Subgroups — C₂×#2598×C₁₃₇ #46884243

Order 35072.

3502 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2598×C₁₃₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#399×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#394×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#392×C₁₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#388×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₂×#386×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₂×#386×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	C₂×#385×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂×#383×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃₇	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃₇	—	2	8	no	—
18	C₂×C₄×D₄×C₁₃₇	C₂²	1	8	yes	complemented
19	C₂×#117×C₁₃₇	—	2	8	no	—
20	C₂×#117×C₁₃₇	C₂²	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
34	#400×C₁₃₇	C₂²	1	8	yes	complemented
35	#399×C₁₃₇	C₂²	1	8	yes	complemented
36	#394×C₁₃₇	C₂²	1	8	yes	complemented
37	#392×C₁₃₇	C₂²	1	8	yes	—
38	#388×C₁₃₇	C₂²	1	16	yes	complemented
39	#386×C₁₃₇	C₂²	1	16	yes	complemented
40	#386×C₁₃₇	C₂²	1	16	yes	complemented
41	#385×C₁₃₇	C₂²	1	16	yes	complemented
42	#383×C₁₃₇	C₂²	1	8	yes	complemented
43	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
44	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
45	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
46	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
47	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
48	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
49	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
50	C₂⁵×C₁₃₇	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃₇	—	2	8	no	—
52	C₂²×D₄×C₁₃₇	—	2	8	no	—
53	C₂²×D₄×C₁₃₇	—	2	8	no	—
54	C₂²×D₄×C₁₃₇	—	2	4	no	—
55	C₂²×D₄×C₁₃₇	—	4	4	no	—
56	C₂²×D₄×C₁₃₇	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₇	C₂³	1	8	yes	—
58	C₂³×C₄×C₁₃₇	—	2	4	no	—
59	C₂³×C₄×C₁₃₇	—	2	4	no	—
60	C₂³×C₄×C₁₃₇	—	2	4	no	—
61	C₂³×C₄×C₁₃₇	—	2	8	no	—
62	C₂³×C₄×C₁₃₇	—	4	4	no	—
63	C₂³×C₄×C₁₃₇	—	4	4	no	—
64	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₇	C₂³	1	8	yes	—
75	C₄×D₄×C₁₃₇	—	2	32	no	—
76	#117×C₁₃₇	—	2	32	no	—
77	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
81	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
89	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
90	C₂×C₂²⋊C₄×C₁₃₇	—	4	4	no	—
91	C₂×C₂²⋊C₄×C₁₃₇	—	4	4	no	—
92	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	8	yes	—
99	C₂×C₄²×C₁₃₇	—	2	4	no	—
100	C₂×C₄²×C₁₃₇	D₄	1	8	yes	complemented
101	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
103	#95×C₁₃₇	C₂³	1	8	yes	—
104	#95×C₁₃₇	C₂³	1	8	yes	—
105	#95×C₁₃₇	C₂³	1	4	yes	—
