Subgroups — C₁₃₇×#34436 #46883822

Order 35072.

2522 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#2378×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2377×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2368×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2364×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2364×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2361×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2339×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2339×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2333×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#2332×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#2329×C₁₃₇	C₂	1	2	yes	maximal, complemented
13	#2325×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#2325×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#2325×C₁₃₇	C₂	1	2	yes	maximal, complemented
16	#2313×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#121×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#387×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₇	C₂²	1	2	yes	—
21	#537×C₁₃₇	C₄	1	16	yes	complemented
22	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×#121×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
39	#391×C₁₃₇	C₂²	1	2	yes	—
40	#391×C₁₃₇	C₂²	1	2	yes	—
41	#391×C₁₃₇	C₂²	1	2	yes	—
42	#391×C₁₃₇	C₂²	1	2	yes	—
43	#390×C₁₃₇	C₂²	1	1	yes	characteristic
44	#390×C₁₃₇	C₂²	1	1	yes	characteristic
45	#390×C₁₃₇	C₂²	1	2	yes	—
46	#389×C₁₃₇	C₂²	1	1	yes	characteristic
47	#389×C₁₃₇	C₂²	1	1	yes	characteristic
48	#389×C₁₃₇	C₂²	1	2	yes	—
49	#388×C₁₃₇	C₂²	1	2	yes	—
50	#388×C₁₃₇	C₂²	1	2	yes	—
51	#388×C₁₃₇	C₂²	1	2	yes	—
52	#388×C₁₃₇	C₂²	1	2	yes	—
53	#388×C₁₃₇	C₂²	1	2	yes	—
54	#388×C₁₃₇	C₂²	1	2	yes	—
55	#388×C₁₃₇	C₂²	1	2	yes	—
56	#388×C₁₃₇	C₂²	1	2	yes	—
57	#387×C₁₃₇	C₂²	1	2	yes	—
58	#387×C₁₃₇	C₂²	1	2	yes	—
59	#387×C₁₃₇	C₂²	1	2	yes	—
60	#387×C₁₃₇	C₂²	1	2	yes	—
61	#387×C₁₃₇	C₂²	1	2	yes	—
62	#387×C₁₃₇	C₂²	1	2	yes	—
63	#387×C₁₃₇	C₂²	1	2	yes	—
64	#387×C₁₃₇	C₂²	1	2	yes	—
65	#387×C₁₃₇	C₂²	1	2	yes	—
66	#387×C₁₃₇	C₂²	1	2	yes	—
67	#387×C₁₃₇	C₂²	1	2	yes	—
68	#387×C₁₃₇	C₂²	1	2	yes	—
69	#386×C₁₃₇	C₂²	1	2	yes	—
70	#386×C₁₃₇	C₂²	1	2	yes	—
71	#386×C₁₃₇	C₂²	1	2	yes	—
72	#386×C₁₃₇	C₂²	1	2	yes	—
73	#386×C₁₃₇	C₂²	1	2	yes	—
74	#386×C₁₃₇	C₂²	1	2	yes	—
75	#386×C₁₃₇	C₂²	1	2	yes	—
76	#386×C₁₃₇	C₂²	1	2	yes	—
77	#386×C₁₃₇	C₂²	1	2	yes	—
78	#386×C₁₃₇	C₂²	1	2	yes	—
79	#386×C₁₃₇	C₂²	1	2	yes	—
80	#386×C₁₃₇	C₂²	1	2	yes	—
81	#385×C₁₃₇	C₂²	1	2	yes	—
82	#385×C₁₃₇	C₂²	1	2	yes	—
83	#385×C₁₃₇	C₂²	1	2	yes	—
84	#385×C₁₃₇	C₂²	1	2	yes	—
85	#381×C₁₃₇	C₂²	1	2	yes	—
86	#381×C₁₃₇	C₂²	1	2	yes	—
87	#381×C₁₃₇	C₂²	1	2	yes	—
88	#380×C₁₃₇	C₂²	1	1	yes	characteristic
89	#380×C₁₃₇	C₂²	1	1	yes	characteristic
90	#380×C₁₃₇	C₂²	1	2	yes	—
91	#380×C₁₃₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
102	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
103	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
