Subgroups — C₂×#1925×C₁₃₇ #46870440

Order 35072.

1454 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#107×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#390×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1925×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
7	C₂×#340×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
16	C₂²×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
17	C₂²×C₄²×C₁₃₇	—	2	1	no	—
18	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#107×C₁₃₇	—	2	4	no	—
20	C₂×#107×C₁₃₇	C₂²	1	4	yes	complemented
21	C₂×#102×C₁₃₇	—	2	4	no	—
22	C₂×#102×C₁₃₇	C₄	1	8	yes	complemented
23	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
24	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
25	#390×C₁₃₇	—	2	2	no	—
26	#390×C₁₃₇	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₁₃₇	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
29	C₂×#95×C₁₃₇	—	2	1	no	—
30	#340×C₁₃₇	C₂²	1	4	yes	complemented
31	#336×C₁₃₇	C₂²	1	4	yes	complemented
32	C₂⁵×C₁₃₇	—	2	1	no	—
33	C₂²×D₄×C₁₃₇	—	2	2	no	—
34	C₂²×D₄×C₁₃₇	—	2	1	no	—
35	C₂²×D₄×C₁₃₇	—	2	2	no	—
36	C₂²×D₄×C₁₃₇	—	2	2	no	—
37	C₂²×D₄×C₁₃₇	—	2	2	no	—
38	C₂²×D₄×C₁₃₇	—	2	2	no	—
39	C₂²×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃₇	—	2	1	no	—
42	C₂³×C₄×C₁₃₇	—	2	1	no	—
43	C₂³×C₄×C₁₃₇	—	2	1	no	—
44	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	—	2	2	no	—
48	C₂²×C₈×C₁₃₇	—	2	2	no	—
49	C₂²×C₈×C₁₃₇	—	2	2	no	—
50	C₂²×C₈×C₁₃₇	—	2	2	no	—
51	C₂²×C₈×C₁₃₇	—	2	2	no	—
52	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₃₇	—	4	4	no	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	4	4	no	—
71	C₂×C₄²×C₁₃₇	—	2	2	no	—
72	C₂×C₄²×C₁₃₇	—	2	2	no	—
73	C₂×C₄²×C₁₃₇	—	2	4	no	—
74	C₂×C₄²×C₁₃₇	—	4	4	no	—
75	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
77	#107×C₁₃₇	—	2	8	no	—
78	#102×C₁₃₇	—	2	8	no	—
79	#102×C₁₃₇	C₂×C₄	1	16	yes	complemented
80	#95×C₁₃₇	—	2	4	no	—
81	C₂⁴×C₁₃₇	—	2	4	no	—
82	C₂⁴×C₁₃₇	—	2	2	no	—
83	C₂⁴×C₁₃₇	—	4	2	no	—
84	C₂⁴×C₁₃₇	—	4	2	no	—
85	C₂⁴×C₁₃₇	—	4	2	no	—
86	C₂⁴×C₁₃₇	—	4	2	no	—
87	C₂⁴×C₁₃₇	—	4	2	no	—
88	C₂⁴×C₁₃₇	—	4	2	no	—
89	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₃₇	—	2	8	no	—
91	C₂×D₄×C₁₃₇	—	2	8	no	—
92	C₂×D₄×C₁₃₇	—	2	4	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	2	2	no	—
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	4	2	no	—
99	C₂×D₄×C₁₃₇	—	4	2	no	—
100	C₂×D₄×C₁₃₇	—	4	4	no	—
101	C₂×D₄×C₁₃₇	—	4	4	no	—
102	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃₇	—	2	2	no	—
104	C₂²×C₄×C₁₃₇	—	2	2	no	—
105	C₂²×C₄×C₁₃₇	—	2	4	no	—
106	C₂²×C₄×C₁₃₇	—	2	4	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	2	2	no	—
109	C₂²×C₄×C₁₃₇	—	2	2	no	—
110	C₂²×C₄×C₁₃₇	—	2	2	no	—
111	C₂²×C₄×C₁₃₇	—	2	2	no	—
112	C₂²×C₄×C₁₃₇	—	2	2	no	—
113	C₂²×C₄×C₁₃₇	—	4	2	no	—
114	C₂²×C₄×C₁₃₇	—	4	2	no	—
115	C₂²×C₄×C₁₃₇	—	4	2	no	—
116	C₂²×C₄×C₁₃₇	—	4	2	no	—
117	C₂²×C₄×C₁₃₇	—	4	2	no	—
118	C₂²×C₄×C₁₃₇	—	4	2	no	—
119	C₂²×C₄×C₁₃₇	—	4	2	no	—
120	C₂²×C₄×C₁₃₇	D₈	1	4	yes	—
121	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
127	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
128	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
129	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
130	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₁₃₇	—	2	8	no	—
132	C₂×C₈×C₁₃₇	—	2	2	no	—
133	C₂×C₈×C₁₃₇	—	2	2	no	—
134	C₂×C₈×C₁₃₇	—	2	2	no	—