106	#95×C₁₃₇	C₂³	1	4	yes	—
107	#95×C₁₃₇	C₂³	1	8	yes	—
108	#95×C₁₃₇	C₂³	1	8	yes	—
109	C₂⁴×C₁₃₇	—	2	2	no	—
110	C₂⁴×C₁₃₇	—	2	4	no	—
111	C₂⁴×C₁₃₇	—	2	4	no	—
112	C₂⁴×C₁₃₇	—	2	2	no	—
113	C₂⁴×C₁₃₇	—	2	4	no	—
114	C₂⁴×C₁₃₇	—	2	4	no	—
115	C₂⁴×C₁₃₇	—	2	4	no	—
116	C₂⁴×C₁₃₇	—	2	4	no	—
117	C₂⁴×C₁₃₇	—	2	4	no	—
118	C₂⁴×C₁₃₇	—	2	4	no	—
119	C₂⁴×C₁₃₇	#41	1	8	yes	—
120	C₂⁴×C₁₃₇	#41	1	4	yes	—
121	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
122	C₂⁴×C₁₃₇	C₂⁴	1	4	yes	—
123	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
124	C₂×D₄×C₁₃₇	—	2	32	no	—
125	C₂×D₄×C₁₃₇	—	2	16	no	—
126	C₂×D₄×C₁₃₇	—	2	16	no	—
127	C₂×D₄×C₁₃₇	—	2	16	no	—
128	C₂×D₄×C₁₃₇	—	2	8	no	—
129	C₂×D₄×C₁₃₇	—	4	8	no	—
130	C₂×D₄×C₁₃₇	—	4	32	no	—
131	C₂²×C₄×C₁₃₇	—	2	32	no	—
132	C₂²×C₄×C₁₃₇	—	2	2	no	—
133	C₂²×C₄×C₁₃₇	—	2	8	no	—
134	C₂²×C₄×C₁₃₇	—	2	2	no	—
135	C₂²×C₄×C₁₃₇	—	2	2	no	—
136	C₂²×C₄×C₁₃₇	—	2	2	no	—
137	C₂²×C₄×C₁₃₇	—	2	4	no	—
138	C₂²×C₄×C₁₃₇	—	2	4	no	—
139	C₂²×C₄×C₁₃₇	—	2	8	no	—
140	C₂²×C₄×C₁₃₇	—	2	8	no	—
141	C₂²×C₄×C₁₃₇	—	2	2	no	—
142	C₂²×C₄×C₁₃₇	—	2	2	no	—
143	C₂²×C₄×C₁₃₇	—	2	4	no	—
144	C₂²×C₄×C₁₃₇	—	2	4	no	—
145	C₂²×C₄×C₁₃₇	—	2	4	no	—
146	C₂²×C₄×C₁₃₇	—	2	4	no	—
147	C₂²×C₄×C₁₃₇	—	2	4	no	—
148	C₂²×C₄×C₁₃₇	—	2	4	no	—
149	C₂²×C₄×C₁₃₇	—	2	4	no	—
150	C₂²×C₄×C₁₃₇	—	2	4	no	—
151	C₂²×C₄×C₁₃₇	—	2	4	no	—
152	C₂²×C₄×C₁₃₇	—	2	4	no	—
153	C₂²×C₄×C₁₃₇	—	2	4	no	—
154	C₂²×C₄×C₁₃₇	—	2	16	no	—
155	C₂²×C₄×C₁₃₇	—	4	8	no	—
156	C₂²×C₄×C₁₃₇	—	4	8	no	—
157	C₂²×C₄×C₁₃₇	—	4	32	no	—
158	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
162	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
171	C₄⋊C₄×C₁₃₇	—	2	8	no	—
172	C₄⋊C₄×C₁₃₇	—	2	8	no	—
173	C₄⋊C₄×C₁₃₇	—	2	8	no	—
174	C₄⋊C₄×C₁₃₇	—	4	8	no	—
175	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
176	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
177	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
178	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
179	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
180	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
181	C₂²⋊C₄×C₁₃₇	—	4	8	no	—
182	C₄²×C₁₃₇	—	2	8	no	—
183	C₄²×C₁₃₇	C₂×D₄	1	16	yes	complemented
184	C₂³×C₁₃₇	—	2	8	no	—
185	C₂³×C₁₃₇	—	2	16	no	—
186	C₂³×C₁₃₇	—	2	16	no	—
187	C₂³×C₁₃₇	—	2	16	no	—
188	C₂³×C₁₃₇	—	2	16	no	—
189	C₂³×C₁₃₇	—	2	2	no	—
190	C₂³×C₁₃₇	—	2	4	no	—
191	C₂³×C₁₃₇	—	2	4	no	—
192	C₂³×C₁₃₇	—	2	2	no	—
193	C₂³×C₁₃₇	—	2	4	no	—
194	C₂³×C₁₃₇	—	2	4	no	—
195	C₂³×C₁₃₇	—	2	4	no	—
196	C₂³×C₁₃₇	—	2	4	no	—
197	C₂³×C₁₃₇	—	2	4	no	—
198	C₂³×C₁₃₇	—	2	4	no	—
199	C₂³×C₁₃₇	—	4	8	no	—
200	C₂³×C₁₃₇	—	4	4	no	—
201	C₂³×C₁₃₇	—	4	8	no	—
202	C₂³×C₁₃₇	—	4	4	no	—
203	C₂³×C₁₃₇	—	4	8	no	—
204	C₂³×C₁₃₇	—	4	8	no	—
205	C₂³×C₁₃₇	—	4	8	no	—