104	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
105	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
106	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
107	C₂×#95×C₁₃₇	C₂²	1	2	yes	—
108	C₂×#41×C₁₃₇	—	4	4	no	—
109	C₂×#41×C₁₃₇	—	4	4	no	—
110	C₂×#41×C₁₃₇	C₂×C₄	1	16	yes	complemented
111	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
131	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	16	yes	complemented
132	C₂²⋊Q₈×C₁₃₇	C₂×C₄	1	16	yes	complemented
133	#121×C₁₃₇	C₂×C₄	1	16	yes	complemented
134	#121×C₁₃₇	C₂×C₄	1	16	yes	complemented
135	#121×C₁₃₇	C₂×C₄	1	8	yes	complemented
136	#121×C₁₃₇	C₂×C₄	1	8	yes	complemented
137	#121×C₁₃₇	C₂×C₄	1	16	yes	complemented
138	C₄×D₄×C₁₃₇	—	4	2	no	—
139	C₄×D₄×C₁₃₇	—	4	2	no	—
140	C₄×D₄×C₁₃₇	—	4	4	no	—
141	C₄×D₄×C₁₃₇	—	4	4	no	—
142	C₄×D₄×C₁₃₇	—	4	4	no	—
143	C₄×D₄×C₁₃₇	—	4	4	no	—
144	C₄×D₄×C₁₃₇	—	4	4	no	—
145	C₂×C₄⋊C₄×C₁₃₇	—	4	2	no	—
146	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	8	yes	complemented
147	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₇	—	4	2	no	—
181	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
191	#95×C₁₃₇	C₂³	1	2	yes	—
192	#95×C₁₃₇	C₂³	1	2	yes	—
193	#95×C₁₃₇	C₂³	1	2	yes	—
194	#95×C₁₃₇	C₂³	1	2	yes	—
195	#95×C₁₃₇	C₂³	1	2	yes	—
196	#95×C₁₃₇	C₂³	1	2	yes	—
197	#95×C₁₃₇	C₂³	1	2	yes	—
198	#95×C₁₃₇	C₂³	1	2	yes	—
199	#95×C₁₃₇	C₂³	1	2	yes	—
200	#95×C₁₃₇	C₂³	1	2	yes	—
201	#95×C₁₃₇	C₂³	1	2	yes	—
202	#95×C₁₃₇	C₂³	1	2	yes	—
203	#95×C₁₃₇	C₂³	1	2	yes	—
204	#95×C₁₃₇	C₂³	1	2	yes	—
205	#95×C₁₃₇	C₂³	1	2	yes	—
206	#95×C₁₃₇	C₂³	1	2	yes	—
207	#95×C₁₃₇	C₂³	1	2	yes	—
208	#95×C₁₃₇	C₂³	1	2	yes	—
209	#95×C₁₃₇	C₂³	1	2	yes	—
210	#95×C₁₃₇	C₂³	1	2	yes	—
211	#95×C₁₃₇	C₂³	1	2	yes	—
212	#95×C₁₃₇	C₂³	1	2	yes	—
213	#95×C₁₃₇	C₂³	1	2	yes	—
214	#95×C₁₃₇	C₂³	1	2	yes	—
215	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
217	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
218	#41×C₁₃₇	—	4	32	no	—
219	C₂×Q₈×C₁₃₇	—	4	2	no	—
220	C₂×Q₈×C₁₃₇	—	4	2	no	—
221	C₂×Q₈×C₁₃₇	C₂²×C₄	1	8	yes	—
222	C₂×D₄×C₁₃₇	—	2	4	no	—
223	C₂×D₄×C₁₃₇	—	2	4	no	—
224	C₂×D₄×C₁₃₇	—	2	4	no	—
225	C₂×D₄×C₁₃₇	—	2	4	no	—
226	C₂×D₄×C₁₃₇	—	4	1	no	—
227	C₂×D₄×C₁₃₇	—	4	1	no	—
228	C₂×D₄×C₁₃₇	—	4	2	no	—
229	C₂×D₄×C₁₃₇	—	4	2	no	—
230	C₂×D₄×C₁₃₇	—	4	1	no	—
231	C₂×D₄×C₁₃₇	—	4	1	no	—
232	C₂×D₄×C₁₃₇	—	4	2	no	—
233	C₂×D₄×C₁₃₇	—	4	2	no	—
234	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
235	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
236	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
237	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
238	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
239	C₂×D₄×C₁₃₇	C₂²×C₄	1	8	yes	—
240	C₂²×C₄×C₁₃₇	—	2	2	no	—
241	C₂²×C₄×C₁₃₇	—	2	2	no	—
242	C₂²×C₄×C₁₃₇	—	2	2	no	—
243	C₂²×C₄×C₁₃₇	—	2	2	no	—
244	C₂²×C₄×C₁₃₇	—	2	2	no	—
245	C₂²×C₄×C₁₃₇	—	2	2	no	—
246	C₂²×C₄×C₁₃₇	—	2	2	no	—
247	C₂²×C₄×C₁₃₇	—	2	2	no	—
248	C₂²×C₄×C₁₃₇	—	2	4	no	—
