Subgroups — C₁₃₇×#35006 #46884392

Order 35072.

2322 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#2857×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	#2854×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2639×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2618×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2560×C₁₃₇	C₂	1	4	yes	maximal, complemented
8	#2558×C₁₃₇	C₂	1	4	yes	maximal, complemented
9	#2512×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2506×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#2452×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	#2445×C₁₃₇	C₂	1	2	yes	maximal, complemented
13	#2325×C₁₃₇	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₁₃₇	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#539×C₁₃₇	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#126×C₁₃₇	C₂²	1	4	yes	—
20	C₂×#125×C₁₃₇	C₂²	1	4	yes	—
21	C₂×#123×C₁₃₇	C₂²	1	4	yes	—
22	C₂×#123×C₁₃₇	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
35	#400×C₁₃₇	C₂²	1	4	yes	—
36	#398×C₁₃₇	C₂²	1	4	yes	—
37	#397×C₁₃₇	C₂²	1	4	yes	—
38	#396×C₁₃₇	C₂²	1	4	yes	—
39	#396×C₁₃₇	C₂²	1	4	yes	—
40	#394×C₁₃₇	C₂²	1	4	yes	—
41	#394×C₁₃₇	C₂²	1	4	yes	—
42	#393×C₁₃₇	C₂²	1	4	yes	—
43	#391×C₁₃₇	C₂²	1	2	yes	—
44	#390×C₁₃₇	C₂²	1	2	yes	—
45	#390×C₁₃₇	C₂²	1	2	yes	—
46	#390×C₁₃₇	C₂²	1	2	yes	—
47	#390×C₁₃₇	C₂²	1	2	yes	—
48	#390×C₁₃₇	C₂²	1	2	yes	—
49	#390×C₁₃₇	C₂²	1	2	yes	—
50	#389×C₁₃₇	C₂²	1	2	yes	—
51	#389×C₁₃₇	C₂²	1	2	yes	—
52	#389×C₁₃₇	C₂²	1	2	yes	—
53	#389×C₁₃₇	C₂²	1	2	yes	—
54	#389×C₁₃₇	C₂²	1	2	yes	—
55	#388×C₁₃₇	C₂²	1	4	yes	—
56	#388×C₁₃₇	C₂²	1	4	yes	—
57	#388×C₁₃₇	C₂²	1	4	yes	—
58	#388×C₁₃₇	C₂²	1	4	yes	—
59	#387×C₁₃₇	C₂²	1	4	yes	—
60	#386×C₁₃₇	C₂²	1	4	yes	—
61	#386×C₁₃₇	C₂²	1	4	yes	—
62	#386×C₁₃₇	C₂²	1	4	yes	—
63	#385×C₁₃₇	C₂²	1	4	yes	—
64	#384×C₁₃₇	C₂²	1	1	yes	characteristic
65	#384×C₁₃₇	C₂²	1	1	yes	characteristic
66	#380×C₁₃₇	C₂²	1	2	yes	—
67	#380×C₁₃₇	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
74	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
75	C₂×#95×C₁₃₇	C₂²	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃₇	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₇	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₁₃₇	—	4	2	no	—
90	#127×C₁₃₇	—	4	2	no	—
91	#126×C₁₃₇	—	2	16	no	—
92	#125×C₁₃₇	—	2	16	no	—
93	#123×C₁₃₇	—	2	16	no	—
94	#123×C₁₃₇	—	2	16	no	—
95	C₂²⋊Q₈×C₁₃₇	—	2	8	no	—
96	C₂²⋊Q₈×C₁₃₇	—	2	16	no	—
97	#121×C₁₃₇	—	2	8	no	—
98	#121×C₁₃₇	—	2	8	no	—
99	#121×C₁₃₇	—	2	8	no	—
100	C₄×D₄×C₁₃₇	—	2	16	no	—
101	C₄×D₄×C₁₃₇	—	4	4	no	—
102	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₃₇	D₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₇	—	2	4	no	—
132	C₂×C₄²×C₁₃₇	—	4	2	no	—
133	C₂×C₄²×C₁₃₇	—	4	2	no	—
134	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
