Subgroups — C₁₃₇×#34983 #46884369

Order 35072.

3038 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#534×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2849×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2623×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2622×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2444×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#2443×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	#2419×C₁₃₇	C₂	1	4	yes	maximal, complemented
10	#2418×C₁₃₇	C₂	1	4	yes	maximal, complemented
11	#2315×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#2308×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#2308×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#386×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#385×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
20	#534×C₁₃₇	—	2	8	no	—
21	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₇	C₂²	1	4	yes	complemented
24	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#120×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#120×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₇	—	2	8	no	—
29	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	complemented
31	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
39	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
40	#400×C₁₃₇	C₂²	1	4	yes	complemented
41	#399×C₁₃₇	C₂²	1	4	yes	complemented
42	#398×C₁₃₇	C₂²	1	4	yes	complemented
43	#397×C₁₃₇	C₂²	1	4	yes	complemented
44	#397×C₁₃₇	C₂²	1	4	yes	complemented
45	#397×C₁₃₇	C₂²	1	4	yes	complemented
46	#394×C₁₃₇	C₂²	1	4	yes	complemented
47	#394×C₁₃₇	C₂²	1	4	yes	complemented
48	#388×C₁₃₇	C₂²	1	4	yes	complemented
49	#388×C₁₃₇	C₂²	1	4	yes	complemented
50	#387×C₁₃₇	C₂²	1	4	yes	complemented
51	#387×C₁₃₇	C₂²	1	4	yes	complemented
52	#386×C₁₃₇	C₂²	1	2	yes	—
53	#386×C₁₃₇	C₂²	1	2	yes	—
54	#386×C₁₃₇	C₂²	1	2	yes	—
55	#386×C₁₃₇	C₂²	1	2	yes	—
56	#386×C₁₃₇	C₂²	1	4	yes	—
57	#386×C₁₃₇	C₂²	1	4	yes	complemented
58	#386×C₁₃₇	C₂²	1	4	yes	complemented
59	#386×C₁₃₇	C₂²	1	4	yes	complemented
60	#386×C₁₃₇	C₂²	1	4	yes	complemented
61	#385×C₁₃₇	C₂²	1	2	yes	complemented
62	#385×C₁₃₇	C₂²	1	2	yes	complemented
63	#385×C₁₃₇	C₂²	1	4	yes	complemented
64	#385×C₁₃₇	C₂²	1	2	yes	complemented
65	#385×C₁₃₇	C₂²	1	2	yes	complemented
66	#385×C₁₃₇	C₂²	1	2	yes	complemented
67	#385×C₁₃₇	C₂²	1	2	yes	complemented
68	#385×C₁₃₇	C₂²	1	4	yes	complemented
69	#381×C₁₃₇	C₂²	1	2	yes	complemented
70	#381×C₁₃₇	C₂²	1	2	yes	complemented
71	#381×C₁₃₇	C₂²	1	4	yes	complemented
72	#380×C₁₃₇	C₂²	1	4	yes	complemented
73	#379×C₁₃₇	C₂²	1	2	yes	complemented
74	#379×C₁₃₇	C₂²	1	2	yes	complemented
75	C₂×#95×C₁₃₇	C₂²	1	2	yes	complemented
76	C₂×#95×C₁₃₇	C₂²	1	2	yes	complemented
77	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₇	—	2	4	no	—
