Subgroups — C₁₃₇×#22796 #46872182

Order 35072.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#2293×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#1954×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#1954×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#1924×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1923×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1842×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1798×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1770×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₄⋊C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
14	#433×C₁₃₇	—	2	8	no	—
15	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#97×C₁₃₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
29	#390×C₁₃₇	C₄	1	1	yes	characteristic
30	#390×C₁₃₇	C₄	1	1	yes	characteristic
31	#389×C₁₃₇	C₄	1	1	yes	characteristic
32	#389×C₁₃₇	C₄	1	1	yes	characteristic
33	#388×C₁₃₇	C₄	1	2	yes	—
34	#388×C₁₃₇	C₄	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
37	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
38	#336×C₁₃₇	C₂²	1	1	yes	characteristic
39	#336×C₁₃₇	C₂²	1	1	yes	characteristic
40	#336×C₁₃₇	C₂²	1	2	yes	—
41	#336×C₁₃₇	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₃₇	—	2	2	no	—
51	C₄×D₄×C₁₃₇	—	2	2	no	—
52	#117×C₁₃₇	—	2	4	no	—
53	#117×C₁₃₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₃₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₃₇	—	2	4	no	—
73	C₄⋊C₈×C₁₃₇	—	2	2	no	—
74	C₄⋊C₈×C₁₃₇	—	2	2	no	—
75	C₄⋊C₈×C₁₃₇	—	2	2	no	—
76	C₄⋊C₈×C₁₃₇	—	4	2	no	—
77	C₄⋊C₈×C₁₃₇	D₄	1	4	yes	complemented
78	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
79	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
80	C₂²⋊C₈×C₁₃₇	—	4	2	no	—
81	C₂²⋊C₈×C₁₃₇	—	4	2	no	—
82	#97×C₁₃₇	—	2	4	no	—
83	C₄×C₈×C₁₃₇	—	2	4	no	—
84	C₄×C₈×C₁₃₇	—	2	2	no	—
85	C₄×C₈×C₁₃₇	—	2	2	no	—
86	#95×C₁₃₇	C₂×C₄	1	2	yes	—
87	#95×C₁₃₇	C₂×C₄	1	2	yes	—
88	#95×C₁₃₇	C₂×C₄	1	2	yes	—
89	C₂⁴×C₁₃₇	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂²×C₄×C₁₃₇	—	2	2	no	—
94	C₂²×C₄×C₁₃₇	—	2	2	no	—
95	C₂²×C₄×C₁₃₇	—	2	2	no	—
96	C₂²×C₄×C₁₃₇	—	2	2	no	—
97	C₂²×C₄×C₁₃₇	—	2	2	no	—
98	C₂²×C₄×C₁₃₇	—	2	2	no	—
99	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃₇	—	2	1	no	—
110	C₂×C₈×C₁₃₇	—	2	1	no	—
111	C₂×C₈×C₁₃₇	—	2	1	no	—
112	C₂×C₈×C₁₃₇	—	2	1	no	—
113	C₂×C₈×C₁₃₇	—	2	2	no	—
114	C₂×C₈×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	—	2	1	no	—
116	C₂×C₈×C₁₃₇	—	2	1	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	1	no	—
120	C₂×C₈×C₁₃₇	—	2	1	no	—
121	C₂×C₈×C₁₃₇	—	2	1	no	—
122	C₂×C₈×C₁₃₇	—	2	1	no	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₁₃₇	—	2	2	no	—
128	C₄⋊C₄×C₁₃₇	—	2	4	no	—
129	C₄⋊C₄×C₁₃₇	—	2	4	no	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
133	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
134	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
135	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
137	C₄²×C₁₃₇	—	2	2	no	—
138	C₄²×C₁₃₇	—	2	2	no	—
139	C₄²×C₁₃₇	—	2	2	no	—
140	C₄²×C₁₃₇	—	2	2	no	—
141	C₄²×C₁₃₇	—	2	2	no	—
142	C₄²×C₁₃₇	—	2	1	no	—
143	C₄²×C₁₃₇	—	2	1	no	—
144	C₄²×C₁₃₇	—	4	1	no	—
145	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃₇	#41	1	2	yes	—
147	C₄²×C₁₃₇	#41	1	2	yes	—
148	C₄²×C₁₃₇	#41	1	2	yes	—
149	C₂³×C₁₃₇	—	2	2	no	—
150	C₂³×C₁₃₇	—	2	2	no	—
151	C₂³×C₁₃₇	—	2	2	no	—
152	C₂³×C₁₃₇	—	2	2	no	—
153	C₂³×C₁₃₇	—	2	2	no	—
154	C₂³×C₁₃₇	—	2	2	no	—