143	#95×C₁₃₇	C₂³	1	2	yes	—
144	#95×C₁₃₇	C₂³	1	2	yes	—
145	#95×C₁₃₇	C₂³	1	2	yes	—
146	#95×C₁₃₇	C₂³	1	2	yes	—
147	#95×C₁₃₇	C₂³	1	4	yes	—
148	#95×C₁₃₇	C₂³	1	4	yes	—
149	#95×C₁₃₇	C₂³	1	4	yes	—
150	#95×C₁₃₇	C₂³	1	4	yes	—
151	#95×C₁₃₇	C₂³	1	4	yes	—
152	#95×C₁₃₇	C₂³	1	4	yes	—
153	C₂⁴×C₁₃₇	C₂⁴	1	4	yes	—
154	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₁₃₇	—	2	4	no	—
156	C₂×Q₈×C₁₃₇	—	4	2	no	—
157	C₂×Q₈×C₁₃₇	—	4	2	no	—
158	C₂×D₄×C₁₃₇	—	2	8	no	—
159	C₂×D₄×C₁₃₇	—	2	8	no	—
160	C₂×D₄×C₁₃₇	—	2	8	no	—
161	C₂×D₄×C₁₃₇	—	2	4	no	—
162	C₂×D₄×C₁₃₇	—	2	4	no	—
163	C₂×D₄×C₁₃₇	—	2	4	no	—
164	C₂×D₄×C₁₃₇	—	2	4	no	—
165	C₂×D₄×C₁₃₇	—	2	4	no	—
166	C₂×D₄×C₁₃₇	—	4	2	no	—
167	C₂×D₄×C₁₃₇	—	4	2	no	—
168	C₂×D₄×C₁₃₇	—	4	2	no	—
169	C₂×D₄×C₁₃₇	—	4	2	no	—
170	C₂²×C₄×C₁₃₇	—	2	2	no	—
171	C₂²×C₄×C₁₃₇	—	2	2	no	—
172	C₂²×C₄×C₁₃₇	—	2	2	no	—
173	C₂²×C₄×C₁₃₇	—	2	2	no	—
174	C₂²×C₄×C₁₃₇	—	2	2	no	—
175	C₂²×C₄×C₁₃₇	—	2	2	no	—
176	C₂²×C₄×C₁₃₇	—	2	8	no	—
177	C₂²×C₄×C₁₃₇	—	4	1	no	—
178	C₂²×C₄×C₁₃₇	—	4	1	no	—
179	C₂²×C₄×C₁₃₇	—	4	1	no	—
180	C₂²×C₄×C₁₃₇	—	4	1	no	—
181	C₂²×C₄×C₁₃₇	—	4	1	no	—
182	C₂²×C₄×C₁₃₇	—	4	1	no	—
183	C₂²×C₄×C₁₃₇	—	4	1	no	—
184	C₂²×C₄×C₁₃₇	—	4	1	no	—
185	C₂²×C₄×C₁₃₇	—	4	1	no	—
186	C₂²×C₄×C₁₃₇	—	4	1	no	—
187	C₂²×C₄×C₁₃₇	—	4	4	no	—
188	C₂²×C₄×C₁₃₇	—	4	4	no	—
189	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
193	C₂²×C₄×C₁₃₇	#41	1	4	yes	—
194	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₁₃₇	—	2	8	no	—
208	C₄⋊C₄×C₁₃₇	—	2	4	no	—
209	C₄⋊C₄×C₁₃₇	—	2	8	no	—
210	C₄⋊C₄×C₁₃₇	—	2	8	no	—
211	C₄⋊C₄×C₁₃₇	—	2	4	no	—
212	C₄⋊C₄×C₁₃₇	—	2	8	no	—
213	C₄⋊C₄×C₁₃₇	—	2	4	no	—
214	C₄⋊C₄×C₁₃₇	—	2	4	no	—
215	C₄⋊C₄×C₁₃₇	—	2	4	no	—
216	C₄⋊C₄×C₁₃₇	—	2	4	no	—
217	C₄⋊C₄×C₁₃₇	—	2	4	no	—
218	C₄⋊C₄×C₁₃₇	—	2	4	no	—
219	C₄⋊C₄×C₁₃₇	—	4	2	no	—
220	C₄⋊C₄×C₁₃₇	—	4	2	no	—
221	C₄⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
222	C₄⋊C₄×C₁₃₇	C₂×D₄	1	8	yes	—
223	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
225	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
226	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
227	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
229	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
230	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
231	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
232	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
234	C₄²×C₁₃₇	—	2	8	no	—
235	C₄²×C₁₃₇	—	2	4	no	—
236	C₄²×C₁₃₇	—	2	4	no	—
237	C₄²×C₁₃₇	—	2	4	no	—
238	C₄²×C₁₃₇	—	2	2	no	—
239	C₄²×C₁₃₇	—	2	2	no	—
240	C₄²×C₁₃₇	—	4	1	no	—
241	C₄²×C₁₃₇	—	4	2	no	—
242	C₄²×C₁₃₇	—	4	1	no	—
243	C₂³×C₁₃₇	—	2	1	no	—
244	C₂³×C₁₃₇	—	2	1	no	—
245	C₂³×C₁₃₇	—	2	1	no	—
246	C₂³×C₁₃₇	—	2	1	no	—
247	C₂³×C₁₃₇	—	2	4	no	—
248	C₂³×C₁₃₇	—	2	4	no	—
249	C₂³×C₁₃₇	—	2	4	no	—
250	C₂³×C₁₃₇	—	2	4	no	—
