Subgroups — C₁₃₇×#34875 #46884261

Order 35072.

2802 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#2609×C₁₃₇	C₂	1	4	yes	maximal, complemented
4	#2599×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2598×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2579×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2534×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2484×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#2482×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#2406×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#2404×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#2396×C₁₃₇	C₂	1	2	yes	maximal, complemented
13	#2392×C₁₃₇	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₁₃₇	C₂	1	2	yes	maximal, complemented
15	C₄×#120×C₁₃₇	C₂	1	2	yes	maximal, complemented
16	#2290×C₁₃₇	C₂	1	4	yes	maximal, complemented
17	#2283×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#120×C₁₃₇	C₂²	1	2	yes	—
22	C₄×#41×C₁₃₇	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#117×C₁₃₇	—	2	8	no	—
31	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
32	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₇	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₃₇	C₂²	1	2	yes	complemented
37	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₇	C₂²	1	2	yes	complemented
44	#400×C₁₃₇	C₂²	1	2	yes	complemented
45	#399×C₁₃₇	C₂²	1	2	yes	—
46	#398×C₁₃₇	C₂²	1	4	yes	complemented
47	#398×C₁₃₇	C₂²	1	2	yes	complemented
48	#397×C₁₃₇	C₂²	1	2	yes	—
49	#396×C₁₃₇	C₂²	1	4	yes	—
50	#396×C₁₃₇	C₂²	1	4	yes	complemented
51	#395×C₁₃₇	C₂²	1	2	yes	complemented
52	#394×C₁₃₇	C₂²	1	4	yes	—
53	#394×C₁₃₇	C₂²	1	2	yes	complemented
54	#393×C₁₃₇	C₂²	1	2	yes	—
55	#392×C₁₃₇	C₂²	1	2	yes	—
56	#388×C₁₃₇	C₂²	1	4	yes	—
57	#388×C₁₃₇	C₂²	1	4	yes	—
58	#388×C₁₃₇	C₂²	1	4	yes	complemented
59	#387×C₁₃₇	C₂²	1	4	yes	complemented
60	#387×C₁₃₇	C₂²	1	4	yes	complemented
61	#387×C₁₃₇	C₂²	1	4	yes	complemented
62	#386×C₁₃₇	C₂²	1	4	yes	—
63	#386×C₁₃₇	C₂²	1	4	yes	—
64	#386×C₁₃₇	C₂²	1	2	yes	—
65	#386×C₁₃₇	C₂²	1	4	yes	—
66	#386×C₁₃₇	C₂²	1	2	yes	—
67	#385×C₁₃₇	C₂²	1	2	yes	—
68	#385×C₁₃₇	C₂²	1	4	yes	—
69	#385×C₁₃₇	C₂²	1	2	yes	—
70	#385×C₁₃₇	C₂²	1	4	yes	complemented
71	#385×C₁₃₇	C₂²	1	4	yes	complemented
72	#383×C₁₃₇	C₂²	1	2	yes	complemented
73	#382×C₁₃₇	C₂²	1	2	yes	complemented
74	#381×C₁₃₇	C₂²	1	2	yes	—
75	#381×C₁₃₇	C₂²	1	1	yes	characteristic
76	#381×C₁₃₇	C₂²	1	1	yes	characteristic
77	#380×C₁₃₇	C₂²	1	2	yes	—
78	#379×C₁₃₇	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	4	yes	complemented