81	C₂²×D₄×C₁₃₇	—	2	4	no	—
82	C₂²×D₄×C₁₃₇	—	2	4	no	—
83	C₂²×D₄×C₁₃₇	—	2	4	no	—
84	C₂²×D₄×C₁₃₇	—	2	4	no	—
85	C₂²×D₄×C₁₃₇	D₄	1	8	yes	—
86	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₇	—	2	4	no	—
93	C₂³×C₄×C₁₃₇	—	2	4	no	—
94	C₂³×C₄×C₁₃₇	—	4	4	no	—
95	C₂³×C₄×C₁₃₇	—	4	4	no	—
96	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
109	#123×C₁₃₇	—	2	8	no	—
110	#123×C₁₃₇	—	2	8	no	—
111	#123×C₁₃₇	—	4	8	no	—
112	#121×C₁₃₇	—	2	8	no	—
113	#121×C₁₃₇	—	2	8	no	—
114	#120×C₁₃₇	—	2	8	no	—
115	#120×C₁₃₇	—	2	8	no	—
116	C₄×D₄×C₁₃₇	—	2	16	no	—
117	C₄×D₄×C₁₃₇	—	2	16	no	—
118	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
119	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
120	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₁₃₇	—	4	4	no	—
133	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃₇	—	2	4	no	—
153	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
154	#95×C₁₃₇	C₂³	1	4	yes	—
155	#95×C₁₃₇	C₂³	1	4	yes	—
156	#95×C₁₃₇	C₂³	1	4	yes	—
157	#95×C₁₃₇	C₂³	1	4	yes	—
158	#95×C₁₃₇	C₂³	1	4	yes	—
159	#95×C₁₃₇	C₂³	1	4	yes	—
160	#95×C₁₃₇	C₂³	1	4	yes	—
161	#95×C₁₃₇	C₂³	1	4	yes	—
162	#95×C₁₃₇	C₂³	1	4	yes	—
163	#95×C₁₃₇	C₂³	1	4	yes	—
164	C₂⁴×C₁₃₇	—	2	2	no	—
165	C₂⁴×C₁₃₇	—	2	2	no	—
166	C₂⁴×C₁₃₇	—	2	2	no	—
167	C₂⁴×C₁₃₇	—	2	2	no	—
168	C₂⁴×C₁₃₇	—	2	2	no	—
169	C₂⁴×C₁₃₇	—	4	2	no	—
170	C₂⁴×C₁₃₇	—	4	2	no	—
171	C₂⁴×C₁₃₇	—	4	2	no	—
172	C₂⁴×C₁₃₇	—	4	2	no	—
173	C₂⁴×C₁₃₇	—	4	2	no	—
174	C₂⁴×C₁₃₇	—	4	2	no	—
175	C₂⁴×C₁₃₇	C₂×D₄	1	4	yes	—
176	C₂⁴×C₁₃₇	C₂×D₄	1	4	yes	—
177	C₂⁴×C₁₃₇	#41	1	4	yes	—
178	C₂⁴×C₁₃₇	#41	1	4	yes	—
179	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
184	C₂×D₄×C₁₃₇	—	2	32	no	—
185	C₂×D₄×C₁₃₇	—	2	4	no	—
186	C₂×D₄×C₁₃₇	—	2	4	no	—
187	C₂×D₄×C₁₃₇	—	2	4	no	—
188	C₂×D₄×C₁₃₇	—	2	4	no	—
189	C₂×D₄×C₁₃₇	—	2	4	no	—
190	C₂×D₄×C₁₃₇	—	2	4	no	—
191	C₂×D₄×C₁₃₇	—	2	4	no	—
192	C₂×D₄×C₁₃₇	—	2	4	no	—
193	C₂×D₄×C₁₃₇	—	2	4	no	—
194	C₂×D₄×C₁₃₇	—	2	4	no	—
195	C₂×D₄×C₁₃₇	—	2	4	no	—
196	C₂×D₄×C₁₃₇	—	2	4	no	—
197	C₂×D₄×C₁₃₇	—	4	4	no	—
198	C₂×D₄×C₁₃₇	—	4	4	no	—
199	C₂×D₄×C₁₃₇	—	4	16	no	—
200	C₂×D₄×C₁₃₇	C₂×D₄	1	8	yes	—
201	C₂×D₄×C₁₃₇	C₂×D₄	1	8	yes	—
202	C₂²×C₄×C₁₃₇	—	2	2	no	—
203	C₂²×C₄×C₁₃₇	—	2	2	no	—
204	C₂²×C₄×C₁₃₇	—	2	2	no	—
205	C₂²×C₄×C₁₃₇	—	2	4	no	—
206	C₂²×C₄×C₁₃₇	—	2	2	no	—
207	C₂²×C₄×C₁₃₇	—	2	2	no	—
208	C₂²×C₄×C₁₃₇	—	2	2	no	—
209	C₂²×C₄×C₁₃₇	—	2	8	no	—
210	C₂²×C₄×C₁₃₇	—	2	4	no	—
211	C₂²×C₄×C₁₃₇	—	2	4	no	—
212	C₂²×C₄×C₁₃₇	—	2	2	no	—
213	C₂²×C₄×C₁₃₇	—	2	4	no	—
214	C₂²×C₄×C₁₃₇	—	2	2	no	—
215	C₂²×C₄×C₁₃₇	—	2	2	no	—
216	C₂²×C₄×C₁₃₇	—	2	2	no	—
217	C₂²×C₄×C₁₃₇	—	2	2	no	—
218	C₂²×C₄×C₁₃₇	—	2	4	no	—
219	C₂²×C₄×C₁₃₇	—	2	4	no	—
220	C₂²×C₄×C₁₃₇	—	2	4	no	—
221	C₂²×C₄×C₁₃₇	—	2	8	no	—
222	C₂²×C₄×C₁₃₇	—	4	2	no	—
223	C₂²×C₄×C₁₃₇	—	4	2	no	—
224	C₂²×C₄×C₁₃₇	—	4	4	no	—
225	C₂²×C₄×C₁₃₇	—	4	2	no	—
226	C₂²×C₄×C₁₃₇	—	4	2	no	—
227	C₂²×C₄×C₁₃₇	—	4	2	no	—