251	C₂³×C₁₃₇	—	2	4	no	—
252	C₂³×C₁₃₇	—	2	4	no	—
253	C₂³×C₁₃₇	—	2	4	no	—
254	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
255	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
256	C₂³×C₁₃₇	C₂×#41	1	2	yes	—
257	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
258	Q₈×C₁₃₇	—	8	4	no	—
259	D₄×C₁₃₇	—	4	16	no	—
260	D₄×C₁₃₇	—	4	8	no	—
261	D₄×C₁₃₇	—	8	4	no	—
262	D₄×C₁₃₇	—	8	4	no	—
263	C₂×C₄×C₁₃₇	—	2	8	no	—
264	C₂×C₄×C₁₃₇	—	2	2	no	—
265	C₂×C₄×C₁₃₇	—	2	2	no	—
266	C₂×C₄×C₁₃₇	—	2	1	no	—
267	C₂×C₄×C₁₃₇	—	2	2	no	—
268	C₂×C₄×C₁₃₇	—	2	1	no	—
269	C₂×C₄×C₁₃₇	—	2	1	no	—
270	C₂×C₄×C₁₃₇	—	2	1	no	—
271	C₂×C₄×C₁₃₇	—	2	1	no	—
272	C₂×C₄×C₁₃₇	—	2	1	no	—
273	C₂×C₄×C₁₃₇	—	2	1	no	—
274	C₂×C₄×C₁₃₇	—	2	2	no	—
275	C₂×C₄×C₁₃₇	—	2	1	no	—
276	C₂×C₄×C₁₃₇	—	2	1	no	—
277	C₂×C₄×C₁₃₇	—	2	1	no	—
278	C₂×C₄×C₁₃₇	—	2	8	no	—
279	C₂×C₄×C₁₃₇	—	2	4	no	—
280	C₂×C₄×C₁₃₇	—	2	4	no	—
281	C₂×C₄×C₁₃₇	—	2	4	no	—
282	C₂×C₄×C₁₃₇	—	2	2	no	—
283	C₂×C₄×C₁₃₇	—	2	4	no	—
284	C₂×C₄×C₁₃₇	—	2	4	no	—
285	C₂×C₄×C₁₃₇	—	2	2	no	—
286	C₂×C₄×C₁₃₇	—	2	2	no	—
287	C₂×C₄×C₁₃₇	—	2	4	no	—
288	C₂×C₄×C₁₃₇	—	2	4	no	—
289	C₂×C₄×C₁₃₇	—	2	4	no	—
290	C₂×C₄×C₁₃₇	—	2	2	no	—
291	C₂×C₄×C₁₃₇	—	2	2	no	—
292	C₂×C₄×C₁₃₇	—	2	2	no	—
293	C₂×C₄×C₁₃₇	—	2	4	no	—
294	C₂×C₄×C₁₃₇	—	4	4	no	—
295	C₂×C₄×C₁₃₇	—	4	4	no	—
296	C₂×C₄×C₁₃₇	—	4	4	no	—
297	C₂×C₄×C₁₃₇	—	4	4	no	—
298	C₂×C₄×C₁₃₇	—	4	4	no	—
299	C₂×C₄×C₁₃₇	—	8	8	no	—
300	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₁₃₇	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
305	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
306	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
307	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
308	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
309	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
310	C₂²×C₁₃₇	—	2	2	no	—
311	C₂²×C₁₃₇	—	2	2	no	—
312	C₂²×C₁₃₇	—	2	2	no	—
313	C₂²×C₁₃₇	—	2	2	no	—
314	C₂²×C₁₃₇	—	2	2	no	—
315	C₂²×C₁₃₇	—	2	2	no	—
316	C₂²×C₁₃₇	—	4	4	no	—
317	C₂²×C₁₃₇	—	4	4	no	—
318	C₂²×C₁₃₇	—	4	4	no	—
319	C₂²×C₁₃₇	—	4	4	no	—
320	C₂²×C₁₃₇	—	4	4	no	—
321	C₂²×C₁₃₇	—	4	4	no	—
322	C₂²×C₁₃₇	—	4	4	no	—
323	C₂²×C₁₃₇	#532	1	4	yes	—
324	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
325	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	C₂²×C₁₃₇	#585	1	1	yes	characteristic
330	C₂²×C₁₃₇	#585	1	1	yes	characteristic
331	C₄×C₁₃₇	—	2	4	no	—
332	C₄×C₁₃₇	—	2	2	no	—
333	C₄×C₁₃₇	—	2	4	no	—
334	C₄×C₁₃₇	—	2	2	no	—
335	C₄×C₁₃₇	—	2	2	no	—
336	C₄×C₁₃₇	—	2	2	no	—
337	C₄×C₁₃₇	—	2	2	no	—
338	C₄×C₁₃₇	—	4	4	no	—
339	C₄×C₁₃₇	—	4	2	no	—
340	C₄×C₁₃₇	—	4	4	no	—
341	C₄×C₁₃₇	—	4	4	no	—
342	C₄×C₁₃₇	—	4	2	no	—
343	C₄×C₁₃₇	#539	1	4	yes	complemented
344	C₂×C₁₃₇	—	2	4	no	—
345	C₂×C₁₃₇	—	8	4	no	—
346	C₂×C₁₃₇	C₂×#532	1	1	yes	characteristic
347	C₂×C₁₃₇	C₂×#539	1	1	yes	characteristic