249	C₂²×C₄×C₁₃₇	—	2	4	no	—
250	C₂²×C₄×C₁₃₇	—	4	1	no	—
251	C₂²×C₄×C₁₃₇	—	4	1	no	—
252	C₂²×C₄×C₁₃₇	—	4	1	no	—
253	C₂²×C₄×C₁₃₇	—	4	1	no	—
254	C₂²×C₄×C₁₃₇	—	4	1	no	—
255	C₂²×C₄×C₁₃₇	—	4	1	no	—
256	C₂²×C₄×C₁₃₇	—	4	2	no	—
257	C₂²×C₄×C₁₃₇	—	4	2	no	—
258	C₂²×C₄×C₁₃₇	—	4	2	no	—
259	C₂²×C₄×C₁₃₇	—	4	2	no	—
260	C₂²×C₄×C₁₃₇	—	4	1	no	—
261	C₂²×C₄×C₁₃₇	—	4	2	no	—
262	C₂²×C₄×C₁₃₇	—	4	2	no	—
263	C₂²×C₄×C₁₃₇	—	4	2	no	—
264	C₂²×C₄×C₁₃₇	—	4	2	no	—
265	C₂²×C₄×C₁₃₇	—	4	2	no	—
266	C₂²×C₄×C₁₃₇	—	4	2	no	—
267	C₂²×C₄×C₁₃₇	—	4	2	no	—
268	C₂²×C₄×C₁₃₇	—	4	2	no	—
269	C₂²×C₄×C₁₃₇	—	4	2	no	—
270	C₂²×C₄×C₁₃₇	—	4	1	no	—
271	C₂²×C₄×C₁₃₇	—	4	1	no	—
272	C₂²×C₄×C₁₃₇	—	4	1	no	—
273	C₂²×C₄×C₁₃₇	—	4	2	no	—
274	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
278	C₂²×C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₁₃₇	—	2	4	no	—
296	C₄⋊C₄×C₁₃₇	—	4	2	no	—
297	C₄⋊C₄×C₁₃₇	—	4	1	no	—
298	C₄⋊C₄×C₁₃₇	—	4	1	no	—
299	C₄⋊C₄×C₁₃₇	—	4	1	no	—
300	C₄⋊C₄×C₁₃₇	—	4	1	no	—
301	C₄⋊C₄×C₁₃₇	—	4	2	no	—
302	C₄⋊C₄×C₁₃₇	—	4	2	no	—
303	C₄⋊C₄×C₁₃₇	—	4	2	no	—
304	C₄⋊C₄×C₁₃₇	—	4	2	no	—
305	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
308	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	—
309	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
310	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
311	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
312	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
313	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
314	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
315	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
316	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
317	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
318	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
319	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
320	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
321	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
322	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
323	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
324	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
326	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₁₃₇	C₂²×C₄	1	8	yes	—
328	C₄²×C₁₃₇	—	2	2	no	—
329	C₄²×C₁₃₇	—	2	2	no	—
330	C₄²×C₁₃₇	—	4	1	no	—
331	C₄²×C₁₃₇	—	4	1	no	—
332	C₄²×C₁₃₇	—	4	2	no	—
333	C₄²×C₁₃₇	—	4	2	no	—
334	C₄²×C₁₃₇	—	4	2	no	—
335	C₄²×C₁₃₇	—	4	2	no	—
336	C₄²×C₁₃₇	—	4	2	no	—
337	C₄²×C₁₃₇	—	4	2	no	—
338	C₂³×C₁₃₇	—	2	1	no	—
339	C₂³×C₁₃₇	—	2	1	no	—
340	C₂³×C₁₃₇	—	2	1	no	—
341	C₂³×C₁₃₇	—	2	1	no	—
342	C₂³×C₁₃₇	—	2	2	no	—
343	C₂³×C₁₃₇	—	2	2	no	—
344	C₂³×C₁₃₇	—	2	2	no	—
345	C₂³×C₁₃₇	—	2	2	no	—
346	C₂³×C₁₃₇	—	2	2	no	—
347	C₂³×C₁₃₇	—	2	2	no	—
348	C₂³×C₁₃₇	—	2	2	no	—
349	C₂³×C₁₃₇	—	2	2	no	—
350	C₂³×C₁₃₇	—	2	2	no	—
351	C₂³×C₁₃₇	—	2	2	no	—
352	C₂³×C₁₃₇	—	2	2	no	—
353	C₂³×C₁₃₇	—	2	2	no	—
354	C₂³×C₁₃₇	C₂³×C₄	1	4	yes	—
355	C₂³×C₁₃₇	C₂³×C₄	1	4	yes	—
356	C₂³×C₁₃₇	C₂³×C₄	1	2	yes	—