135	C₂×C₈×C₁₃₇	—	2	2	no	—
136	C₂×C₈×C₁₃₇	—	2	2	no	—
137	C₂×C₈×C₁₃₇	—	4	4	no	—
138	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	—
139	C₄⋊C₄×C₁₃₇	—	2	4	no	—
140	C₄⋊C₄×C₁₃₇	—	2	4	no	—
141	C₄⋊C₄×C₁₃₇	—	2	2	no	—
142	C₄⋊C₄×C₁₃₇	—	2	2	no	—
143	C₄⋊C₄×C₁₃₇	—	2	2	no	—
144	C₄⋊C₄×C₁₃₇	—	2	2	no	—
145	C₄⋊C₄×C₁₃₇	—	4	2	no	—
146	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
147	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
148	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
149	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
150	C₄²×C₁₃₇	—	2	4	no	—
151	C₄²×C₁₃₇	—	2	2	no	—
152	C₄²×C₁₃₇	—	2	2	no	—
153	C₄²×C₁₃₇	—	4	8	no	—
154	C₂³×C₁₃₇	—	2	4	no	—
155	C₂³×C₁₃₇	—	4	2	no	—
156	C₂³×C₁₃₇	—	4	2	no	—
157	C₂³×C₁₃₇	—	4	2	no	—
158	C₂³×C₁₃₇	—	4	2	no	—
159	C₂³×C₁₃₇	—	4	2	no	—
160	C₂³×C₁₃₇	—	4	2	no	—
161	C₂³×C₁₃₇	—	4	8	no	—
162	C₂³×C₁₃₇	—	4	8	no	—
163	C₂³×C₁₃₇	—	4	8	no	—
164	C₂³×C₁₃₇	—	8	4	no	—
165	C₂³×C₁₃₇	—	8	4	no	—
166	C₂³×C₁₃₇	—	8	4	no	—
167	C₂³×C₁₃₇	—	8	4	no	—
168	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
169	C₂³×C₁₃₇	#121	1	2	yes	—
170	C₂³×C₁₃₇	#123	1	2	yes	—
171	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
172	C₂³×C₁₃₇	#135	1	2	yes	—
173	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
174	C₂³×C₁₃₇	#137	1	2	yes	—
175	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
176	D₄×C₁₃₇	—	2	4	no	—
177	D₄×C₁₃₇	—	2	4	no	—
178	D₄×C₁₃₇	—	4	2	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	D₄×C₁₃₇	—	4	8	no	—
181	C₂×C₄×C₁₃₇	—	2	2	no	—
182	C₂×C₄×C₁₃₇	—	2	2	no	—
183	C₂×C₄×C₁₃₇	—	2	8	no	—
184	C₂×C₄×C₁₃₇	—	2	4	no	—
185	C₂×C₄×C₁₃₇	—	2	4	no	—
186	C₂×C₄×C₁₃₇	—	2	2	no	—
187	C₂×C₄×C₁₃₇	—	2	2	no	—
188	C₂×C₄×C₁₃₇	—	2	2	no	—
189	C₂×C₄×C₁₃₇	—	4	2	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	4	2	no	—
192	C₂×C₄×C₁₃₇	—	4	2	no	—
193	C₂×C₄×C₁₃₇	—	4	8	no	—
194	C₂×C₄×C₁₃₇	—	4	8	no	—
195	C₂×C₄×C₁₃₇	—	4	4	no	—
196	C₂×C₄×C₁₃₇	—	4	2	no	—
197	C₂×C₄×C₁₃₇	—	4	2	no	—
198	C₂×C₄×C₁₃₇	—	4	2	no	—
199	C₂×C₄×C₁₃₇	—	8	4	no	—
200	C₂×C₄×C₁₃₇	#117	1	4	yes	—
201	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
202	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₁₃₇	#121	1	2	yes	—
204	C₂×C₄×C₁₃₇	#123	1	2	yes	—
205	C₂×C₄×C₁₃₇	#124	1	4	yes	—
206	C₂×C₄×C₁₃₇	#126	1	4	yes	—
207	C₂×C₄×C₁₃₇	C₂×D₈	1	4	yes	—
208	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
214	C₈×C₁₃₇	—	2	4	no	—
215	C₈×C₁₃₇	—	4	2	no	—
216	C₂²×C₁₃₇	—	4	4	no	—
217	C₂²×C₁₃₇	—	4	4	no	—
218	C₂²×C₁₃₇	—	4	4	no	—
219	C₂²×C₁₃₇	—	8	2	no	—
220	C₂²×C₁₃₇	—	8	2	no	—
221	C₂²×C₁₃₇	—	8	16	no	—
222	C₂²×C₁₃₇	—	8	2	no	—
223	C₂²×C₁₃₇	—	8	2	no	—
224	C₂²×C₁₃₇	#388	1	4	yes	—
225	C₂²×C₁₃₇	C₄×D₈	1	4	yes	—
226	C₂²×C₁₃₇	#440	1	4	yes	—
227	C₂²×C₁₃₇	#459	1	4	yes	—
228	C₂²×C₁₃₇	#464	1	4	yes	—
229	C₂²×C₁₃₇	#480	1	4	yes	—
230	C₂²×C₁₃₇	#482	1	4	yes	—
231	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
233	C₂²×C₁₃₇	C₂×#123	1	1	yes	characteristic
234	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
235	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
236	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂²×C₁₃₇	C₂×#137	1	1	yes	characteristic
238	C₄×C₁₃₇	—	2	4	no	—
239	C₄×C₁₃₇	—	4	2	no	—
240	C₄×C₁₃₇	—	4	4	no	—
241	C₄×C₁₃₇	—	4	4	no	—
242	C₄×C₁₃₇	—	8	2	no	—
243	C₄×C₁₃₇	#388	1	4	yes	—
244	C₄×C₁₃₇	C₂×#117	1	1	yes	characteristic
245	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