228	C₂²×C₄×C₁₃₇	—	4	2	no	—
229	C₂²×C₄×C₁₃₇	—	4	2	no	—
230	C₂²×C₄×C₁₃₇	—	4	2	no	—
231	C₂²×C₄×C₁₃₇	—	4	2	no	—
232	C₂²×C₄×C₁₃₇	—	4	2	no	—
233	C₂²×C₄×C₁₃₇	—	4	2	no	—
234	C₂²×C₄×C₁₃₇	—	4	16	no	—
235	C₂²×C₄×C₁₃₇	—	4	16	no	—
236	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
237	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
247	C₄⋊C₄×C₁₃₇	—	2	8	no	—
248	C₄⋊C₄×C₁₃₇	—	2	4	no	—
249	C₄⋊C₄×C₁₃₇	—	2	4	no	—
250	C₄⋊C₄×C₁₃₇	—	2	8	no	—
251	C₄⋊C₄×C₁₃₇	—	4	4	no	—
252	C₄⋊C₄×C₁₃₇	—	4	4	no	—
253	C₄⋊C₄×C₁₃₇	—	4	4	no	—
254	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
266	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
270	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
273	C₄²×C₁₃₇	—	2	8	no	—
274	C₂³×C₁₃₇	—	2	2	no	—
275	C₂³×C₁₃₇	—	2	2	no	—
276	C₂³×C₁₃₇	—	2	2	no	—
277	C₂³×C₁₃₇	—	2	2	no	—
278	C₂³×C₁₃₇	—	2	2	no	—
279	C₂³×C₁₃₇	—	2	2	no	—
280	C₂³×C₁₃₇	—	2	8	no	—
281	C₂³×C₁₃₇	—	2	2	no	—
282	C₂³×C₁₃₇	—	2	2	no	—
283	C₂³×C₁₃₇	—	2	4	no	—
284	C₂³×C₁₃₇	—	2	4	no	—
285	C₂³×C₁₃₇	—	2	2	no	—
286	C₂³×C₁₃₇	—	2	2	no	—
287	C₂³×C₁₃₇	—	2	2	no	—
288	C₂³×C₁₃₇	—	2	4	no	—
289	C₂³×C₁₃₇	—	2	4	no	—
290	C₂³×C₁₃₇	—	4	4	no	—
291	C₂³×C₁₃₇	—	4	4	no	—
292	C₂³×C₁₃₇	—	4	4	no	—
293	C₂³×C₁₃₇	—	4	4	no	—
294	C₂³×C₁₃₇	—	4	8	no	—
295	C₂³×C₁₃₇	—	4	8	no	—
296	C₂³×C₁₃₇	—	4	8	no	—
297	C₂³×C₁₃₇	—	4	8	no	—
298	C₂³×C₁₃₇	—	4	8	no	—
299	C₂³×C₁₃₇	—	4	4	no	—
300	C₂³×C₁₃₇	—	8	2	no	—
301	C₂³×C₁₃₇	—	8	2	no	—
302	C₂³×C₁₃₇	—	8	4	no	—
303	C₂³×C₁₃₇	#123	1	16	yes	complemented
304	C₂³×C₁₃₇	C₂²×D₄	1	4	yes	—
305	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
306	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
307	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
309	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
310	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
311	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
312	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
313	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
314	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
315	D₄×C₁₃₇	—	2	16	no	—
316	D₄×C₁₃₇	—	2	16	no	—
317	D₄×C₁₃₇	—	4	8	no	—
318	D₄×C₁₃₇	—	4	8	no	—
319	D₄×C₁₃₇	—	8	4	no	—
320	D₄×C₁₃₇	—	8	4	no	—
321	C₂×C₄×C₁₃₇	—	2	8	no	—
322	C₂×C₄×C₁₃₇	—	2	8	no	—
323	C₂×C₄×C₁₃₇	—	2	2	no	—
324	C₂×C₄×C₁₃₇	—	2	2	no	—
325	C₂×C₄×C₁₃₇	—	2	2	no	—
326	C₂×C₄×C₁₃₇	—	2	2	no	—
327	C₂×C₄×C₁₃₇	—	2	2	no	—
328	C₂×C₄×C₁₃₇	—	2	2	no	—
329	C₂×C₄×C₁₃₇	—	2	2	no	—
330	C₂×C₄×C₁₃₇	—	2	2	no	—
331	C₂×C₄×C₁₃₇	—	2	2	no	—
332	C₂×C₄×C₁₃₇	—	2	2	no	—
333	C₂×C₄×C₁₃₇	—	2	4	no	—
334	C₂×C₄×C₁₃₇	—	2	4	no	—
335	C₂×C₄×C₁₃₇	—	2	2	no	—
336	C₂×C₄×C₁₃₇	—	2	2	no	—
337	C₂×C₄×C₁₃₇	—	2	4	no	—
338	C₂×C₄×C₁₃₇	—	2	4	no	—
339	C₂×C₄×C₁₃₇	—	2	2	no	—
340	C₂×C₄×C₁₃₇	—	2	4	no	—
341	C₂×C₄×C₁₃₇	—	2	4	no	—
342	C₂×C₄×C₁₃₇	—	2	2	no	—
343	C₂×C₄×C₁₃₇	—	2	4	no	—
344	C₂×C₄×C₁₃₇	—	2	4	no	—
