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
52	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
53	#127×C₁₃₇	—	2	2	no	—
54	#127×C₁₃₇	—	2	2	no	—
55	#125×C₁₃₇	—	2	2	no	—
56	#125×C₁₃₇	D₄	1	4	yes	—
57	#124×C₁₃₇	—	4	4	no	—
58	#124×C₁₃₇	—	4	4	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
73	C₂×C₄²×C₁₃₇	—	2	1	no	—
74	C₂×C₄²×C₁₃₇	—	2	1	no	—
75	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
82	#107×C₁₃₇	—	2	4	no	—
83	#106×C₁₃₇	—	2	4	no	—
84	C₄⋊C₈×C₁₃₇	—	2	4	no	—
85	#102×C₁₃₇	—	2	4	no	—
86	#102×C₁₃₇	—	2	4	no	—
87	#102×C₁₃₇	—	2	4	no	—
88	#102×C₁₃₇	—	2	4	no	—
89	#97×C₁₃₇	—	2	2	no	—
90	#97×C₁₃₇	—	2	2	no	—
91	#95×C₁₃₇	—	2	1	no	—
92	#95×C₁₃₇	—	2	1	no	—
93	#95×C₁₃₇	—	2	1	no	—
94	#95×C₁₃₇	—	2	1	no	—
95	#95×C₁₃₇	—	2	1	no	—
96	#95×C₁₃₇	—	2	1	no	—
97	C₂⁴×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	4	2	no	—
99	C₂×Q₈×C₁₃₇	—	4	2	no	—
100	C₂×Q₈×C₁₃₇	—	4	2	no	—
101	C₂×D₄×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	2	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	4	2	no	—
108	C₂×D₄×C₁₃₇	—	4	2	no	—
109	C₂×D₄×C₁₃₇	—	4	2	no	—
110	C₂×D₄×C₁₃₇	—	4	2	no	—
111	C₂×D₄×C₁₃₇	—	4	2	no	—
112	C₂×D₄×C₁₃₇	—	4	2	no	—
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	—	2	1	no	—
115	C₂²×C₄×C₁₃₇	—	2	1	no	—
116	C₂²×C₄×C₁₃₇	—	2	1	no	—
117	C₂²×C₄×C₁₃₇	—	2	2	no	—
118	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
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	#41	1	4	yes	—
131	C₄⋊C₄×C₁₃₇	—	2	4	no	—
132	C₄⋊C₄×C₁₃₇	—	2	4	no	—
133	C₄⋊C₄×C₁₃₇	—	2	1	no	—
134	C₄⋊C₄×C₁₃₇	—	2	1	no	—
135	C₄⋊C₄×C₁₃₇	—	2	2	no	—
136	C₄⋊C₄×C₁₃₇	—	2	2	no	—
137	C₄⋊C₄×C₁₃₇	—	2	2	no	—
138	C₄⋊C₄×C₁₃₇	—	2	2	no	—
139	C₄⋊C₄×C₁₃₇	—	4	2	no	—
140	C₄⋊C₄×C₁₃₇	—	4	2	no	—
141	C₄⋊C₄×C₁₃₇	—	4	2	no	—
142	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
145	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
146	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
147	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
148	C₄²×C₁₃₇	—	2	2	no	—
149	C₄²×C₁₃₇	—	2	2	no	—
150	C₄²×C₁₃₇	—	2	2	no	—
151	C₄²×C₁₃₇	—	2	2	no	—
152	C₄²×C₁₃₇	—	4	1	no	—
153	C₄²×C₁₃₇	—	4	1	no	—
154	C₄²×C₁₃₇	—	4	2	no	—
155	C₄²×C₁₃₇	—	4	2	no	—
156	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃₇	#41	1	2	yes	—
158	C₂³×C₁₃₇	—	4	2	no	—
159	C₂³×C₁₃₇	—	4	2	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	2	no	—
162	C₂³×C₁₃₇	—	4	2	no	—
163	C₂³×C₁₃₇	—	4	2	no	—
164	C₂³×C₁₃₇	—	4	2	no	—
165	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃₇	—	8	4	no	—
167	D₄×C₁₃₇	—	4	2	no	—
168	D₄×C₁₃₇	—	4	2	no	—
169	D₄×C₁₃₇	—	4	2	no	—
170	D₄×C₁₃₇	—	4	2	no	—
171	D₄×C₁₃₇	—	8	4	no	—
172	D₄×C₁₃₇	—	8	4	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	2	no	—
182	C₂×C₄×C₁₃₇	—	2	2	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	—	4	1	no	—
190	C₂×C₄×C₁₃₇	—	4	1	no	—
191	C₂×C₄×C₁₃₇	—	4	1	no	—
192	C₂×C₄×C₁₃₇	—	4	1	no	—
193	C₂×C₄×C₁₃₇	—	4	2	no	—
194	C₂×C₄×C₁₃₇	—	4	1	no	—
195	C₂×C₄×C₁₃₇	—	4	1	no	—
196	C₂×C₄×C₁₃₇	—	4	1	no	—
197	C₂×C₄×C₁₃₇	—	4	2	no	—
198	C₂×C₄×C₁₃₇	—	4	2	no	—
199	C₂×C₄×C₁₃₇	—	4	1	no	—