206	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₃₇	C₂×#41	1	8	yes	—
208	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
209	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
210	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
211	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
212	C₂³×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
213	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
214	D₄×C₁₃₇	—	2	32	no	—
215	D₄×C₁₃₇	—	4	32	no	—
216	C₂×C₄×C₁₃₇	—	2	32	no	—
217	C₂×C₄×C₁₃₇	—	2	8	no	—
218	C₂×C₄×C₁₃₇	—	2	8	no	—
219	C₂×C₄×C₁₃₇	—	2	8	no	—
220	C₂×C₄×C₁₃₇	—	2	8	no	—
221	C₂×C₄×C₁₃₇	—	2	2	no	—
222	C₂×C₄×C₁₃₇	—	2	2	no	—
223	C₂×C₄×C₁₃₇	—	2	2	no	—
224	C₂×C₄×C₁₃₇	—	2	2	no	—
225	C₂×C₄×C₁₃₇	—	2	4	no	—
226	C₂×C₄×C₁₃₇	—	2	4	no	—
227	C₂×C₄×C₁₃₇	—	2	2	no	—
228	C₂×C₄×C₁₃₇	—	2	2	no	—
229	C₂×C₄×C₁₃₇	—	2	4	no	—
230	C₂×C₄×C₁₃₇	—	2	4	no	—
231	C₂×C₄×C₁₃₇	—	2	4	no	—
232	C₂×C₄×C₁₃₇	—	2	4	no	—
233	C₂×C₄×C₁₃₇	—	2	4	no	—
234	C₂×C₄×C₁₃₇	—	2	4	no	—
235	C₂×C₄×C₁₃₇	—	2	4	no	—
236	C₂×C₄×C₁₃₇	—	2	4	no	—
237	C₂×C₄×C₁₃₇	—	2	4	no	—
238	C₂×C₄×C₁₃₇	—	2	4	no	—
239	C₂×C₄×C₁₃₇	—	2	4	no	—
240	C₂×C₄×C₁₃₇	—	4	32	no	—
241	C₂×C₄×C₁₃₇	—	4	4	no	—
242	C₂×C₄×C₁₃₇	—	4	4	no	—
243	C₂×C₄×C₁₃₇	—	4	8	no	—
244	C₂×C₄×C₁₃₇	—	4	8	no	—
245	C₂×C₄×C₁₃₇	—	4	8	no	—
246	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
250	C₂²×C₁₃₇	—	2	4	no	—
251	C₂²×C₁₃₇	—	2	8	no	—
252	C₂²×C₁₃₇	—	2	8	no	—
253	C₂²×C₁₃₇	—	2	8	no	—
254	C₂²×C₁₃₇	—	2	8	no	—
255	C₂²×C₁₃₇	—	4	16	no	—
256	C₂²×C₁₃₇	—	4	32	no	—
257	C₂²×C₁₃₇	—	4	4	no	—
258	C₂²×C₁₃₇	—	4	2	no	—
259	C₂²×C₁₃₇	—	4	4	no	—
260	C₂²×C₁₃₇	—	4	2	no	—
261	C₂²×C₁₃₇	—	4	4	no	—
262	C₂²×C₁₃₇	—	4	4	no	—
263	C₂²×C₁₃₇	—	4	4	no	—
264	C₂²×C₁₃₇	#525	1	4	yes	—
265	C₂²×C₁₃₇	#525	1	4	yes	—
266	C₂²×C₁₃₇	#535	1	4	yes	—
267	C₂²×C₁₃₇	#551	1	8	yes	—
268	C₂²×C₁₃₇	#553	1	8	yes	—
269	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
271	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
272	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
273	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
274	C₄×C₁₃₇	—	2	4	no	—
275	C₄×C₁₃₇	—	2	4	no	—
276	C₄×C₁₃₇	—	2	4	no	—
277	C₄×C₁₃₇	—	2	4	no	—
278	C₄×C₁₃₇	—	4	2	no	—
279	C₄×C₁₃₇	—	4	2	no	—
280	C₄×C₁₃₇	—	4	4	no	—
281	C₄×C₁₃₇	—	4	4	no	—
282	C₄×C₁₃₇	—	4	4	no	—
283	C₂×C₁₃₇	—	4	4	no	—
284	C₂×C₁₃₇	—	4	8	no	—
285	C₂×C₁₃₇	#2598	1	8	yes	direct product factor
286	C₂×C₁₃₇	C₂×#525	1	1	yes	characteristic
287	C₂×C₁₃₇	C₂×#525	1	1	yes	characteristic
288	C₂×C₁₃₇	C₂×#535	1	1	yes	characteristic
289	C₂×C₁₃₇	C₂×#551	1	2	yes	—
290	C₂×C₁₃₇	C₂×#553	1	2	yes	—
291	C₂×#2598	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₁₃₇	C₂×#2598	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×C₄×D₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