357	C₂³×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
358	C₂³×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
359	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
360	Q₈×C₁₃₇	—	4	8	no	—
361	D₄×C₁₃₇	—	2	16	no	—
362	D₄×C₁₃₇	—	2	16	no	—
363	D₄×C₁₃₇	—	4	4	no	—
364	D₄×C₁₃₇	—	4	4	no	—
365	D₄×C₁₃₇	—	4	8	no	—
366	D₄×C₁₃₇	—	4	8	no	—
367	C₂×C₄×C₁₃₇	—	2	8	no	—
368	C₂×C₄×C₁₃₇	—	2	1	no	—
369	C₂×C₄×C₁₃₇	—	2	1	no	—
370	C₂×C₄×C₁₃₇	—	2	1	no	—
371	C₂×C₄×C₁₃₇	—	2	1	no	—
372	C₂×C₄×C₁₃₇	—	2	1	no	—
373	C₂×C₄×C₁₃₇	—	2	2	no	—
374	C₂×C₄×C₁₃₇	—	2	2	no	—
375	C₂×C₄×C₁₃₇	—	2	2	no	—
376	C₂×C₄×C₁₃₇	—	2	2	no	—
377	C₂×C₄×C₁₃₇	—	2	2	no	—
378	C₂×C₄×C₁₃₇	—	2	2	no	—
379	C₂×C₄×C₁₃₇	—	2	2	no	—
380	C₂×C₄×C₁₃₇	—	2	2	no	—
381	C₂×C₄×C₁₃₇	—	2	1	no	—
382	C₂×C₄×C₁₃₇	—	2	1	no	—
383	C₂×C₄×C₁₃₇	—	2	1	no	—
384	C₂×C₄×C₁₃₇	—	2	1	no	—
385	C₂×C₄×C₁₃₇	—	2	2	no	—
386	C₂×C₄×C₁₃₇	—	2	1	no	—
387	C₂×C₄×C₁₃₇	—	2	2	no	—
388	C₂×C₄×C₁₃₇	—	2	2	no	—
389	C₂×C₄×C₁₃₇	—	2	2	no	—
390	C₂×C₄×C₁₃₇	—	2	2	no	—
391	C₂×C₄×C₁₃₇	—	2	2	no	—
392	C₂×C₄×C₁₃₇	—	2	2	no	—
393	C₂×C₄×C₁₃₇	—	2	2	no	—
394	C₂×C₄×C₁₃₇	—	2	1	no	—
395	C₂×C₄×C₁₃₇	—	2	1	no	—
396	C₂×C₄×C₁₃₇	—	2	2	no	—
397	C₂×C₄×C₁₃₇	—	2	2	no	—
398	C₂×C₄×C₁₃₇	—	2	1	no	—
399	C₂×C₄×C₁₃₇	—	2	2	no	—
400	C₂×C₄×C₁₃₇	—	2	2	no	—
401	C₂×C₄×C₁₃₇	—	2	2	no	—
402	C₂×C₄×C₁₃₇	—	2	1	no	—
403	C₂×C₄×C₁₃₇	—	2	2	no	—
404	C₂×C₄×C₁₃₇	—	2	2	no	—
405	C₂×C₄×C₁₃₇	—	2	2	no	—
406	C₂×C₄×C₁₃₇	—	2	2	no	—
407	C₂×C₄×C₁₃₇	—	2	2	no	—
408	C₂×C₄×C₁₃₇	—	4	4	no	—
409	C₂×C₄×C₁₃₇	—	4	4	no	—
410	C₂×C₄×C₁₃₇	—	4	8	no	—
411	C₂×C₄×C₁₃₇	—	4	8	no	—
412	C₂×C₄×C₁₃₇	—	4	4	no	—
413	C₂×C₄×C₁₃₇	—	4	4	no	—
414	C₂×C₄×C₁₃₇	—	8	4	no	—
415	C₂×C₄×C₁₃₇	—	8	4	no	—
416	C₂×C₄×C₁₃₇	—	8	2	no	—
417	C₂×C₄×C₁₃₇	—	8	2	no	—
418	C₂×C₄×C₁₃₇	—	8	4	no	—
419	C₂×C₄×C₁₃₇	—	8	4	no	—
420	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₁₃₇	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
423	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
424	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
425	C₂×C₄×C₁₃₇	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
427	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
428	C₂²×C₁₃₇	—	2	2	no	—
429	C₂²×C₁₃₇	—	2	2	no	—
430	C₂²×C₁₃₇	—	2	2	no	—
431	C₂²×C₁₃₇	—	2	2	no	—
432	C₂²×C₁₃₇	—	2	2	no	—
433	C₂²×C₁₃₇	—	2	2	no	—
434	C₂²×C₁₃₇	—	2	4	no	—
435	C₂²×C₁₃₇	—	2	4	no	—
436	C₂²×C₁₃₇	—	2	4	no	—
437	C₂²×C₁₃₇	—	2	4	no	—
438	C₂²×C₁₃₇	—	2	4	no	—
439	C₂²×C₁₃₇	—	2	4	no	—
440	C₂²×C₁₃₇	—	4	2	no	—
441	C₂²×C₁₃₇	—	4	2	no	—
442	C₂²×C₁₃₇	—	4	2	no	—
443	C₂²×C₁₃₇	—	4	2	no	—
444	C₂²×C₁₃₇	—	4	2	no	—
445	C₂²×C₁₃₇	—	4	2	no	—
446	C₂²×C₁₃₇	—	4	2	no	—
447	C₂²×C₁₃₇	—	4	2	no	—
448	C₂²×C₁₃₇	#518	1	4	yes	—
449	C₂²×C₁₃₇	C₂⁴×C₄	1	1	yes	characteristic
450	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂²×C₁₃₇	#585	1	1	yes	characteristic
455	C₂²×C₁₃₇	#585	1	1	yes	characteristic
456	C₄×C₁₃₇	—	2	4	no	—
457	C₄×C₁₃₇	—	2	4	no	—
458	C₄×C₁₃₇	—	2	4	no	—
459	C₄×C₁₃₇	—	2	2	no	—
460	C₄×C₁₃₇	—	2	2	no	—
461	C₄×C₁₃₇	—	2	4	no	—
