Subgroups — C₂×#1950×C₁₃₇ #46870562

Order 35072.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₁₃₇	C₂	1	2	yes	maximal
2	C₂×#423×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×M₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1950×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#341×C₁₃₇	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₁₃₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#108×C₁₃₇	—	2	8	no	—
13	C₂×#108×C₁₃₇	C₂²	1	8	yes	—
14	#423×C₁₃₇	—	2	2	no	—
15	#423×C₁₃₇	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
17	C₂×C₄⋊C₈×C₁₃₇	—	2	1	no	—
18	C₂×C₄⋊C₈×C₁₃₇	C₄	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₄	1	4	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₄	1	2	yes	—
21	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	4	yes	—
22	C₄×M₁₆×C₁₃₇	—	2	2	no	—
23	C₄×M₁₆×C₁₃₇	C₂²	1	4	yes	—
24	C₂×#97×C₁₃₇	—	2	1	no	—
25	C₂×C₄×C₈×C₁₃₇	—	2	1	no	—
26	#341×C₁₃₇	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₃₇	Q₈	1	1	yes	characteristic
28	C₂³×C₄×C₁₃₇	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
30	C₂×M₁₆×C₁₃₇	—	2	1	no	—
31	C₂×M₁₆×C₁₃₇	—	2	1	no	—
32	C₂×M₁₆×C₁₃₇	—	2	2	no	—
33	C₂×M₁₆×C₁₃₇	—	2	2	no	—
34	C₂×M₁₆×C₁₃₇	—	2	2	no	—
35	C₂×M₁₆×C₁₃₇	—	2	4	no	—
36	C₂×M₁₆×C₁₃₇	—	2	4	no	—
37	C₂×M₁₆×C₁₃₇	D₄	1	4	yes	—
38	C₂×M₁₆×C₁₃₇	Q₈	1	4	yes	—
39	C₂×M₁₆×C₁₃₇	C₂³	1	4	yes	—
40	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
41	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₇	—	2	4	no	—
43	C₂²×C₈×C₁₃₇	—	2	1	no	—
44	C₂²×C₈×C₁₃₇	—	2	1	no	—
45	C₂²×C₈×C₁₃₇	—	2	4	no	—
46	C₂²×C₈×C₁₃₇	—	2	2	no	—
47	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₃₇	C₂³	1	4	yes	—
50	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
54	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₇	Q₈	1	2	yes	—
57	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
58	#108×C₁₃₇	—	2	16	no	—
59	C₄⋊C₈×C₁₃₇	—	2	4	no	—
60	C₄⋊C₈×C₁₃₇	—	2	4	no	—
61	C₄⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
62	C₄⋊C₈×C₁₃₇	C₂×C₄	1	8	yes	—
63	#97×C₁₃₇	—	2	4	no	—
64	C₄×C₈×C₁₃₇	—	2	4	no	—
65	C₂⁴×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
66	C₂²×C₄×C₁₃₇	—	2	4	no	—
67	C₂²×C₄×C₁₃₇	—	4	2	no	—
68	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₃₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
84	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
85	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
86	M₁₆×C₁₃₇	—	2	4	no	—
87	M₁₆×C₁₃₇	—	2	4	no	—
88	M₁₆×C₁₃₇	—	2	2	no	—
89	M₁₆×C₁₃₇	—	2	2	no	—
90	M₁₆×C₁₃₇	—	2	4	no	—
91	M₁₆×C₁₃₇	—	2	4	no	—
92	M₁₆×C₁₃₇	—	4	4	no	—
93	M₁₆×C₁₃₇	C₂×D₄	1	4	yes	—
94	M₁₆×C₁₃₇	C₂×Q₈	1	4	yes	—
95	C₂×C₈×C₁₃₇	—	2	8	no	—
96	C₂×C₈×C₁₃₇	—	2	8	no	—
97	C₂×C₈×C₁₃₇	—	2	4	no	—
98	C₂×C₈×C₁₃₇	—	2	4	no	—
99	C₂×C₈×C₁₃₇	—	2	2	no	—
100	C₂×C₈×C₁₃₇	—	2	2	no	—
101	C₂×C₈×C₁₃₇	—	2	4	no	—
102	C₂×C₈×C₁₃₇	—	2	4	no	—
103	C₂×C₈×C₁₃₇	—	2	4	no	—
104	C₂×C₈×C₁₃₇	—	4	4	no	—
105	C₂×C₈×C₁₃₇	C₂²×C₄	1	8	yes	—
106	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
107	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
108	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
109	C₄²×C₁₃₇	C₄⋊C₄	1	2	yes	—
110	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
111	C₄²×C₁₃₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
113	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
114	C₂³×C₁₃₇	—	2	2	no	—
115	C₂³×C₁₃₇	—	2	2	no	—
116	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₁₃₇	#125	1	2	yes	—
119	C₂³×C₁₃₇	C₄⋊Q₈	1	2	yes	—
120	C₂³×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
121	C₂×C₄×C₁₃₇	—	2	2	no	—
122	C₂×C₄×C₁₃₇	—	2	2	no	—
123	C₂×C₄×C₁₃₇	—	2	2	no	—