200	C₂×C₄×C₁₃₇	—	4	1	no	—
201	C₂×C₄×C₁₃₇	—	4	1	no	—
202	C₂×C₄×C₁₃₇	#121	1	2	yes	—
203	C₂×C₄×C₁₃₇	#121	1	2	yes	—
204	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
210	C₈×C₁₃₇	—	2	4	no	—
211	C₈×C₁₃₇	—	4	2	no	—
212	C₂²×C₁₃₇	—	8	2	no	—
213	C₂²×C₁₃₇	—	8	2	no	—
214	C₂²×C₁₃₇	—	8	2	no	—
215	C₂²×C₁₃₇	—	8	2	no	—
216	C₂²×C₁₃₇	—	8	2	no	—
217	C₂²×C₁₃₇	—	8	2	no	—
218	C₂²×C₁₃₇	—	8	2	no	—
219	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
220	C₂²×C₁₃₇	#532	1	1	yes	characteristic
221	C₂²×C₁₃₇	#536	1	1	yes	characteristic
222	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂²×C₁₃₇	#575	1	1	yes	characteristic
225	C₂²×C₁₃₇	#575	1	1	yes	characteristic
226	C₄×C₁₃₇	—	2	2	no	—
227	C₄×C₁₃₇	—	2	2	no	—
228	C₄×C₁₃₇	—	2	2	no	—
229	C₄×C₁₃₇	—	2	2	no	—
230	C₄×C₁₃₇	—	4	1	no	—
231	C₄×C₁₃₇	—	4	1	no	—
232	C₄×C₁₃₇	—	4	2	no	—
233	C₄×C₁₃₇	—	4	2	no	—
234	C₄×C₁₃₇	—	8	1	no	—
235	C₄×C₁₃₇	—	8	1	no	—
236	C₄×C₁₃₇	—	8	2	no	—
237	C₄×C₁₃₇	#548	1	2	yes	—
238	C₄×C₁₃₇	#556	1	2	yes	—
239	C₂×C₁₃₇	—	16	2	no	—
240	C₂×C₁₃₇	#2545	1	1	yes	characteristic
241	C₂×C₁₃₇	#3038	1	1	yes	characteristic
242	C₂×C₁₃₇	#3040	1	1	yes	characteristic
243	C₂×C₁₃₇	#3171	1	1	yes	characteristic
244	C₂×C₁₃₇	#3180	1	1	yes	characteristic
245	C₂×C₁₃₇	#3234	1	1	yes	characteristic
246	C₂×C₁₃₇	#3235	1	1	yes	characteristic
247	#28661	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₁₃₇	#28661	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#501	C₂×C₁₃₇	1	1	yes	characteristic, complemented
250	C₂×#490	C₂×C₁₃₇	1	1	yes	characteristic
251	#2858	C₂×C₁₃₇	1	1	yes	characteristic
252	C₄×#125	C₂×C₁₃₇	1	1	yes	characteristic, complemented
253	#2067	C₂×C₁₃₇	1	2	yes	complemented
254	#2065	C₂×C₁₃₇	1	2	yes	complemented
255	#1993	C₂×C₁₃₇	1	1	yes	characteristic, complemented
256	#1961	C₂×C₁₃₇	1	1	yes	characteristic
257	#1926	C₂×C₁₃₇	1	2	yes	complemented
258	#1925	C₂×C₁₃₇	1	2	yes	complemented
259	#1767	C₂×C₁₃₇	1	1	yes	characteristic, complemented
260	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
261	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
263	C₂×#124	—	2	1	no	—
264	C₂×#124	—	2	1	no	—
265	#501	—	2	4	no	—
266	#490	—	2	4	no	—
267	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
268	C₂×#106	C₂²×C₁₃₇	1	2	yes	—
269	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
270	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
271	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
272	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
273	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
274	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
275	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
276	#390	—	2	1	no	—
277	#390	—	2	1	no	—
278	#390	C₂²×C₁₃₇	1	2	yes	—
279	#390	C₂²×C₁₃₇	1	2	yes	—
280	#389	C₂²×C₁₃₇	1	1	yes	characteristic
281	#389	C₂²×C₁₃₇	1	1	yes	characteristic
282	#387	—	2	1	no	—
283	#387	—	2	1	no	—
284	#382	C₂²×C₁₃₇	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	—	2	1	no	—
287	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
289	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