247	C₄×C₁₃₇	C₂×#126	1	1	yes	characteristic
248	C₂×C₁₃₇	—	8	4	no	—
249	C₂×C₁₃₇	#1925	1	8	yes	direct product factor
250	C₂×C₁₃₇	C₂×#388	1	1	yes	characteristic
251	C₂×C₁₃₇	C₂×C₄×D₈	1	1	yes	characteristic
252	C₂×C₁₃₇	C₂×#440	1	1	yes	characteristic
253	C₂×C₁₃₇	C₂×#459	1	1	yes	characteristic
254	C₂×C₁₃₇	C₂×#464	1	1	yes	characteristic
255	C₂×C₁₃₇	C₂×#480	1	1	yes	characteristic
256	C₂×C₁₃₇	C₂×#482	1	1	yes	characteristic
257	C₂×#1925	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₁₃₇	C₂×#1925	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×#107	C₂×C₁₃₇	1	1	yes	characteristic, complemented
260	C₂²×#102	C₂×C₁₃₇	1	1	yes	characteristic
261	C₂²×#102	C₂×C₁₃₇	1	1	yes	characteristic
262	C₂×#390	C₂×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
264	#1925	C₂×C₁₃₇	1	8	yes	direct product factor
265	C₂×#340	C₂×C₁₃₇	1	1	yes	characteristic, complemented
266	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic, complemented
267	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	—	2	1	no	—
274	C₂²×C₂²⋊C₄	—	2	1	no	—
275	C₂²×C₄²	—	2	1	no	—
276	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
277	C₂×#107	—	2	4	no	—
278	C₂×#107	C₂²×C₁₃₇	1	4	yes	complemented
279	C₂×#102	—	2	4	no	—
280	C₂×#102	C₄×C₁₃₇	1	8	yes	complemented
281	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
282	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
283	#390	—	2	2	no	—
284	#390	C₂²×C₁₃₇	1	4	yes	—
285	C₄×C₄⋊C₄	—	2	2	no	—
286	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
287	C₂×#95	—	2	1	no	—
288	#340	C₂²×C₁₃₇	1	4	yes	complemented
289	#336	C₂²×C₁₃₇	1	4	yes	complemented
290	C₂⁵	—	2	1	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
298	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
311	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	—
321	C₂×C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	4	4	no	—
328	C₂×C₂²⋊C₄	—	4	4	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	4	no	—
332	C₂×C₄²	—	4	4	no	—
333	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
335	#107	—	2	8	no	—
336	#102	—	2	8	no	—
337	#102	C₂×C₄×C₁₃₇	1	16	yes	complemented
338	#95	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	2	no	—
341	C₂⁴	—	4	2	no	—
342	C₂⁴	—	4	2	no	—
343	C₂⁴	—	4	2	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	4	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	—	2	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	D₈×C₁₃₇	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
384	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
385	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
386	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
387	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
389	C₂×C₈	—	2	8	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	4	no	—
396	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
405	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	8	4	no	—
423	C₂³	—	8	4	no	—
424	C₂³	—	8	4	no	—
425	C₂³	—	8	4	no	—
426	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
427	C₂³	#121×C₁₃₇	1	2	yes	—
428	C₂³	#123×C₁₃₇	1	2	yes	—
429	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
430	C₂³	#135×C₁₃₇	1	2	yes	—
431	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
432	C₂³	#137×C₁₃₇	1	2	yes	—
433	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