84	#376×C₁₃₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₇	C₂³	1	1	yes	characteristic
86	C₂×#41×C₁₃₇	—	2	8	no	—
87	C₂×#41×C₁₃₇	—	2	4	no	—
88	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₇	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₇	—	2	4	no	—
93	C₂³×C₄×C₁₃₇	—	2	8	no	—
94	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
105	#123×C₁₃₇	—	2	8	no	—
106	#120×C₁₃₇	—	2	8	no	—
107	C₄×Q₈×C₁₃₇	—	2	4	no	—
108	C₄×Q₈×C₁₃₇	—	2	4	no	—
109	C₄×D₄×C₁₃₇	—	2	8	no	—
110	C₄×D₄×C₁₃₇	—	2	8	no	—
111	C₄×D₄×C₁₃₇	—	2	16	no	—
112	C₄×D₄×C₁₃₇	—	2	4	no	—
113	C₄×D₄×C₁₃₇	—	2	4	no	—
114	#117×C₁₃₇	—	2	4	no	—
115	#117×C₁₃₇	—	2	8	no	—
116	#117×C₁₃₇	—	2	8	no	—
117	#117×C₁₃₇	—	2	8	no	—
118	#117×C₁₃₇	—	2	8	no	—
119	#117×C₁₃₇	—	2	8	no	—
120	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
121	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
122	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
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	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	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	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃₇	—	2	4	no	—
152	C₂×C₄²×C₁₃₇	—	2	8	no	—
153	C₂×C₄²×C₁₃₇	D₄	1	8	yes	complemented
154	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₇	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
164	#95×C₁₃₇	C₂³	1	4	yes	—
165	#95×C₁₃₇	C₂³	1	2	yes	—
166	#95×C₁₃₇	C₂³	1	2	yes	—
167	#95×C₁₃₇	C₂³	1	4	yes	—
168	#95×C₁₃₇	C₂³	1	4	yes	—
169	#95×C₁₃₇	C₂³	1	4	yes	—
170	#95×C₁₃₇	C₂³	1	4	yes	—
171	#95×C₁₃₇	C₂³	1	4	yes	—
172	#95×C₁₃₇	C₂³	1	2	yes	—
173	#95×C₁₃₇	C₂³	1	2	yes	—
174	#95×C₁₃₇	C₂³	1	4	yes	—
175	#95×C₁₃₇	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₇	—	2	2	no	—
177	C₂⁴×C₁₃₇	—	2	4	no	—
178	C₂⁴×C₁₃₇	—	2	4	no	—
179	C₂⁴×C₁₃₇	—	4	2	no	—
180	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
183	#41×C₁₃₇	—	2	32	no	—
184	C₂×Q₈×C₁₃₇	—	2	2	no	—
185	C₂×Q₈×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	8	no	—
190	C₂×D₄×C₁₃₇	—	2	8	no	—
191	C₂×D₄×C₁₃₇	—	2	2	no	—
192	C₂×D₄×C₁₃₇	—	4	4	no	—
193	C₂×D₄×C₁₃₇	#41	1	8	yes	—
194	C₂²×C₄×C₁₃₇	—	2	32	no	—
195	C₂²×C₄×C₁₃₇	—	2	2	no	—
196	C₂²×C₄×C₁₃₇	—	2	4	no	—
197	C₂²×C₄×C₁₃₇	—	2	4	no	—
198	C₂²×C₄×C₁₃₇	—	2	4	no	—
199	C₂²×C₄×C₁₃₇	—	2	4	no	—
200	C₂²×C₄×C₁₃₇	—	2	4	no	—
201	C₂²×C₄×C₁₃₇	—	2	4	no	—
202	C₂²×C₄×C₁₃₇	—	2	4	no	—
203	C₂²×C₄×C₁₃₇	—	2	4	no	—
204	C₂²×C₄×C₁₃₇	—	2	4	no	—
205	C₂²×C₄×C₁₃₇	—	2	4	no	—
206	C₂²×C₄×C₁₃₇	—	2	4	no	—
207	C₂²×C₄×C₁₃₇	—	2	2	no	—
208	C₂²×C₄×C₁₃₇	—	2	2	no	—
209	C₂²×C₄×C₁₃₇	—	2	4	no	—
210	C₂²×C₄×C₁₃₇	—	2	4	no	—
211	C₂²×C₄×C₁₃₇	—	2	4	no	—
212	C₂²×C₄×C₁₃₇	—	2	8	no	—