294	C₂²×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
295	#2598	C₂×C₁₃₇	1	16	yes	direct product factor
296	C₂×#400	C₂×C₁₃₇	1	1	yes	characteristic, complemented
297	C₂×#399	C₂×C₁₃₇	1	1	yes	characteristic, complemented
298	C₂×#394	C₂×C₁₃₇	1	1	yes	characteristic, complemented
299	C₂×#392	C₂×C₁₃₇	1	1	yes	characteristic
300	C₂×#388	C₂×C₁₃₇	1	2	yes	complemented
301	C₂×#386	C₂×C₁₃₇	1	2	yes	complemented
302	C₂×#386	C₂×C₁₃₇	1	2	yes	complemented
303	C₂×#385	C₂×C₁₃₇	1	2	yes	complemented
304	C₂×#383	C₂×C₁₃₇	1	1	yes	characteristic, complemented
305	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
306	C₂³×D₄	C₂²×C₁₃₇	1	2	yes	—
307	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
308	C₂⁴×C₄	C₂²×C₁₃₇	1	2	yes	—
309	C₂×C₄×D₄	—	2	8	no	—
310	C₂×C₄×D₄	C₂²×C₁₃₇	1	8	yes	complemented
311	C₂×#117	—	2	8	no	—
312	C₂×#117	C₂²×C₁₃₇	1	8	yes	complemented
313	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
314	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
315	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
317	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
323	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
324	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
326	#400	C₂²×C₁₃₇	1	8	yes	complemented
327	#399	C₂²×C₁₃₇	1	8	yes	complemented
328	#394	C₂²×C₁₃₇	1	8	yes	complemented
329	#392	C₂²×C₁₃₇	1	8	yes	—
330	#388	C₂²×C₁₃₇	1	16	yes	complemented
331	#386	C₂²×C₁₃₇	1	16	yes	complemented
332	#386	C₂²×C₁₃₇	1	16	yes	complemented
333	#385	C₂²×C₁₃₇	1	16	yes	complemented
334	#383	C₂²×C₁₃₇	1	8	yes	complemented
335	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
336	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
337	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
338	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
339	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
340	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
341	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
342	C₂⁵	C₂³×C₁₃₇	1	2	yes	—
343	C₂²×D₄	—	2	8	no	—
344	C₂²×D₄	—	2	8	no	—
345	C₂²×D₄	—	2	8	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	4	4	no	—
348	C₂²×D₄	C₂³×C₁₃₇	1	4	yes	—
349	C₂²×D₄	C₂³×C₁₃₇	1	8	yes	—
350	C₂³×C₄	—	2	4	no	—
351	C₂³×C₄	—	2	4	no	—
352	C₂³×C₄	—	2	4	no	—
353	C₂³×C₄	—	2	8	no	—
354	C₂³×C₄	—	4	4	no	—
355	C₂³×C₄	—	4	4	no	—
356	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
360	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
362	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₁₃₇	1	8	yes	—
367	C₄×D₄	—	2	32	no	—
368	#117	—	2	32	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	4	no	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	4	4	no	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	8	yes	—