348	C₂×C₁₃₇	#3455	1	1	yes	characteristic
349	C₂×C₁₃₇	#3496	1	1	yes	characteristic
350	C₂×C₁₃₇	#3497	1	1	yes	characteristic
351	C₂×C₁₃₇	#3505	1	1	yes	characteristic
352	C₂×C₁₃₇	#3507	1	1	yes	characteristic
353	#35006	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₁₃₇	#35006	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#539	C₂×C₁₃₇	1	2	yes	complemented
356	#2857	C₂×C₁₃₇	1	1	yes	characteristic, complemented
357	#2856	C₂×C₁₃₇	1	1	yes	characteristic
358	#2854	C₂×C₁₃₇	1	2	yes	complemented
359	#2639	C₂×C₁₃₇	1	2	yes	complemented
360	#2618	C₂×C₁₃₇	1	2	yes	complemented
361	#2560	C₂×C₁₃₇	1	4	yes	complemented
362	#2558	C₂×C₁₃₇	1	4	yes	complemented
363	#2512	C₂×C₁₃₇	1	2	yes	complemented
364	#2506	C₂×C₁₃₇	1	2	yes	complemented
365	#2452	C₂×C₁₃₇	1	2	yes	complemented
366	#2445	C₂×C₁₃₇	1	2	yes	complemented
367	#2325	C₂×C₁₃₇	1	2	yes	complemented
368	C₄×#121	C₂×C₁₃₇	1	2	yes	complemented
369	C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	1	1	yes	characteristic, complemented
370	#539	—	2	16	no	—
371	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
372	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
373	C₂×#126	C₂²×C₁₃₇	1	4	yes	—
374	C₂×#125	C₂²×C₁₃₇	1	4	yes	—
375	C₂×#123	C₂²×C₁₃₇	1	4	yes	—
376	C₂×#123	C₂²×C₁₃₇	1	4	yes	—
377	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	4	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
379	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
380	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
381	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
383	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
384	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
389	#400	C₂²×C₁₃₇	1	4	yes	—
390	#398	C₂²×C₁₃₇	1	4	yes	—
391	#397	C₂²×C₁₃₇	1	4	yes	—
392	#396	C₂²×C₁₃₇	1	4	yes	—
393	#396	C₂²×C₁₃₇	1	4	yes	—
394	#394	C₂²×C₁₃₇	1	4	yes	—
395	#394	C₂²×C₁₃₇	1	4	yes	—
396	#393	C₂²×C₁₃₇	1	4	yes	—
397	#391	C₂²×C₁₃₇	1	2	yes	—
398	#390	C₂²×C₁₃₇	1	2	yes	—
399	#390	C₂²×C₁₃₇	1	2	yes	—
400	#390	C₂²×C₁₃₇	1	2	yes	—
401	#390	C₂²×C₁₃₇	1	2	yes	—
402	#390	C₂²×C₁₃₇	1	2	yes	—
403	#390	C₂²×C₁₃₇	1	2	yes	—
404	#389	C₂²×C₁₃₇	1	2	yes	—
405	#389	C₂²×C₁₃₇	1	2	yes	—
406	#389	C₂²×C₁₃₇	1	2	yes	—
407	#389	C₂²×C₁₃₇	1	2	yes	—
408	#389	C₂²×C₁₃₇	1	2	yes	—
409	#388	C₂²×C₁₃₇	1	4	yes	—
410	#388	C₂²×C₁₃₇	1	4	yes	—
411	#388	C₂²×C₁₃₇	1	4	yes	—
412	#388	C₂²×C₁₃₇	1	4	yes	—
413	#387	C₂²×C₁₃₇	1	4	yes	—
414	#386	C₂²×C₁₃₇	1	4	yes	—
415	#386	C₂²×C₁₃₇	1	4	yes	—
416	#386	C₂²×C₁₃₇	1	4	yes	—
417	#385	C₂²×C₁₃₇	1	4	yes	—
418	#384	C₂²×C₁₃₇	1	1	yes	characteristic
419	#384	C₂²×C₁₃₇	1	1	yes	characteristic
420	#380	C₂²×C₁₃₇	1	2	yes	—
421	#380	C₂²×C₁₃₇	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
425	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
428	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