213	C₂²×C₄×C₁₃₇	—	4	2	no	—
214	C₂²×C₄×C₁₃₇	—	4	4	no	—
215	C₂²×C₄×C₁₃₇	—	4	2	no	—
216	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₁₃₇	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₁₃₇	#41	1	8	yes	complemented
220	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₃₇	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₇	—	2	4	no	—
235	C₄⋊C₄×C₁₃₇	—	2	4	no	—
236	C₄⋊C₄×C₁₃₇	—	2	4	no	—
237	C₄⋊C₄×C₁₃₇	—	2	4	no	—
238	C₄⋊C₄×C₁₃₇	—	2	4	no	—
239	C₄⋊C₄×C₁₃₇	—	2	4	no	—
240	C₄⋊C₄×C₁₃₇	—	2	2	no	—
241	C₄⋊C₄×C₁₃₇	—	2	2	no	—
242	C₄⋊C₄×C₁₃₇	—	2	8	no	—
243	C₄⋊C₄×C₁₃₇	—	2	8	no	—
244	C₄⋊C₄×C₁₃₇	—	4	4	no	—
245	C₄⋊C₄×C₁₃₇	—	4	4	no	—
246	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
247	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
251	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₇	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
260	C₂²⋊C₄×C₁₃₇	—	4	4	no	—
261	C₄²×C₁₃₇	—	2	4	no	—
262	C₄²×C₁₃₇	—	2	4	no	—
263	C₄²×C₁₃₇	—	2	4	no	—
264	C₄²×C₁₃₇	—	2	4	no	—
265	C₄²×C₁₃₇	—	2	4	no	—
266	C₄²×C₁₃₇	—	2	8	no	—
267	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
269	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
270	C₄²×C₁₃₇	C₂×D₄	1	4	yes	—
271	C₂³×C₁₃₇	—	2	2	no	—
272	C₂³×C₁₃₇	—	2	2	no	—
273	C₂³×C₁₃₇	—	2	8	no	—
274	C₂³×C₁₃₇	—	2	2	no	—
275	C₂³×C₁₃₇	—	2	2	no	—
276	C₂³×C₁₃₇	—	2	4	no	—
277	C₂³×C₁₃₇	—	2	4	no	—
278	C₂³×C₁₃₇	—	2	2	no	—
279	C₂³×C₁₃₇	—	2	2	no	—
280	C₂³×C₁₃₇	—	2	4	no	—
281	C₂³×C₁₃₇	—	2	4	no	—
282	C₂³×C₁₃₇	—	4	16	no	—
283	C₂³×C₁₃₇	—	4	4	no	—
284	C₂³×C₁₃₇	—	4	4	no	—
285	C₂³×C₁₃₇	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
287	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
288	C₂³×C₁₃₇	C₂×#41	1	4	yes	—
289	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
290	Q₈×C₁₃₇	—	2	8	no	—
291	D₄×C₁₃₇	—	2	8	no	—
292	D₄×C₁₃₇	—	2	16	no	—
293	D₄×C₁₃₇	—	4	16	no	—
294	C₂×C₄×C₁₃₇	—	2	16	no	—
295	C₂×C₄×C₁₃₇	—	2	8	no	—
296	C₂×C₄×C₁₃₇	—	2	16	no	—
297	C₂×C₄×C₁₃₇	—	2	8	no	—
298	C₂×C₄×C₁₃₇	—	2	2	no	—
299	C₂×C₄×C₁₃₇	—	2	2	no	—
300	C₂×C₄×C₁₃₇	—	2	2	no	—
301	C₂×C₄×C₁₃₇	—	2	2	no	—
302	C₂×C₄×C₁₃₇	—	2	2	no	—
303	C₂×C₄×C₁₃₇	—	2	2	no	—
304	C₂×C₄×C₁₃₇	—	2	2	no	—
305	C₂×C₄×C₁₃₇	—	2	2	no	—
306	C₂×C₄×C₁₃₇	—	2	2	no	—
307	C₂×C₄×C₁₃₇	—	2	8	no	—
308	C₂×C₄×C₁₃₇	—	2	16	no	—
309	C₂×C₄×C₁₃₇	—	2	2	no	—
310	C₂×C₄×C₁₃₇	—	2	2	no	—
311	C₂×C₄×C₁₃₇	—	2	2	no	—
312	C₂×C₄×C₁₃₇	—	2	2	no	—
313	C₂×C₄×C₁₃₇	—	2	4	no	—
314	C₂×C₄×C₁₃₇	—	2	4	no	—
315	C₂×C₄×C₁₃₇	—	2	4	no	—
316	C₂×C₄×C₁₃₇	—	2	4	no	—
317	C₂×C₄×C₁₃₇	—	2	4	no	—
318	C₂×C₄×C₁₃₇	—	2	4	no	—
319	C₂×C₄×C₁₃₇	—	2	4	no	—
320	C₂×C₄×C₁₃₇	—	2	4	no	—