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	—	2	8	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	4	4	no	—
383	C₂×C₂²⋊C₄	—	4	4	no	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	8	yes	—
391	C₂×C₄²	—	2	4	no	—
392	C₂×C₄²	D₄×C₁₃₇	1	8	yes	complemented
393	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
394	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
395	#95	C₂³×C₁₃₇	1	8	yes	—
396	#95	C₂³×C₁₃₇	1	8	yes	—
397	#95	C₂³×C₁₃₇	1	4	yes	—
398	#95	C₂³×C₁₃₇	1	4	yes	—
399	#95	C₂³×C₁₃₇	1	8	yes	—
400	#95	C₂³×C₁₃₇	1	8	yes	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	#41×C₁₃₇	1	8	yes	—
412	C₂⁴	#41×C₁₃₇	1	4	yes	—
413	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
414	C₂⁴	C₂⁴×C₁₃₇	1	4	yes	—
415	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
416	C₂×D₄	—	2	32	no	—
417	C₂×D₄	—	2	16	no	—
418	C₂×D₄	—	2	16	no	—
419	C₂×D₄	—	2	16	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	4	32	no	—
423	C₂²×C₄	—	2	32	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	4	8	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	4	32	no	—
450	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
453	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	4	8	no	—
467	C₂²⋊C₄	—	2	16	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	16	no	—
471	C₂²⋊C₄	—	2	16	no	—
472	C₂²⋊C₄	—	4	8	no	—
473	C₂²⋊C₄	—	4	8	no	—
474	C₄²	—	2	8	no	—
475	C₄²	C₂×D₄×C₁₃₇	1	16	yes	complemented
476	C₂³	—	2	8	no	—
477	C₂³	—	2	16	no	—
478	C₂³	—	2	16	no	—
479	C₂³	—	2	16	no	—
480	C₂³	—	2	16	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	4	8	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	8	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	8	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	8	no	—
498	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
499	C₂³	C₂×#41×C₁₃₇	1	8	yes	—
500	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
501	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
502	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
503	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
504	C₂³	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
505	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
506	D₄	—	2	32	no	—
507	D₄	—	4	32	no	—
508	C₂×C₄	—	2	32	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	32	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
541	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	2	8	no	—
547	C₂²	—	4	16	no	—
548	C₂²	—	4	32	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	#525×C₁₃₇	1	4	yes	—
557	C₂²	#525×C₁₃₇	1	4	yes	—
558	C₂²	#535×C₁₃₇	1	4	yes	—