345	C₂×C₄×C₁₃₇	—	2	4	no	—
346	C₂×C₄×C₁₃₇	—	2	4	no	—
347	C₂×C₄×C₁₃₇	—	4	8	no	—
348	C₂×C₄×C₁₃₇	—	4	8	no	—
349	C₂×C₄×C₁₃₇	—	4	16	no	—
350	C₂×C₄×C₁₃₇	—	4	8	no	—
351	C₂×C₄×C₁₃₇	—	4	4	no	—
352	C₂×C₄×C₁₃₇	—	4	4	no	—
353	C₂×C₄×C₁₃₇	—	4	4	no	—
354	C₂×C₄×C₁₃₇	—	4	4	no	—
355	C₂×C₄×C₁₃₇	—	8	2	no	—
356	C₂×C₄×C₁₃₇	—	8	2	no	—
357	C₂×C₄×C₁₃₇	—	8	4	no	—
358	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
359	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
360	C₂²×C₁₃₇	—	2	4	no	—
361	C₂²×C₁₃₇	—	2	4	no	—
362	C₂²×C₁₃₇	—	2	4	no	—
363	C₂²×C₁₃₇	—	2	2	no	—
364	C₂²×C₁₃₇	—	2	2	no	—
365	C₂²×C₁₃₇	—	2	2	no	—
366	C₂²×C₁₃₇	—	2	2	no	—
367	C₂²×C₁₃₇	—	2	2	no	—
368	C₂²×C₁₃₇	—	2	2	no	—
369	C₂²×C₁₃₇	—	2	4	no	—
370	C₂²×C₁₃₇	—	2	4	no	—
371	C₂²×C₁₃₇	—	2	4	no	—
372	C₂²×C₁₃₇	—	2	4	no	—
373	C₂²×C₁₃₇	—	2	4	no	—
374	C₂²×C₁₃₇	—	2	4	no	—
375	C₂²×C₁₃₇	—	4	16	no	—
376	C₂²×C₁₃₇	—	4	16	no	—
377	C₂²×C₁₃₇	—	4	4	no	—
378	C₂²×C₁₃₇	—	4	4	no	—
379	C₂²×C₁₃₇	—	4	2	no	—
380	C₂²×C₁₃₇	—	4	4	no	—
381	C₂²×C₁₃₇	—	4	2	no	—
382	C₂²×C₁₃₇	—	4	2	no	—
383	C₂²×C₁₃₇	—	4	4	no	—
384	C₂²×C₁₃₇	—	8	8	no	—
385	C₂²×C₁₃₇	C₂×#123	1	4	yes	—
386	C₂²×C₁₃₇	C₂×#123	1	4	yes	—
387	C₂²×C₁₃₇	C₂×#123	1	4	yes	—
388	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
389	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
392	C₂²×C₁₃₇	#585	1	2	yes	—
393	C₄×C₁₃₇	—	2	4	no	—
394	C₄×C₁₃₇	—	2	4	no	—
395	C₄×C₁₃₇	—	4	2	no	—
396	C₄×C₁₃₇	—	4	4	no	—
397	C₄×C₁₃₇	—	4	2	no	—
398	C₄×C₁₃₇	—	4	2	no	—
399	C₄×C₁₃₇	—	4	2	no	—
400	C₄×C₁₃₇	—	4	2	no	—
401	C₄×C₁₃₇	—	4	2	no	—
402	C₄×C₁₃₇	—	4	4	no	—
403	C₂×C₁₃₇	—	2	4	no	—
404	C₂×C₁₃₇	—	2	4	no	—
405	C₂×C₁₃₇	—	2	4	no	—
406	C₂×C₁₃₇	—	4	4	no	—
407	C₂×C₁₃₇	—	8	2	no	—
408	C₂×C₁₃₇	C₂²×#123	1	1	yes	characteristic
409	C₂×C₁₃₇	#3459	1	2	yes	—
410	C₂×C₁₃₇	#3484	1	1	yes	characteristic
411	C₂×C₁₃₇	#3485	1	1	yes	characteristic
412	C₂×C₁₃₇	#3505	1	2	yes	—
413	#34983	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₁₃₇	#34983	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#534	C₂×C₁₃₇	1	1	yes	characteristic
416	C₂²×C₄×D₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
417	#2853	C₂×C₁₃₇	1	2	yes	complemented
418	#2849	C₂×C₁₃₇	1	2	yes	complemented
419	#2623	C₂×C₁₃₇	1	2	yes	complemented
420	#2622	C₂×C₁₃₇	1	2	yes	complemented
421	#2444	C₂×C₁₃₇	1	4	yes	complemented
422	#2443	C₂×C₁₃₇	1	4	yes	complemented
423	#2419	C₂×C₁₃₇	1	4	yes	complemented
424	#2418	C₂×C₁₃₇	1	4	yes	complemented
425	#2315	C₂×C₁₃₇	1	1	yes	characteristic, complemented
426	#2308	C₂×C₁₃₇	1	1	yes	characteristic, complemented
427	#2308	C₂×C₁₃₇	1	1	yes	characteristic, complemented
428	C₂×#386	C₂×C₁₃₇	1	1	yes	characteristic, complemented
429	C₂×#385	C₂×C₁₃₇	1	1	yes	characteristic, complemented
430	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
431	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