321	C₂×C₄×C₁₃₇	—	2	4	no	—
322	C₂×C₄×C₁₃₇	—	2	4	no	—
323	C₂×C₄×C₁₃₇	—	4	4	no	—
324	C₂×C₄×C₁₃₇	—	4	8	no	—
325	C₂×C₄×C₁₃₇	—	4	4	no	—
326	C₂×C₄×C₁₃₇	—	4	4	no	—
327	C₂×C₄×C₁₃₇	—	4	8	no	—
328	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
335	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
336	C₂×C₄×C₁₃₇	C₂×#41	1	4	yes	—
337	C₂²×C₁₃₇	—	2	2	no	—
338	C₂²×C₁₃₇	—	2	2	no	—
339	C₂²×C₁₃₇	—	2	8	no	—
340	C₂²×C₁₃₇	—	2	4	no	—
341	C₂²×C₁₃₇	—	2	4	no	—
342	C₂²×C₁₃₇	—	2	8	no	—
343	C₂²×C₁₃₇	—	2	8	no	—
344	C₂²×C₁₃₇	—	4	16	no	—
345	C₂²×C₁₃₇	—	4	2	no	—
346	C₂²×C₁₃₇	—	4	2	no	—
347	C₂²×C₁₃₇	—	4	2	no	—
348	C₂²×C₁₃₇	—	4	2	no	—
349	C₂²×C₁₃₇	—	4	4	no	—
350	C₂²×C₁₃₇	—	4	4	no	—
351	C₂²×C₁₃₇	#525	1	4	yes	—
352	C₂²×C₁₃₇	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
354	C₂²×C₁₃₇	C₂²×#41	1	2	yes	—
355	C₂²×C₁₃₇	#585	1	2	yes	—
356	C₄×C₁₃₇	—	2	2	no	—
357	C₄×C₁₃₇	—	2	2	no	—
358	C₄×C₁₃₇	—	2	4	no	—
359	C₄×C₁₃₇	—	2	2	no	—
360	C₄×C₁₃₇	—	2	4	no	—
361	C₄×C₁₃₇	—	2	2	no	—
362	C₄×C₁₃₇	—	2	2	no	—
363	C₄×C₁₃₇	—	4	2	no	—
364	C₄×C₁₃₇	—	4	2	no	—
365	C₄×C₁₃₇	—	4	2	no	—
366	C₄×C₁₃₇	—	4	2	no	—
367	C₄×C₁₃₇	—	4	4	no	—
368	C₄×C₁₃₇	—	4	4	no	—
369	C₄×C₁₃₇	#525	1	4	yes	—
370	C₂×C₁₃₇	—	2	4	no	—
371	C₂×C₁₃₇	—	4	4	no	—
372	C₂×C₁₃₇	—	4	4	no	—
373	C₂×C₁₃₇	C₂×#525	1	1	yes	characteristic
374	C₂×C₁₃₇	C₂×#525	1	1	yes	characteristic
375	C₂×C₁₃₇	#3449	1	1	yes	characteristic
376	C₂×C₁₃₇	#3475	1	4	yes	—
377	#34875	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₁₃₇	#34875	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×C₄×#41	C₂×C₁₃₇	1	1	yes	characteristic, complemented
380	C₂²×#117	C₂×C₁₃₇	1	1	yes	characteristic, complemented
381	#2609	C₂×C₁₃₇	1	4	yes	complemented
382	#2599	C₂×C₁₃₇	1	2	yes	complemented
383	#2598	C₂×C₁₃₇	1	2	yes	complemented
384	#2579	C₂×C₁₃₇	1	2	yes	complemented
385	#2534	C₂×C₁₃₇	1	2	yes	complemented
386	#2484	C₂×C₁₃₇	1	1	yes	characteristic, complemented
387	#2482	C₂×C₁₃₇	1	1	yes	characteristic, complemented
388	#2406	C₂×C₁₃₇	1	1	yes	characteristic, complemented
389	#2404	C₂×C₁₃₇	1	1	yes	characteristic
390	#2396	C₂×C₁₃₇	1	2	yes	complemented
391	#2392	C₂×C₁₃₇	1	2	yes	complemented
392	C₄×#123	C₂×C₁₃₇	1	2	yes	complemented
393	C₄×#120	C₂×C₁₃₇	1	2	yes	complemented
394	#2290	C₂×C₁₃₇	1	4	yes	complemented
395	#2283	C₂×C₁₃₇	1	1	yes	characteristic, complemented
396	C₂²×#41	C₂²×C₁₃₇	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×C₁₃₇	1	1	yes	characteristic
398	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
399	C₂×#120	C₂²×C₁₃₇	1	2	yes	—
400	C₄×#41	—	2	8	no	—
401	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