462	C₄×C₁₃₇	—	2	2	no	—
463	C₄×C₁₃₇	—	2	2	no	—
464	C₄×C₁₃₇	—	4	1	no	—
465	C₄×C₁₃₇	—	4	2	no	—
466	C₄×C₁₃₇	—	4	2	no	—
467	C₄×C₁₃₇	—	4	1	no	—
468	C₄×C₁₃₇	—	4	2	no	—
469	C₄×C₁₃₇	—	4	2	no	—
470	C₄×C₁₃₇	—	4	2	no	—
471	C₄×C₁₃₇	—	4	2	no	—
472	C₂×C₁₃₇	—	2	4	no	—
473	C₂×C₁₃₇	—	4	4	no	—
474	C₂×C₁₃₇	—	4	4	no	—
475	C₂×C₁₃₇	C₂×#518	1	1	yes	characteristic
476	C₂×C₁₃₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₁₃₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
478	C₂×C₁₃₇	#3534	1	1	yes	characteristic
479	C₂×C₁₃₇	#3536	1	1	yes	characteristic
480	C₂×C₁₃₇	#3559	1	1	yes	characteristic
481	C₂×C₁₃₇	#3560	1	1	yes	characteristic
482	#34436	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
483	C₁₃₇	#34436	1	1	yes	characteristic, direct product factor, Sylow
484	C₂×#537	C₂×C₁₃₇	1	1	yes	characteristic
485	#2378	C₂×C₁₃₇	1	2	yes	complemented
486	#2377	C₂×C₁₃₇	1	2	yes	complemented
487	#2368	C₂×C₁₃₇	1	2	yes	complemented
488	#2364	C₂×C₁₃₇	1	2	yes	complemented
489	#2364	C₂×C₁₃₇	1	2	yes	complemented
490	#2361	C₂×C₁₃₇	1	2	yes	complemented
491	#2339	C₂×C₁₃₇	1	2	yes	complemented
492	#2339	C₂×C₁₃₇	1	2	yes	complemented
493	#2333	C₂×C₁₃₇	1	2	yes	complemented
494	#2332	C₂×C₁₃₇	1	2	yes	complemented
495	#2329	C₂×C₁₃₇	1	2	yes	complemented
496	#2325	C₂×C₁₃₇	1	2	yes	complemented
497	#2325	C₂×C₁₃₇	1	1	yes	characteristic, complemented
498	#2325	C₂×C₁₃₇	1	1	yes	characteristic, complemented
499	#2313	C₂×C₁₃₇	1	1	yes	characteristic, complemented
500	C₄×#121	C₂×C₁₃₇	1	1	yes	characteristic, complemented
501	C₄×#121	C₂×C₁₃₇	1	1	yes	characteristic, complemented
502	C₂×#387	C₂×C₁₃₇	1	1	yes	characteristic, complemented
503	C₂²×#41	C₂²×C₁₃₇	1	2	yes	—
504	#537	C₄×C₁₃₇	1	16	yes	complemented
505	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
507	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
508	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
509	C₂×#121	C₂²×C₁₃₇	1	1	yes	characteristic
510	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
511	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
516	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
517	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
518	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
519	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
520	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
521	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
522	#391	C₂²×C₁₃₇	1	2	yes	—
523	#391	C₂²×C₁₃₇	1	2	yes	—
524	#391	C₂²×C₁₃₇	1	2	yes	—
525	#391	C₂²×C₁₃₇	1	2	yes	—
526	#390	C₂²×C₁₃₇	1	1	yes	characteristic
527	#390	C₂²×C₁₃₇	1	2	yes	—
528	#390	C₂²×C₁₃₇	1	1	yes	characteristic
529	#389	C₂²×C₁₃₇	1	1	yes	characteristic
530	#389	C₂²×C₁₃₇	1	2	yes	—
531	#389	C₂²×C₁₃₇	1	1	yes	characteristic
532	#388	C₂²×C₁₃₇	1	2	yes	—
533	#388	C₂²×C₁₃₇	1	2	yes	—
534	#388	C₂²×C₁₃₇	1	2	yes	—
535	#388	C₂²×C₁₃₇	1	2	yes	—
536	#388	C₂²×C₁₃₇	1	2	yes	—
537	#388	C₂²×C₁₃₇	1	2	yes	—
538	#388	C₂²×C₁₃₇	1	2	yes	—