155	C₂³×C₁₃₇	—	2	2	no	—
156	C₂³×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
157	D₄×C₁₃₇	—	4	4	no	—
158	C₂×C₄×C₁₃₇	—	2	1	no	—
159	C₂×C₄×C₁₃₇	—	2	1	no	—
160	C₂×C₄×C₁₃₇	—	2	1	no	—
161	C₂×C₄×C₁₃₇	—	2	1	no	—
162	C₂×C₄×C₁₃₇	—	2	1	no	—
163	C₂×C₄×C₁₃₇	—	2	1	no	—
164	C₂×C₄×C₁₃₇	—	2	1	no	—
165	C₂×C₄×C₁₃₇	—	2	1	no	—
166	C₂×C₄×C₁₃₇	—	2	2	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	2	1	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	1	no	—
173	C₂×C₄×C₁₃₇	—	2	2	no	—
174	C₂×C₄×C₁₃₇	—	2	2	no	—
175	C₂×C₄×C₁₃₇	—	2	2	no	—
176	C₂×C₄×C₁₃₇	—	2	1	no	—
177	C₂×C₄×C₁₃₇	—	2	2	no	—
178	C₂×C₄×C₁₃₇	—	4	2	no	—
179	C₂×C₄×C₁₃₇	—	4	2	no	—
180	C₂×C₄×C₁₃₇	—	4	2	no	—
181	C₂×C₄×C₁₃₇	—	4	2	no	—
182	C₂×C₄×C₁₃₇	#117	1	2	yes	—
183	C₂×C₄×C₁₃₇	#117	1	2	yes	—
184	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃₇	#131	1	2	yes	—
187	C₂×C₄×C₁₃₇	#131	1	2	yes	—
188	C₂×C₄×C₁₃₇	#131	1	2	yes	—
189	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₁₃₇	—	2	2	no	—
196	C₈×C₁₃₇	—	2	2	no	—
197	C₈×C₁₃₇	—	4	2	no	—
198	C₈×C₁₃₇	—	4	2	no	—
199	C₈×C₁₃₇	—	4	1	no	—
200	C₈×C₁₃₇	—	4	1	no	—
201	C₂²×C₁₃₇	—	4	2	no	—
202	C₂²×C₁₃₇	—	4	2	no	—
203	C₂²×C₁₃₇	—	4	2	no	—
204	C₂²×C₁₃₇	—	4	2	no	—
205	C₂²×C₁₃₇	—	4	2	no	—
206	C₂²×C₁₃₇	—	4	2	no	—
207	C₂²×C₁₃₇	—	4	2	no	—
208	C₂²×C₁₃₇	C₂×#117	1	1	yes	characteristic
209	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₁₃₇	#520	1	1	yes	characteristic
211	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
212	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
213	C₂²×C₁₃₇	C₂×#131	1	1	yes	characteristic
214	C₂²×C₁₃₇	#568	1	1	yes	characteristic
215	C₄×C₁₃₇	—	2	2	no	—
216	C₄×C₁₃₇	—	2	2	no	—
217	C₄×C₁₃₇	—	2	2	no	—
218	C₄×C₁₃₇	—	2	2	no	—
219	C₄×C₁₃₇	—	4	2	no	—
220	C₄×C₁₃₇	—	4	2	no	—
221	C₄×C₁₃₇	—	4	2	no	—
222	C₄×C₁₃₇	—	4	1	no	—
223	C₄×C₁₃₇	#433	1	4	yes	complemented
224	C₄×C₁₃₇	#547	1	1	yes	characteristic
225	C₄×C₁₃₇	#550	1	1	yes	characteristic
226	C₄×C₁₃₇	#555	1	1	yes	characteristic
227	C₄×C₁₃₇	#556	1	1	yes	characteristic
228	C₂×C₁₃₇	—	8	2	no	—
229	C₂×C₁₃₇	#2354	1	1	yes	characteristic
230	C₂×C₁₃₇	C₂×#433	1	1	yes	characteristic
231	C₂×C₁₃₇	#2925	1	1	yes	characteristic
232	C₂×C₁₃₇	#2931	1	1	yes	characteristic
233	C₂×C₁₃₇	#2935	1	1	yes	characteristic
234	C₂×C₁₃₇	#2993	1	1	yes	characteristic
235	C₂×C₁₃₇	#2994	1	1	yes	characteristic
236	#22796	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₇	#22796	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#433	C₂×C₁₃₇	1	2	yes	complemented
239	#2293	C₂×C₁₃₇	1	1	yes	characteristic
240	#1954	C₂×C₁₃₇	1	1	yes	characteristic
241	#1954	C₂×C₁₃₇	1	1	yes	characteristic
242	#1924	C₂×C₁₃₇	1	2	yes	complemented
243	#1923	C₂×C₁₃₇	1	2	yes	complemented
244	#1842	C₂×C₁₃₇	1	1	yes	characteristic, complemented
245	#1798	C₂×C₁₃₇	1	2	yes	complemented
246	#1770	C₂×C₁₃₇	1	1	yes	characteristic, complemented
247	C₈×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
248	C₄×C₄⋊C₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
249	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
251	#433	—	2	8	no	—
252	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₁₃₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₁₃₇	1	2	yes	—
262	C₂×#97	C₂²×C₁₃₇	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
266	#390	C₄×C₁₃₇	1	1	yes	characteristic
267	#390	C₄×C₁₃₇	1	1	yes	characteristic
268	#389	C₄×C₁₃₇	1	1	yes	characteristic
269	#389	C₄×C₁₃₇	1	1	yes	characteristic