402	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
403	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃₇	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
407	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic, complemented
408	C₂×#117	—	2	8	no	—
409	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
410	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
411	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
412	C₂×#117	C₂²×C₁₃₇	1	2	yes	—
413	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
414	C₂×#117	C₂²×C₁₃₇	1	2	yes	complemented
415	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
419	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
420	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
421	C₂²×C₄²	C₂²×C₁₃₇	1	2	yes	complemented
422	#400	C₂²×C₁₃₇	1	2	yes	complemented
423	#399	C₂²×C₁₃₇	1	2	yes	—
424	#398	C₂²×C₁₃₇	1	4	yes	complemented
425	#398	C₂²×C₁₃₇	1	2	yes	complemented
426	#397	C₂²×C₁₃₇	1	2	yes	—
427	#396	C₂²×C₁₃₇	1	4	yes	—
428	#396	C₂²×C₁₃₇	1	4	yes	complemented
429	#395	C₂²×C₁₃₇	1	2	yes	complemented
430	#394	C₂²×C₁₃₇	1	4	yes	—
431	#394	C₂²×C₁₃₇	1	2	yes	complemented
432	#393	C₂²×C₁₃₇	1	2	yes	—
433	#392	C₂²×C₁₃₇	1	2	yes	—
434	#388	C₂²×C₁₃₇	1	4	yes	—
435	#388	C₂²×C₁₃₇	1	4	yes	—
436	#388	C₂²×C₁₃₇	1	4	yes	complemented
437	#387	C₂²×C₁₃₇	1	4	yes	complemented
438	#387	C₂²×C₁₃₇	1	4	yes	complemented
439	#387	C₂²×C₁₃₇	1	4	yes	complemented
440	#386	C₂²×C₁₃₇	1	2	yes	—
441	#386	C₂²×C₁₃₇	1	2	yes	—
442	#386	C₂²×C₁₃₇	1	4	yes	—
443	#386	C₂²×C₁₃₇	1	4	yes	—
444	#386	C₂²×C₁₃₇	1	4	yes	—
445	#385	C₂²×C₁₃₇	1	2	yes	—
446	#385	C₂²×C₁₃₇	1	2	yes	—
447	#385	C₂²×C₁₃₇	1	4	yes	—
448	#385	C₂²×C₁₃₇	1	4	yes	complemented
449	#385	C₂²×C₁₃₇	1	4	yes	complemented
450	#383	C₂²×C₁₃₇	1	2	yes	complemented
451	#382	C₂²×C₁₃₇	1	2	yes	complemented
452	#381	C₂²×C₁₃₇	1	1	yes	characteristic
453	#381	C₂²×C₁₃₇	1	1	yes	characteristic
454	#381	C₂²×C₁₃₇	1	2	yes	—
455	#380	C₂²×C₁₃₇	1	2	yes	—
456	#379	C₂²×C₁₃₇	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	complemented
458	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
459	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	4	yes	complemented
462	#376	C₂²×C₁₃₇	1	2	yes	complemented
463	C₂⁵	C₂³×C₁₃₇	1	1	yes	characteristic
464	C₂×#41	—	2	8	no	—
465	C₂×#41	—	2	4	no	—
466	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₃₇	1	4	yes	—
469	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
470	C₂³×C₄	—	2	4	no	—
471	C₂³×C₄	—	2	8	no	—
472	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
475	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