434	D₄	—	2	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	4	8	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	4	no	—
458	C₂×C₄	#117×C₁₃₇	1	4	yes	—
459	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
460	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
461	C₂×C₄	#121×C₁₃₇	1	2	yes	—
462	C₂×C₄	#123×C₁₃₇	1	2	yes	—
463	C₂×C₄	#124×C₁₃₇	1	4	yes	—
464	C₂×C₄	#126×C₁₃₇	1	4	yes	—
465	C₂×C₄	C₂×D₈×C₁₃₇	1	4	yes	—
466	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
468	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
470	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
472	C₈	—	2	4	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	16	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	#388×C₁₃₇	1	4	yes	—
483	C₂²	C₄×D₈×C₁₃₇	1	4	yes	—
484	C₂²	#440×C₁₃₇	1	4	yes	—
485	C₂²	#459×C₁₃₇	1	4	yes	—
486	C₂²	#464×C₁₃₇	1	4	yes	—
487	C₂²	#480×C₁₃₇	1	4	yes	—
488	C₂²	#482×C₁₃₇	1	4	yes	—
489	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
490	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
491	C₂²	C₂×#123×C₁₃₇	1	1	yes	characteristic
492	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
493	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
494	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
495	C₂²	C₂×#137×C₁₃₇	1	1	yes	characteristic
496	C₄	—	2	4	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	4	no	—
500	C₄	—	8	2	no	—
501	C₄	#388×C₁₃₇	1	4	yes	—
502	C₄	C₂×#117×C₁₃₇	1	1	yes	characteristic
503	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
504	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
505	C₄	C₂×#126×C₁₃₇	1	1	yes	characteristic
506	C₂	—	8	4	no	—
507	C₂	#1925×C₁₃₇	1	8	yes	direct product factor
508	C₂	C₂×#388×C₁₃₇	1	1	yes	characteristic
509	C₂	C₂×C₄×D₈×C₁₃₇	1	1	yes	characteristic
510	C₂	C₂×#440×C₁₃₇	1	1	yes	characteristic
511	C₂	C₂×#459×C₁₃₇	1	1	yes	characteristic
512	C₂	C₂×#464×C₁₃₇	1	1	yes	characteristic
513	C₂	C₂×#480×C₁₃₇	1	1	yes	characteristic
514	C₂	C₂×#482×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂³×D₄×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#107×C₁₃₇	C₂	semidirect
5. C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	semidirect
6. #1925×C₁₃₇	C₂	direct (N × H)
7. C₂×#340×C₁₃₇	C₂	semidirect
8. C₂×#336×C₁₃₇	C₂	semidirect
20. C₂×#107×C₁₃₇	C₂²	semidirect
22. C₂×#102×C₁₃₇	C₄	semidirect
28. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
30. #340×C₁₃₇	C₂²	semidirect
31. #336×C₁₃₇	C₂²	semidirect
79. #102×C₁₃₇	C₂×C₄	semidirect
249. C₂×C₁₃₇	#1925	direct (N × H)
257. C₂×#1925	C₁₃₇	direct (N × H)
258. C₁₃₇	C₂×#1925	direct (N × H)
259. C₂²×#107	C₂×C₁₃₇	semidirect
263. C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	semidirect
264. #1925	C₂×C₁₃₇	direct (N × H)
265. C₂×#340	C₂×C₁₃₇	semidirect
266. C₂×#336	C₂×C₁₃₇	semidirect
278. C₂×#107	C₂²×C₁₃₇	semidirect
280. C₂×#102	C₄×C₁₃₇	semidirect
286. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
288. #340	C₂²×C₁₃₇	semidirect
289. #336	C₂²×C₁₃₇	semidirect
337. #102	C₂×C₄×C₁₃₇	semidirect
507. C₂	#1925×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#107×C₁₃₇	2
C₂²×#102×C₁₃₇	2
C₂×#390×C₁₃₇	2
C₂×C₄×C₄⋊C₄×C₁₃₇	2
#1925×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₂×#336×C₁₃₇	2
C₂×#1925	137

Subgroups — C2×#1925×C137 #46870440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1925×C₁₃₇ #46870440