432	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
433	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
434	#534	—	2	8	no	—
435	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
436	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
437	C₂×#123	C₂²×C₁₃₇	1	4	yes	complemented
438	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
439	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
440	C₂×#120	C₂²×C₁₃₇	1	2	yes	—
441	C₂×#120	C₂²×C₁₃₇	1	2	yes	—
442	C₂×C₄×D₄	—	2	8	no	—
443	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
444	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	complemented
445	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
446	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
447	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
452	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
453	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
454	#400	C₂²×C₁₃₇	1	4	yes	complemented
455	#399	C₂²×C₁₃₇	1	4	yes	complemented
456	#398	C₂²×C₁₃₇	1	4	yes	complemented
457	#397	C₂²×C₁₃₇	1	4	yes	complemented
458	#397	C₂²×C₁₃₇	1	4	yes	complemented
459	#397	C₂²×C₁₃₇	1	4	yes	complemented
460	#394	C₂²×C₁₃₇	1	4	yes	complemented
461	#394	C₂²×C₁₃₇	1	4	yes	complemented
462	#388	C₂²×C₁₃₇	1	4	yes	complemented
463	#388	C₂²×C₁₃₇	1	4	yes	complemented
464	#387	C₂²×C₁₃₇	1	4	yes	complemented
465	#387	C₂²×C₁₃₇	1	4	yes	complemented
466	#386	C₂²×C₁₃₇	1	2	yes	—
467	#386	C₂²×C₁₃₇	1	2	yes	—
468	#386	C₂²×C₁₃₇	1	4	yes	—
469	#386	C₂²×C₁₃₇	1	2	yes	—
470	#386	C₂²×C₁₃₇	1	2	yes	—
471	#386	C₂²×C₁₃₇	1	4	yes	complemented
472	#386	C₂²×C₁₃₇	1	4	yes	complemented
473	#386	C₂²×C₁₃₇	1	4	yes	complemented
474	#386	C₂²×C₁₃₇	1	4	yes	complemented
475	#385	C₂²×C₁₃₇	1	2	yes	complemented
476	#385	C₂²×C₁₃₇	1	2	yes	complemented
477	#385	C₂²×C₁₃₇	1	2	yes	complemented
478	#385	C₂²×C₁₃₇	1	2	yes	complemented
479	#385	C₂²×C₁₃₇	1	2	yes	complemented
480	#385	C₂²×C₁₃₇	1	4	yes	complemented
481	#385	C₂²×C₁₃₇	1	2	yes	complemented
482	#385	C₂²×C₁₃₇	1	4	yes	complemented
483	#381	C₂²×C₁₃₇	1	2	yes	complemented
484	#381	C₂²×C₁₃₇	1	2	yes	complemented
485	#381	C₂²×C₁₃₇	1	4	yes	complemented
486	#380	C₂²×C₁₃₇	1	4	yes	complemented
487	#379	C₂²×C₁₃₇	1	2	yes	complemented
488	#379	C₂²×C₁₃₇	1	2	yes	complemented
489	C₂×#95	C₂²×C₁₃₇	1	2	yes	complemented
490	C₂×#95	C₂²×C₁₃₇	1	2	yes	complemented
491	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
492	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
493	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	D₄×C₁₃₇	1	8	yes	—
500	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
501	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
503	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
504	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