539	#388	C₂²×C₁₃₇	1	2	yes	—
540	#387	C₂²×C₁₃₇	1	2	yes	—
541	#387	C₂²×C₁₃₇	1	2	yes	—
542	#387	C₂²×C₁₃₇	1	2	yes	—
543	#387	C₂²×C₁₃₇	1	2	yes	—
544	#387	C₂²×C₁₃₇	1	2	yes	—
545	#387	C₂²×C₁₃₇	1	2	yes	—
546	#387	C₂²×C₁₃₇	1	2	yes	—
547	#387	C₂²×C₁₃₇	1	2	yes	—
548	#387	C₂²×C₁₃₇	1	2	yes	—
549	#387	C₂²×C₁₃₇	1	2	yes	—
550	#387	C₂²×C₁₃₇	1	2	yes	—
551	#387	C₂²×C₁₃₇	1	2	yes	—
552	#386	C₂²×C₁₃₇	1	2	yes	—
553	#386	C₂²×C₁₃₇	1	2	yes	—
554	#386	C₂²×C₁₃₇	1	2	yes	—
555	#386	C₂²×C₁₃₇	1	2	yes	—
556	#386	C₂²×C₁₃₇	1	2	yes	—
557	#386	C₂²×C₁₃₇	1	2	yes	—
558	#386	C₂²×C₁₃₇	1	2	yes	—
559	#386	C₂²×C₁₃₇	1	2	yes	—
560	#386	C₂²×C₁₃₇	1	2	yes	—
561	#386	C₂²×C₁₃₇	1	2	yes	—
562	#386	C₂²×C₁₃₇	1	2	yes	—
563	#386	C₂²×C₁₃₇	1	2	yes	—
564	#385	C₂²×C₁₃₇	1	2	yes	—
565	#385	C₂²×C₁₃₇	1	2	yes	—
566	#385	C₂²×C₁₃₇	1	2	yes	—
567	#385	C₂²×C₁₃₇	1	2	yes	—
568	#381	C₂²×C₁₃₇	1	2	yes	—
569	#381	C₂²×C₁₃₇	1	2	yes	—
570	#381	C₂²×C₁₃₇	1	2	yes	—
571	#380	C₂²×C₁₃₇	1	1	yes	characteristic
572	#380	C₂²×C₁₃₇	1	1	yes	characteristic
573	#380	C₂²×C₁₃₇	1	2	yes	—
574	#380	C₂²×C₁₃₇	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
584	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
585	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
586	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
587	C₂×#95	C₂²×C₁₃₇	1	2	yes	—
588	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
589	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
590	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
591	C₂×#41	—	4	4	no	—
592	C₂×#41	—	4	4	no	—
593	C₂×#41	C₂×C₄×C₁₃₇	1	16	yes	complemented
594	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
595	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
596	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
597	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
599	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
601	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
606	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
608	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
609	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
613	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
614	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	16	yes	complemented
615	C₂²⋊Q₈	C₂×C₄×C₁₃₇	1	16	yes	complemented
616	#121	C₂×C₄×C₁₃₇	1	16	yes	complemented
617	#121	C₂×C₄×C₁₃₇	1	16	yes	complemented
618	#121	C₂×C₄×C₁₃₇	1	8	yes	complemented
619	#121	C₂×C₄×C₁₃₇	1	8	yes	complemented
620	#121	C₂×C₄×C₁₃₇	1	16	yes	complemented
621	C₄×D₄	—	4	2	no	—
622	C₄×D₄	—	4	2	no	—
623	C₄×D₄	—	4	4	no	—
624	C₄×D₄	—	4	4	no	—
625	C₄×D₄	—	4	4	no	—
626	C₄×D₄	—	4	4	no	—
627	C₄×D₄	—	4	4	no	—
628	C₂×C₄⋊C₄	—	4	2	no	—
629	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	8	yes	complemented
630	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
663	C₂×C₄²	—	4	2	no	—
664	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
667	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