290	#340	C₂²×C₁₃₇	1	2	yes	—
291	#340	C₂²×C₁₃₇	1	2	yes	—
292	#336	C₂²×C₁₃₇	1	2	yes	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	#127	—	2	2	no	—
302	#127	—	2	2	no	—
303	#125	—	2	2	no	—
304	#125	D₄×C₁₃₇	1	4	yes	—
305	#124	—	4	4	no	—
306	#124	—	4	4	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
330	#107	—	2	4	no	—
331	#106	—	2	4	no	—
332	C₄⋊C₈	—	2	4	no	—
333	#102	—	2	4	no	—
334	#102	—	2	4	no	—
335	#102	—	2	4	no	—
336	#102	—	2	4	no	—
337	#97	—	2	2	no	—
338	#97	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	C₂⁴	—	2	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	#41×C₁₃₇	1	4	yes	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
391	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
405	C₄²	#41×C₁₃₇	1	2	yes	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
414	Q₈	—	8	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	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	2	no	—
430	C₂×C₄	—	2	2	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	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	#121×C₁₃₇	1	2	yes	—
451	C₂×C₄	#121×C₁₃₇	1	2	yes	—
452	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
453	C₂×C₄	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
456	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
457	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
468	C₂²	#532×C₁₃₇	1	1	yes	characteristic
469	C₂²	#536×C₁₃₇	1	1	yes	characteristic
470	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
471	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
472	C₂²	#575×C₁₃₇	1	1	yes	characteristic
473	C₂²	#575×C₁₃₇	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	#548×C₁₃₇	1	2	yes	—
486	C₄	#556×C₁₃₇	1	2	yes	—
487	C₂	—	16	2	no	—
488	C₂	#2545×C₁₃₇	1	1	yes	characteristic
489	C₂	#3038×C₁₃₇	1	1	yes	characteristic
490	C₂	#3040×C₁₃₇	1	1	yes	characteristic
491	C₂	#3171×C₁₃₇	1	1	yes	characteristic
492	C₂	#3180×C₁₃₇	1	1	yes	characteristic
493	C₂	#3234×C₁₃₇	1	1	yes	characteristic
494	C₂	#3235×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#127×C₁₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ C₄³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#501×C₁₃₇	C₂	semidirect
4. C₄×#125×C₁₃₇	C₂	semidirect
5. #2067×C₁₃₇	C₂	semidirect
6. #2065×C₁₃₇	C₂	semidirect
7. #1993×C₁₃₇	C₂	semidirect
9. #1926×C₁₃₇	C₂	semidirect
10. #1925×C₁₃₇	C₂	semidirect
11. #1767×C₁₃₇	C₂	semidirect
247. #28661	C₁₃₇	direct (N × H)
248. C₁₃₇	#28661	direct (N × H)
249. C₂×#501	C₂×C₁₃₇	semidirect
252. C₄×#125	C₂×C₁₃₇	semidirect
253. #2067	C₂×C₁₃₇	semidirect
254. #2065	C₂×C₁₃₇	semidirect
255. #1993	C₂×C₁₃₇	semidirect
257. #1926	C₂×C₁₃₇	semidirect
258. #1925	C₂×C₁₃₇	semidirect
259. #1767	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×#501×C₁₃₇	2
C₂×#490×C₁₃₇	2
#2858×C₁₃₇	2
C₄×#125×C₁₃₇	2
#2067×C₁₃₇	2
#2065×C₁₃₇	2
#1993×C₁₃₇	2
#1961×C₁₃₇	2
#1926×C₁₃₇	2
#1925×C₁₃₇	2
#1767×C₁₃₇	2
#28661	137

Subgroups — C137×#28661 #46878047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28661 #46878047