559	C₂²	#551×C₁₃₇	1	8	yes	—
560	C₂²	#553×C₁₃₇	1	8	yes	—
561	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
562	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
563	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
564	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
565	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
566	C₄	—	2	4	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₂	—	4	4	no	—
576	C₂	—	4	8	no	—
577	C₂	#2598×C₁₃₇	1	8	yes	direct product factor
578	C₂	C₂×#525×C₁₃₇	1	1	yes	characteristic
579	C₂	C₂×#525×C₁₃₇	1	1	yes	characteristic
580	C₂	C₂×#535×C₁₃₇	1	1	yes	characteristic
581	C₂	C₂×#551×C₁₃₇	1	2	yes	—
582	C₂	C₂×#553×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂×#392×C₁₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₁₃₇	C₂	semidirect
2. C₂²×#117×C₁₃₇	C₂	semidirect
3. #2598×C₁₃₇	C₂	direct (N × H)
4. C₂×#400×C₁₃₇	C₂	semidirect
5. C₂×#399×C₁₃₇	C₂	semidirect
6. C₂×#394×C₁₃₇	C₂	semidirect
8. C₂×#388×C₁₃₇	C₂	semidirect
9. C₂×#386×C₁₃₇	C₂	semidirect
10. C₂×#386×C₁₃₇	C₂	semidirect
11. C₂×#385×C₁₃₇	C₂	semidirect
12. C₂×#383×C₁₃₇	C₂	semidirect
18. C₂×C₄×D₄×C₁₃₇	C₂²	semidirect
20. C₂×#117×C₁₃₇	C₂²	semidirect
34. #400×C₁₃₇	C₂²	semidirect
35. #399×C₁₃₇	C₂²	semidirect
36. #394×C₁₃₇	C₂²	semidirect
38. #388×C₁₃₇	C₂²	semidirect
39. #386×C₁₃₇	C₂²	semidirect
40. #386×C₁₃₇	C₂²	semidirect
41. #385×C₁₃₇	C₂²	semidirect
42. #383×C₁₃₇	C₂²	semidirect
100. C₂×C₄²×C₁₃₇	D₄	semidirect
183. C₄²×C₁₃₇	C₂×D₄	semidirect
285. C₂×C₁₃₇	#2598	direct (N × H)
291. C₂×#2598	C₁₃₇	direct (N × H)
292. C₁₃₇	C₂×#2598	direct (N × H)
293. C₂²×C₄×D₄	C₂×C₁₃₇	semidirect
294. C₂²×#117	C₂×C₁₃₇	semidirect
295. #2598	C₂×C₁₃₇	direct (N × H)
296. C₂×#400	C₂×C₁₃₇	semidirect
297. C₂×#399	C₂×C₁₃₇	semidirect
298. C₂×#394	C₂×C₁₃₇	semidirect
300. C₂×#388	C₂×C₁₃₇	semidirect
301. C₂×#386	C₂×C₁₃₇	semidirect
302. C₂×#386	C₂×C₁₃₇	semidirect
303. C₂×#385	C₂×C₁₃₇	semidirect
304. C₂×#383	C₂×C₁₃₇	semidirect
310. C₂×C₄×D₄	C₂²×C₁₃₇	semidirect
312. C₂×#117	C₂²×C₁₃₇	semidirect
326. #400	C₂²×C₁₃₇	semidirect
327. #399	C₂²×C₁₃₇	semidirect
328. #394	C₂²×C₁₃₇	semidirect
330. #388	C₂²×C₁₃₇	semidirect
331. #386	C₂²×C₁₃₇	semidirect
332. #386	C₂²×C₁₃₇	semidirect
333. #385	C₂²×C₁₃₇	semidirect
334. #383	C₂²×C₁₃₇	semidirect
392. C₂×C₄²	D₄×C₁₃₇	semidirect
475. C₄²	C₂×D₄×C₁₃₇	semidirect
577. C₂	#2598×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×C₄×D₄×C₁₃₇	2
C₂²×#117×C₁₃₇	2
#2598×C₁₃₇	2
C₂×#400×C₁₃₇	2
C₂×#399×C₁₃₇	2
C₂×#394×C₁₃₇	2
C₂×#392×C₁₃₇	2
C₂×#388×C₁₃₇	2
C₂×#386×C₁₃₇	2
C₂×#385×C₁₃₇	2
C₂×#383×C₁₃₇	2
C₂×#2598	137

Subgroups — C2×#2598×C137 #46884243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2598×C₁₃₇ #46884243