505	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
506	C₂³×C₄	—	2	4	no	—
507	C₂³×C₄	—	2	4	no	—
508	C₂³×C₄	—	4	4	no	—
509	C₂³×C₄	—	4	4	no	—
510	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
521	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
523	#123	—	2	8	no	—
524	#123	—	2	8	no	—
525	#123	—	4	8	no	—
526	#121	—	2	8	no	—
527	#121	—	2	8	no	—
528	#120	—	2	8	no	—
529	#120	—	2	8	no	—
530	C₄×D₄	—	2	16	no	—
531	C₄×D₄	—	2	16	no	—
532	C₂×C₄⋊C₄	—	2	4	no	—
533	C₂×C₄⋊C₄	—	4	4	no	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₂²⋊C₄	—	2	4	no	—
546	C₂×C₂²⋊C₄	—	4	4	no	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
566	C₂×C₄²	—	2	4	no	—
567	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
568	#95	C₂³×C₁₃₇	1	4	yes	—
569	#95	C₂³×C₁₃₇	1	4	yes	—
570	#95	C₂³×C₁₃₇	1	4	yes	—
571	#95	C₂³×C₁₃₇	1	4	yes	—
572	#95	C₂³×C₁₃₇	1	4	yes	—
573	#95	C₂³×C₁₃₇	1	4	yes	—
574	#95	C₂³×C₁₃₇	1	4	yes	—
575	#95	C₂³×C₁₃₇	1	4	yes	—
576	#95	C₂³×C₁₃₇	1	4	yes	—
577	#95	C₂³×C₁₃₇	1	4	yes	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	—	4	2	no	—
585	C₂⁴	—	4	2	no	—
586	C₂⁴	—	4	2	no	—
587	C₂⁴	—	4	2	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	C₂×D₄×C₁₃₇	1	4	yes	—
590	C₂⁴	C₂×D₄×C₁₃₇	1	4	yes	—
591	C₂⁴	#41×C₁₃₇	1	4	yes	—
592	C₂⁴	#41×C₁₃₇	1	4	yes	—
593	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
594	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
595	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
596	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
597	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
598	C₂×D₄	—	2	32	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	16	no	—
614	C₂×D₄	C₂×D₄×C₁₃₇	1	8	yes	—
615	C₂×D₄	C₂×D₄×C₁₃₇	1	8	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	16	no	—
649	C₂²×C₄	—	4	16	no	—
650	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
661	C₄⋊C₄	—	2	8	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	4	4	no	—
683	C₂²⋊C₄	—	4	4	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	—	4	4	no	—
686	C₂²⋊C₄	—	4	4	no	—
687	C₄²	—	2	8	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	8	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	4	no	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	4	4	no	—
705	C₂³	—	4	4	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	4	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	4	8	no	—
712	C₂³	—	4	8	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	8	2	no	—
715	C₂³	—	8	2	no	—
716	C₂³	—	8	4	no	—
717	C₂³	#123×C₁₃₇	1	16	yes	complemented
718	C₂³	C₂²×D₄×C₁₃₇	1	4	yes	—
719	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
720	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
721	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
722	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