270	#388	C₄×C₁₃₇	1	2	yes	—
271	#388	C₄×C₁₃₇	1	2	yes	—
272	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
274	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
275	#336	C₂²×C₁₃₇	1	2	yes	—
276	#336	C₂²×C₁₃₇	1	2	yes	—
277	#336	C₂²×C₁₃₇	1	1	yes	characteristic
278	#336	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂²×D₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₇	1	2	yes	—
301	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
304	C₂×C₄²	C₂×C₄×C₁₃₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
309	C₄⋊C₈	—	2	4	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	4	2	no	—
314	C₄⋊C₈	D₄×C₁₃₇	1	4	yes	complemented
315	C₂²⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	—	4	2	no	—
318	C₂²⋊C₈	—	4	2	no	—
319	#97	—	2	4	no	—
320	C₄×C₈	—	2	4	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	#95	C₂×C₄×C₁₃₇	1	2	yes	—
324	#95	C₂×C₄×C₁₃₇	1	2	yes	—
325	#95	C₂×C₄×C₁₃₇	1	2	yes	—
326	C₂⁴	C₂²×C₄×C₁₃₇	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
383	C₄²	#41×C₁₃₇	1	2	yes	—
384	C₄²	#41×C₁₃₇	1	2	yes	—
385	C₄²	#41×C₁₃₇	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
394	D₄	—	4	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	#117×C₁₃₇	1	2	yes	—
420	C₂×C₄	#117×C₁₃₇	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
422	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
423	C₂×C₄	#131×C₁₃₇	1	2	yes	—
424	C₂×C₄	#131×C₁₃₇	1	2	yes	—
425	C₂×C₄	#131×C₁₃₇	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
431	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×#117×C₁₃₇	1	1	yes	characteristic
446	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
447	C₂²	#520×C₁₃₇	1	1	yes	characteristic
448	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
449	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
450	C₂²	C₂×#131×C₁₃₇	1	1	yes	characteristic
451	C₂²	#568×C₁₃₇	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	#433×C₁₃₇	1	4	yes	complemented
461	C₄	#547×C₁₃₇	1	1	yes	characteristic
462	C₄	#550×C₁₃₇	1	1	yes	characteristic
463	C₄	#555×C₁₃₇	1	1	yes	characteristic
464	C₄	#556×C₁₃₇	1	1	yes	characteristic
465	C₂	—	8	2	no	—
466	C₂	#2354×C₁₃₇	1	1	yes	characteristic
467	C₂	C₂×#433×C₁₃₇	1	1	yes	characteristic
468	C₂	#2925×C₁₃₇	1	1	yes	characteristic
469	C₂	#2931×C₁₃₇	1	1	yes	characteristic
470	C₂	#2935×C₁₃₇	1	1	yes	characteristic
471	C₂	#2993×C₁₃₇	1	1	yes	characteristic
472	C₂	#2994×C₁₃₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#433×C₁₃₇	C₂	semidirect
5. #1924×C₁₃₇	C₂	semidirect
6. #1923×C₁₃₇	C₂	semidirect
7. #1842×C₁₃₇	C₂	semidirect
8. #1798×C₁₃₇	C₂	semidirect
9. #1770×C₁₃₇	C₂	semidirect
10. C₈×C₄⋊C₄×C₁₃₇	C₂	semidirect
11. C₄×C₄⋊C₈×C₁₃₇	C₂	semidirect
77. C₄⋊C₈×C₁₃₇	D₄	semidirect
223. C₄×C₁₃₇	#433	semidirect
236. #22796	C₁₃₇	direct (N × H)
237. C₁₃₇	#22796	direct (N × H)
238. C₂×#433	C₂×C₁₃₇	semidirect
242. #1924	C₂×C₁₃₇	semidirect
243. #1923	C₂×C₁₃₇	semidirect
244. #1842	C₂×C₁₃₇	semidirect
245. #1798	C₂×C₁₃₇	semidirect
246. #1770	C₂×C₁₃₇	semidirect
247. C₈×C₄⋊C₄	C₂×C₁₃₇	semidirect
248. C₄×C₄⋊C₈	C₂×C₁₃₇	semidirect
314. C₄⋊C₈	D₄×C₁₃₇	semidirect
460. C₄	#433×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₁₃₇	2
#2293×C₁₃₇	2
#1954×C₁₃₇	2
#1924×C₁₃₇	2
#1923×C₁₃₇	2
#1842×C₁₃₇	2
#1798×C₁₃₇	2
#1770×C₁₃₇	2
C₈×C₄⋊C₄×C₁₃₇	2
C₄×C₄⋊C₈×C₁₃₇	2
#22796	137

Subgroups — C137×#22796 #46872182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#22796 #46872182