429	C₂×#95	C₂²×C₁₃₇	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
431	C₂²×D₄	C₂³×C₁₃₇	1	4	yes	—
432	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
433	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
434	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
435	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₁₃₇	1	4	yes	—
439	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
443	C₄⋊Q₈	—	4	2	no	—
444	#127	—	4	2	no	—
445	#126	—	2	16	no	—
446	#125	—	2	16	no	—
447	#123	—	2	16	no	—
448	#123	—	2	16	no	—
449	C₂²⋊Q₈	—	2	8	no	—
450	C₂²⋊Q₈	—	2	16	no	—
451	#121	—	2	8	no	—
452	#121	—	2	8	no	—
453	#121	—	2	8	no	—
454	C₄×D₄	—	2	16	no	—
455	C₄×D₄	—	4	4	no	—
456	C₂×C₄⋊C₄	—	2	4	no	—
457	C₂×C₄⋊C₄	D₄×C₁₃₇	1	8	yes	complemented
458	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
485	C₂×C₄²	—	2	4	no	—
486	C₂×C₄²	—	4	2	no	—
487	C₂×C₄²	—	4	2	no	—
488	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
489	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
490	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
494	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
497	#95	C₂³×C₁₃₇	1	2	yes	—
498	#95	C₂³×C₁₃₇	1	2	yes	—
499	#95	C₂³×C₁₃₇	1	2	yes	—
500	#95	C₂³×C₁₃₇	1	2	yes	—
501	#95	C₂³×C₁₃₇	1	4	yes	—
502	#95	C₂³×C₁₃₇	1	4	yes	—
503	#95	C₂³×C₁₃₇	1	4	yes	—
504	#95	C₂³×C₁₃₇	1	4	yes	—
505	#95	C₂³×C₁₃₇	1	4	yes	—
506	#95	C₂³×C₁₃₇	1	4	yes	—
507	C₂⁴	C₂⁴×C₁₃₇	1	4	yes	—
508	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	4	2	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	1	no	—
535	C₂²×C₄	—	4	1	no	—
536	C₂²×C₄	—	4	1	no	—
537	C₂²×C₄	—	4	1	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	1	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
545	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
546	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
547	C₂²×C₄	#41×C₁₃₇	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	8	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
576	C₄⋊C₄	C₂×D₄×C₁₃₇	1	8	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	—	4	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	4	4	no	—
588	C₄²	—	2	8	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	4	1	no	—
595	C₄²	—	4	2	no	—
596	C₄²	—	4	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	4	no	—
608	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
609	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
610	C₂³	C₂×#41×C₁₃₇	1	2	yes	—
611	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
612	Q₈	—	8	4	no	—
613	D₄	—	4	16	no	—
614	D₄	—	4	8	no	—
615	D₄	—	8	4	no	—
616	D₄	—	8	4	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	—	8	8	no	—
654	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃₇	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