124	C₂×C₄×C₁₃₇	—	2	4	no	—
125	C₂×C₄×C₁₃₇	—	2	4	no	—
126	C₂×C₄×C₁₃₇	—	4	2	no	—
127	C₂×C₄×C₁₃₇	—	4	2	no	—
128	C₂×C₄×C₁₃₇	#108	1	4	yes	complemented
129	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₁₃₇	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₁₃₇	#121	1	2	yes	—
140	C₂×C₄×C₁₃₇	#121	1	2	yes	—
141	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₁₃₇	#125	1	2	yes	—
144	C₂×C₄×C₁₃₇	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₃₇	—	2	8	no	—
152	C₈×C₁₃₇	—	2	4	no	—
153	C₈×C₁₃₇	—	2	4	no	—
154	C₈×C₁₃₇	—	4	4	no	—
155	C₂²×C₁₃₇	—	2	1	no	—
156	C₂²×C₁₃₇	—	2	1	no	—
157	C₂²×C₁₃₇	—	2	1	no	—
158	C₂²×C₁₃₇	—	2	1	no	—
159	C₂²×C₁₃₇	—	2	4	no	—
160	C₂²×C₁₃₇	—	2	4	no	—
161	C₂²×C₁₃₇	#389	1	2	yes	—
162	C₂²×C₁₃₇	#389	1	2	yes	—
163	C₂²×C₁₃₇	C₂×#108	1	2	yes	—
164	C₂²×C₁₃₇	#430	1	2	yes	—
165	C₂²×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₁₃₇	C₂×#125	1	1	yes	characteristic
167	C₂²×C₁₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
168	C₄×C₁₃₇	—	2	2	no	—
169	C₄×C₁₃₇	—	2	2	no	—
170	C₄×C₁₃₇	—	2	2	no	—
171	C₄×C₁₃₇	#389	1	2	yes	—
172	C₄×C₁₃₇	#389	1	2	yes	—
173	C₄×C₁₃₇	C₂×#108	1	4	yes	complemented
174	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₁₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
176	C₄×C₁₃₇	C₂×#121	1	1	yes	characteristic
177	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₁₃₇	—	2	1	no	—
179	C₂×C₁₃₇	—	2	1	no	—
180	C₂×C₁₃₇	—	2	2	no	—
181	C₂×C₁₃₇	#1950	1	4	yes	direct product factor
182	C₂×C₁₃₇	C₂×#389	1	1	yes	characteristic
183	C₂×C₁₃₇	C₂²×#108	1	1	yes	characteristic
184	C₂×C₁₃₇	C₂×#430	1	1	yes	characteristic
185	C₂×#1950	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₇	C₂×#1950	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×#108	C₂×C₁₃₇	1	2	yes	—
188	C₂×#423	C₂×C₁₃₇	1	1	yes	characteristic
189	C₂²×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic
190	C₂×C₄×M₁₆	C₂×C₁₃₇	1	1	yes	characteristic
191	#1950	C₂×C₁₃₇	1	8	yes	direct product factor
192	C₂×#341	C₂×C₁₃₇	1	2	yes	—
193	C₂²×M₁₆	C₂²×C₁₃₇	1	2	yes	—
194	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₁₃₇	1	2	yes	—
197	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
198	C₂×#108	—	2	8	no	—
199	C₂×#108	C₂²×C₁₃₇	1	8	yes	—
200	#423	—	2	2	no	—
201	#423	C₂²×C₁₃₇	1	4	yes	—
202	C₂×C₄⋊C₈	—	2	1	no	—
203	C₂×C₄⋊C₈	—	2	1	no	—
204	C₂×C₄⋊C₈	C₄×C₁₃₇	1	2	yes	—
205	C₂×C₄⋊C₈	C₄×C₁₃₇	1	4	yes	—
206	C₂×C₄⋊C₈	C₄×C₁₃₇	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	4	yes	—
208	C₄×M₁₆	—	2	2	no	—
209	C₄×M₁₆	C₂²×C₁₃₇	1	4	yes	—
210	C₂×#97	—	2	1	no	—
211	C₂×C₄×C₈	—	2	1	no	—
212	#341	C₂²×C₁₃₇	1	8	yes	—
213	C₂³×C₄	Q₈×C₁₃₇	1	1	yes	characteristic
214	C₂³×C₄	Q₈×C₁₃₇	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
216	C₂×M₁₆	—	2	1	no	—
217	C₂×M₁₆	—	2	1	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	4	no	—
223	C₂×M₁₆	D₄×C₁₃₇	1	4	yes	—
224	C₂×M₁₆	Q₈×C₁₃₇	1	4	yes	—
225	C₂×M₁₆	C₂³×C₁₃₇	1	4	yes	—
226	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
227	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	4	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
234	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
235	C₂²×C₈	C₂³×C₁₃₇	1	4	yes	—
236	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
238	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₁₃₇	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
242	C₂×C₄²	Q₈×C₁₃₇	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
244	#108	—	2	16	no	—
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
248	C₄⋊C₈	C₂×C₄×C₁₃₇	1	8	yes	—
249	#97	—	2	4	no	—
250	C₄×C₈	—	2	4	no	—
251	C₂⁴	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