723	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
724	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
725	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
726	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
727	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
728	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
729	D₄	—	2	16	no	—
730	D₄	—	2	16	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	8	4	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	8	no	—
736	C₂×C₄	—	2	8	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	16	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	8	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	8	2	no	—
770	C₂×C₄	—	8	2	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
773	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	4	16	no	—
790	C₂²	—	4	16	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	8	8	no	—
799	C₂²	C₂×#123×C₁₃₇	1	4	yes	—
800	C₂²	C₂×#123×C₁₃₇	1	4	yes	—
801	C₂²	C₂×#123×C₁₃₇	1	4	yes	—
802	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
803	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
804	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
805	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
806	C₂²	#585×C₁₃₇	1	2	yes	—
807	C₄	—	2	4	no	—
808	C₄	—	2	4	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	4	no	—
817	C₂	—	2	4	no	—
818	C₂	—	2	4	no	—
819	C₂	—	2	4	no	—
820	C₂	—	4	4	no	—
821	C₂	—	8	2	no	—
822	C₂	C₂²×#123×C₁₃₇	1	1	yes	characteristic
823	C₂	#3459×C₁₃₇	1	2	yes	—
824	C₂	#3484×C₁₃₇	1	1	yes	characteristic
825	C₂	#3485×C₁₃₇	1	1	yes	characteristic
826	C₂	#3505×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂×#534×C₁₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₁₃₇	C₂	semidirect
3. #2853×C₁₃₇	C₂	semidirect
4. #2849×C₁₃₇	C₂	semidirect
5. #2623×C₁₃₇	C₂	semidirect
6. #2622×C₁₃₇	C₂	semidirect
7. #2444×C₁₃₇	C₂	semidirect
8. #2443×C₁₃₇	C₂	semidirect
9. #2419×C₁₃₇	C₂	semidirect
10. #2418×C₁₃₇	C₂	semidirect
11. #2315×C₁₃₇	C₂	semidirect
12. #2308×C₁₃₇	C₂	semidirect
13. #2308×C₁₃₇	C₂	semidirect
14. C₂×#386×C₁₃₇	C₂	semidirect
15. C₂×#385×C₁₃₇	C₂	semidirect
19. C₂⁴×C₄×C₁₃₇	C₂²	semidirect
23. C₂×#123×C₁₃₇	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃₇	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₁₃₇	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₃₇	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
39. C₂²×C₄²×C₁₃₇	C₂²	semidirect
40. #400×C₁₃₇	C₂²	semidirect
41. #399×C₁₃₇	C₂²	semidirect
42. #398×C₁₃₇	C₂²	semidirect
43. #397×C₁₃₇	C₂²	semidirect
44. #397×C₁₃₇	C₂²	semidirect
45. #397×C₁₃₇	C₂²	semidirect
46. #394×C₁₃₇	C₂²	semidirect
47. #394×C₁₃₇	C₂²	semidirect
48. #388×C₁₃₇	C₂²	semidirect
49. #388×C₁₃₇	C₂²	semidirect
50. #387×C₁₃₇	C₂²	semidirect
51. #387×C₁₃₇	C₂²	semidirect