668	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
674	#95	C₂³×C₁₃₇	1	2	yes	—
675	#95	C₂³×C₁₃₇	1	2	yes	—
676	#95	C₂³×C₁₃₇	1	2	yes	—
677	#95	C₂³×C₁₃₇	1	2	yes	—
678	#95	C₂³×C₁₃₇	1	2	yes	—
679	#95	C₂³×C₁₃₇	1	2	yes	—
680	#95	C₂³×C₁₃₇	1	2	yes	—
681	#95	C₂³×C₁₃₇	1	2	yes	—
682	#95	C₂³×C₁₃₇	1	2	yes	—
683	#95	C₂³×C₁₃₇	1	2	yes	—
684	#95	C₂³×C₁₃₇	1	2	yes	—
685	#95	C₂³×C₁₃₇	1	2	yes	—
686	#95	C₂³×C₁₃₇	1	2	yes	—
687	#95	C₂³×C₁₃₇	1	2	yes	—
688	#95	C₂³×C₁₃₇	1	2	yes	—
689	#95	C₂³×C₁₃₇	1	2	yes	—
690	#95	C₂³×C₁₃₇	1	2	yes	—
691	#95	C₂³×C₁₃₇	1	2	yes	—
692	#95	C₂³×C₁₃₇	1	2	yes	—
693	#95	C₂³×C₁₃₇	1	2	yes	—
694	#95	C₂³×C₁₃₇	1	2	yes	—
695	#95	C₂³×C₁₃₇	1	2	yes	—
696	#95	C₂³×C₁₃₇	1	2	yes	—
697	#95	C₂³×C₁₃₇	1	2	yes	—
698	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
699	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
700	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
701	#41	—	4	32	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	C₂²×C₄×C₁₃₇	1	8	yes	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
720	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
722	C₂×D₄	C₂²×C₄×C₁₃₇	1	8	yes	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
758	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
759	C₂²×C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
760	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
761	C₂²×C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
789	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
790	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
791	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	—
792	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
809	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
810	C₂²⋊C₄	C₂²×C₄×C₁₃₇	1	8	yes	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	4	1	no	—
814	C₄²	—	4	1	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	C₂³×C₄×C₁₃₇	1	4	yes	—
838	C₂³	C₂³×C₄×C₁₃₇	1	4	yes	—
839	C₂³	C₂³×C₄×C₁₃₇	1	2	yes	—
840	C₂³	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
841	C₂³	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
842	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
843	Q₈	—	4	8	no	—
844	D₄	—	2	16	no	—
845	D₄	—	2	16	no	—
846	D₄	—	4	8	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	8	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	—	8	4	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
904	C₂×C₄	C₂³×C₄×C₁₃₇	1	2	yes	—
905	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
907	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
908	C₂×C₄	C₂³×C₄×C₁₃₇	1	4	yes	—
909	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
910	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	#518×C₁₃₇	1	4	yes	—
932	C₂²	C₂⁴×C₄×C₁₃₇	1	1	yes	characteristic
933	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
934	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