258	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	2	yes	—
259	C₂²×C₄	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
265	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
266	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
267	C₂²×C₄	C₂×Q₈×C₁₃₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
269	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
270	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
272	M₁₆	—	2	4	no	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	2	no	—
275	M₁₆	—	2	2	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	4	4	no	—
279	M₁₆	C₂×D₄×C₁₃₇	1	4	yes	—
280	M₁₆	C₂×Q₈×C₁₃₇	1	4	yes	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	C₂²×C₄×C₁₃₇	1	8	yes	—
292	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
293	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
294	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
295	C₄²	C₄⋊C₄×C₁₃₇	1	2	yes	—
296	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
297	C₄²	C₂²×C₄×C₁₃₇	1	2	yes	—
298	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
299	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
303	C₂³	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
304	C₂³	#125×C₁₃₇	1	2	yes	—
305	C₂³	C₄⋊Q₈×C₁₃₇	1	2	yes	—
306	C₂³	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	#108×C₁₃₇	1	4	yes	complemented
315	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
318	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	2	yes	—
321	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
322	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
323	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
324	C₂×C₄	C₄×Q₈×C₁₃₇	1	2	yes	—
325	C₂×C₄	#121×C₁₃₇	1	2	yes	—
326	C₂×C₄	#121×C₁₃₇	1	2	yes	—
327	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
328	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
329	C₂×C₄	#125×C₁₃₇	1	2	yes	—
330	C₂×C₄	C₄⋊Q₈×C₁₃₇	1	2	yes	—
331	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
334	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	2	4	no	—
339	C₈	—	2	4	no	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	#389×C₁₃₇	1	2	yes	—
348	C₂²	#389×C₁₃₇	1	2	yes	—
349	C₂²	C₂×#108×C₁₃₇	1	2	yes	—
350	C₂²	#430×C₁₃₇	1	2	yes	—
351	C₂²	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
352	C₂²	C₂×#125×C₁₃₇	1	1	yes	characteristic
353	C₂²	C₂×C₄⋊Q₈×C₁₃₇	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	#389×C₁₃₇	1	2	yes	—
358	C₄	#389×C₁₃₇	1	2	yes	—
359	C₄	C₂×#108×C₁₃₇	1	4	yes	complemented
360	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
361	C₄	C₂×C₄×Q₈×C₁₃₇	1	1	yes	characteristic
362	C₄	C₂×#121×C₁₃₇	1	1	yes	characteristic
363	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	#1950×C₁₃₇	1	4	yes	direct product factor
368	C₂	C₂×#389×C₁₃₇	1	1	yes	characteristic
369	C₂	C₂²×#108×C₁₃₇	1	1	yes	characteristic
370	C₂	C₂×#430×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
socle	C₂³×C₁₃₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃₇	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. #1950×C₁₃₇	C₂	direct (N × H)
128. C₂×C₄×C₁₃₇	#108	semidirect
173. C₄×C₁₃₇	C₂×#108	semidirect
181. C₂×C₁₃₇	#1950	direct (N × H)
185. C₂×#1950	C₁₃₇	direct (N × H)
186. C₁₃₇	C₂×#1950	direct (N × H)
191. #1950	C₂×C₁₃₇	direct (N × H)
314. C₂×C₄	#108×C₁₃₇	semidirect
359. C₄	C₂×#108×C₁₃₇	semidirect
367. C₂	#1950×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×#108×C₁₃₇	2
C₂×#423×C₁₃₇	2
C₂²×C₄⋊C₈×C₁₃₇	2
C₂×C₄×M₁₆×C₁₃₇	2
#1950×C₁₃₇	2
C₂×#341×C₁₃₇	2
C₂×#1950	137

Subgroups — C2×#1950×C137 #46870562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1950×C₁₃₇ #46870562