658	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
659	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
660	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
661	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
662	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
663	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	4	4	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	4	4	no	—
677	C₂²	#532×C₁₃₇	1	4	yes	—
678	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
679	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
680	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
681	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
682	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
683	C₂²	#585×C₁₃₇	1	1	yes	characteristic
684	C₂²	#585×C₁₃₇	1	1	yes	characteristic
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	2	no	—
697	C₄	#539×C₁₃₇	1	4	yes	complemented
698	C₂	—	2	4	no	—
699	C₂	—	8	4	no	—
700	C₂	C₂×#532×C₁₃₇	1	1	yes	characteristic
701	C₂	C₂×#539×C₁₃₇	1	1	yes	characteristic
702	C₂	#3455×C₁₃₇	1	1	yes	characteristic
703	C₂	#3496×C₁₃₇	1	1	yes	characteristic
704	C₂	#3497×C₁₃₇	1	1	yes	characteristic
705	C₂	#3505×C₁₃₇	1	1	yes	characteristic
706	C₂	#3507×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	#2856×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
1. C₂×#539×C₁₃₇	C₂	semidirect
2. #2857×C₁₃₇	C₂	semidirect
4. #2854×C₁₃₇	C₂	semidirect
5. #2639×C₁₃₇	C₂	semidirect
6. #2618×C₁₃₇	C₂	semidirect
7. #2560×C₁₃₇	C₂	semidirect
8. #2558×C₁₃₇	C₂	semidirect
9. #2512×C₁₃₇	C₂	semidirect
10. #2506×C₁₃₇	C₂	semidirect
11. #2452×C₁₃₇	C₂	semidirect
12. #2445×C₁₃₇	C₂	semidirect
13. #2325×C₁₃₇	C₂	semidirect
14. C₄×#121×C₁₃₇	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₁₃₇	C₂	semidirect
103. C₂×C₄⋊C₄×C₁₃₇	D₄	semidirect
343. C₄×C₁₃₇	#539	semidirect
353. #35006	C₁₃₇	direct (N × H)
354. C₁₃₇	#35006	direct (N × H)
355. C₂×#539	C₂×C₁₃₇	semidirect
356. #2857	C₂×C₁₃₇	semidirect
358. #2854	C₂×C₁₃₇	semidirect
359. #2639	C₂×C₁₃₇	semidirect
360. #2618	C₂×C₁₃₇	semidirect
361. #2560	C₂×C₁₃₇	semidirect
362. #2558	C₂×C₁₃₇	semidirect
363. #2512	C₂×C₁₃₇	semidirect
364. #2506	C₂×C₁₃₇	semidirect
365. #2452	C₂×C₁₃₇	semidirect
366. #2445	C₂×C₁₃₇	semidirect
367. #2325	C₂×C₁₃₇	semidirect
368. C₄×#121	C₂×C₁₃₇	semidirect
369. C₂×C₄×C₄⋊C₄	C₂×C₁₃₇	semidirect
457. C₂×C₄⋊C₄	D₄×C₁₃₇	semidirect
697. C₄	#539×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₁₃₇	2
#2857×C₁₃₇	2
#2856×C₁₃₇	2
#2854×C₁₃₇	2
#2639×C₁₃₇	2
#2618×C₁₃₇	2
#2560×C₁₃₇	2
#2558×C₁₃₇	2
#2512×C₁₃₇	2
#2506×C₁₃₇	2
#2452×C₁₃₇	2
#2445×C₁₃₇	2
#2325×C₁₃₇	2
C₄×#121×C₁₃₇	2
C₂×C₄×C₄⋊C₄×C₁₃₇	2
#35006	137

Subgroups — C137×#35006 #46884392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#35006 #46884392