935	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
936	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
937	C₂²	#585×C₁₃₇	1	1	yes	characteristic
938	C₂²	#585×C₁₃₇	1	1	yes	characteristic
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₂	—	2	4	no	—
956	C₂	—	4	4	no	—
957	C₂	—	4	4	no	—
958	C₂	C₂×#518×C₁₃₇	1	1	yes	characteristic
959	C₂	C₄×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
960	C₂	C₄×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
961	C₂	#3534×C₁₃₇	1	1	yes	characteristic
962	C₂	#3536×C₁₃₇	1	1	yes	characteristic
963	C₂	#3559×C₁₃₇	1	1	yes	characteristic
964	C₂	#3560×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₇
Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂×#537×C₁₃₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2378×C₁₃₇	C₂	semidirect
3. #2377×C₁₃₇	C₂	semidirect
4. #2368×C₁₃₇	C₂	semidirect
5. #2364×C₁₃₇	C₂	semidirect
6. #2364×C₁₃₇	C₂	semidirect
7. #2361×C₁₃₇	C₂	semidirect
8. #2339×C₁₃₇	C₂	semidirect
9. #2339×C₁₃₇	C₂	semidirect
10. #2333×C₁₃₇	C₂	semidirect
11. #2332×C₁₃₇	C₂	semidirect
12. #2329×C₁₃₇	C₂	semidirect
13. #2325×C₁₃₇	C₂	semidirect
14. #2325×C₁₃₇	C₂	semidirect
15. #2325×C₁₃₇	C₂	semidirect
16. #2313×C₁₃₇	C₂	semidirect
17. C₄×#121×C₁₃₇	C₂	semidirect
18. C₄×#121×C₁₃₇	C₂	semidirect
19. C₂×#387×C₁₃₇	C₂	semidirect
21. #537×C₁₃₇	C₄	semidirect
110. C₂×#41×C₁₃₇	C₂×C₄	semidirect
131. C₂²⋊Q₈×C₁₃₇	C₂×C₄	semidirect
132. C₂²⋊Q₈×C₁₃₇	C₂×C₄	semidirect
133. #121×C₁₃₇	C₂×C₄	semidirect
134. #121×C₁₃₇	C₂×C₄	semidirect
135. #121×C₁₃₇	C₂×C₄	semidirect
136. #121×C₁₃₇	C₂×C₄	semidirect
137. #121×C₁₃₇	C₂×C₄	semidirect
146. C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	semidirect
482. #34436	C₁₃₇	direct (N × H)
483. C₁₃₇	#34436	direct (N × H)
485. #2378	C₂×C₁₃₇	semidirect
486. #2377	C₂×C₁₃₇	semidirect
487. #2368	C₂×C₁₃₇	semidirect
488. #2364	C₂×C₁₃₇	semidirect
489. #2364	C₂×C₁₃₇	semidirect
490. #2361	C₂×C₁₃₇	semidirect
491. #2339	C₂×C₁₃₇	semidirect
492. #2339	C₂×C₁₃₇	semidirect
493. #2333	C₂×C₁₃₇	semidirect
494. #2332	C₂×C₁₃₇	semidirect
495. #2329	C₂×C₁₃₇	semidirect
496. #2325	C₂×C₁₃₇	semidirect
497. #2325	C₂×C₁₃₇	semidirect
498. #2325	C₂×C₁₃₇	semidirect
499. #2313	C₂×C₁₃₇	semidirect
500. C₄×#121	C₂×C₁₃₇	semidirect
501. C₄×#121	C₂×C₁₃₇	semidirect
502. C₂×#387	C₂×C₁₃₇	semidirect
504. #537	C₄×C₁₃₇	semidirect
593. C₂×#41	C₂×C₄×C₁₃₇	semidirect
614. C₂²⋊Q₈	C₂×C₄×C₁₃₇	semidirect
615. C₂²⋊Q₈	C₂×C₄×C₁₃₇	semidirect
616. #121	C₂×C₄×C₁₃₇	semidirect
617. #121	C₂×C₄×C₁₃₇	semidirect
618. #121	C₂×C₄×C₁₃₇	semidirect
619. #121	C₂×C₄×C₁₃₇	semidirect
620. #121	C₂×C₄×C₁₃₇	semidirect
629. C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₁₃₇	2
#2378×C₁₃₇	2
#2377×C₁₃₇	2
#2368×C₁₃₇	2
#2364×C₁₃₇	2
#2361×C₁₃₇	2
#2339×C₁₃₇	2
#2333×C₁₃₇	2
#2332×C₁₃₇	2
#2329×C₁₃₇	2
#2325×C₁₃₇	2
#2313×C₁₃₇	2
C₄×#121×C₁₃₇	2
C₂×#387×C₁₃₇	2
#34436	137

Subgroups — C137×#34436 #46883822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34436 #46883822