57. #386×C₁₃₇	C₂²	semidirect
58. #386×C₁₃₇	C₂²	semidirect
59. #386×C₁₃₇	C₂²	semidirect
60. #386×C₁₃₇	C₂²	semidirect
61. #385×C₁₃₇	C₂²	semidirect
62. #385×C₁₃₇	C₂²	semidirect
63. #385×C₁₃₇	C₂²	semidirect
64. #385×C₁₃₇	C₂²	semidirect
65. #385×C₁₃₇	C₂²	semidirect
66. #385×C₁₃₇	C₂²	semidirect
67. #385×C₁₃₇	C₂²	semidirect
68. #385×C₁₃₇	C₂²	semidirect
69. #381×C₁₃₇	C₂²	semidirect
70. #381×C₁₃₇	C₂²	semidirect
71. #381×C₁₃₇	C₂²	semidirect
72. #380×C₁₃₇	C₂²	semidirect
73. #379×C₁₃₇	C₂²	semidirect
74. #379×C₁₃₇	C₂²	semidirect
75. C₂×#95×C₁₃₇	C₂²	semidirect
76. C₂×#95×C₁₃₇	C₂²	semidirect
303. C₂³×C₁₃₇	#123	semidirect
413. #34983	C₁₃₇	direct (N × H)
414. C₁₃₇	#34983	direct (N × H)
416. C₂²×C₄×D₄	C₂×C₁₃₇	semidirect
417. #2853	C₂×C₁₃₇	semidirect
418. #2849	C₂×C₁₃₇	semidirect
419. #2623	C₂×C₁₃₇	semidirect
420. #2622	C₂×C₁₃₇	semidirect
421. #2444	C₂×C₁₃₇	semidirect
422. #2443	C₂×C₁₃₇	semidirect
423. #2419	C₂×C₁₃₇	semidirect
424. #2418	C₂×C₁₃₇	semidirect
425. #2315	C₂×C₁₃₇	semidirect
426. #2308	C₂×C₁₃₇	semidirect
427. #2308	C₂×C₁₃₇	semidirect
428. C₂×#386	C₂×C₁₃₇	semidirect
429. C₂×#385	C₂×C₁₃₇	semidirect
433. C₂⁴×C₄	C₂²×C₁₃₇	semidirect
437. C₂×#123	C₂²×C₁₃₇	semidirect
444. C₂×C₄×D₄	C₂²×C₁₃₇	semidirect
445. C₂²×C₄⋊C₄	C₂²×C₁₃₇	semidirect
446. C₂²×C₄⋊C₄	C₂²×C₁₃₇	semidirect
451. C₂²×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
452. C₂²×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
453. C₂²×C₄²	C₂²×C₁₃₇	semidirect
454. #400	C₂²×C₁₃₇	semidirect
455. #399	C₂²×C₁₃₇	semidirect
456. #398	C₂²×C₁₃₇	semidirect
457. #397	C₂²×C₁₃₇	semidirect
458. #397	C₂²×C₁₃₇	semidirect
459. #397	C₂²×C₁₃₇	semidirect
460. #394	C₂²×C₁₃₇	semidirect
461. #394	C₂²×C₁₃₇	semidirect
462. #388	C₂²×C₁₃₇	semidirect
463. #388	C₂²×C₁₃₇	semidirect
464. #387	C₂²×C₁₃₇	semidirect
465. #387	C₂²×C₁₃₇	semidirect
471. #386	C₂²×C₁₃₇	semidirect
472. #386	C₂²×C₁₃₇	semidirect
473. #386	C₂²×C₁₃₇	semidirect
474. #386	C₂²×C₁₃₇	semidirect
475. #385	C₂²×C₁₃₇	semidirect
476. #385	C₂²×C₁₃₇	semidirect
477. #385	C₂²×C₁₃₇	semidirect
478. #385	C₂²×C₁₃₇	semidirect
479. #385	C₂²×C₁₃₇	semidirect
480. #385	C₂²×C₁₃₇	semidirect
481. #385	C₂²×C₁₃₇	semidirect
482. #385	C₂²×C₁₃₇	semidirect
483. #381	C₂²×C₁₃₇	semidirect
484. #381	C₂²×C₁₃₇	semidirect
485. #381	C₂²×C₁₃₇	semidirect
486. #380	C₂²×C₁₃₇	semidirect
487. #379	C₂²×C₁₃₇	semidirect
488. #379	C₂²×C₁₃₇	semidirect
489. C₂×#95	C₂²×C₁₃₇	semidirect
490. C₂×#95	C₂²×C₁₃₇	semidirect
717. C₂³	#123×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#534×C₁₃₇	2
C₂²×C₄×D₄×C₁₃₇	2
#2853×C₁₃₇	2
#2849×C₁₃₇	2
#2623×C₁₃₇	2
#2622×C₁₃₇	2
#2444×C₁₃₇	2
#2443×C₁₃₇	2
#2419×C₁₃₇	2
#2418×C₁₃₇	2
#2315×C₁₃₇	2
#2308×C₁₃₇	2
C₂×#386×C₁₃₇	2
C₂×#385×C₁₃₇	2
#34983	137

Subgroups — C137×#34983 #46884369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34983 #46884369