476	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
477	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
482	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
483	#123	—	2	8	no	—
484	#120	—	2	8	no	—
485	C₄×Q₈	—	2	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×D₄	—	2	8	no	—
488	C₄×D₄	—	2	8	no	—
489	C₄×D₄	—	2	16	no	—
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	4	no	—
492	#117	—	2	4	no	—
493	#117	—	2	8	no	—
494	#117	—	2	8	no	—
495	#117	—	2	8	no	—
496	#117	—	2	8	no	—
497	#117	—	2	8	no	—
498	C₂×C₄⋊C₄	—	2	4	no	—
499	C₂×C₄⋊C₄	—	2	4	no	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	4	yes	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₂²⋊C₄	—	2	4	no	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	4	yes	—
529	C₂×C₄²	—	2	4	no	—
530	C₂×C₄²	—	2	8	no	—
531	C₂×C₄²	D₄×C₁₃₇	1	8	yes	complemented
532	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
537	C₂×C₄²	C₂³×C₁₃₇	1	4	yes	—
538	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
542	#95	C₂³×C₁₃₇	1	4	yes	—
543	#95	C₂³×C₁₃₇	1	2	yes	—
544	#95	C₂³×C₁₃₇	1	2	yes	—
545	#95	C₂³×C₁₃₇	1	4	yes	—
546	#95	C₂³×C₁₃₇	1	4	yes	—
547	#95	C₂³×C₁₃₇	1	4	yes	—
548	#95	C₂³×C₁₃₇	1	4	yes	—
549	#95	C₂³×C₁₃₇	1	4	yes	—
550	#95	C₂³×C₁₃₇	1	2	yes	—
551	#95	C₂³×C₁₃₇	1	2	yes	—
552	#95	C₂³×C₁₃₇	1	4	yes	—
553	#95	C₂³×C₁₃₇	1	4	yes	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	4	2	no	—
558	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
559	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
560	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
561	#41	—	2	32	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	#41×C₁₃₇	1	8	yes	—
572	C₂²×C₄	—	2	32	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	8	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
595	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
596	C₂²×C₄	C₂×D₄×C₁₃₇	1	4	yes	—
597	C₂²×C₄	#41×C₁₃₇	1	8	yes	complemented
598	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₇	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	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	—	2	8	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	8	no	—
645	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
646	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
647	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
648	C₄²	C₂×D₄×C₁₃₇	1	4	yes	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	8	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	4	16	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	4	no	—
663	C₂³	C₂²×D₄×C₁₃₇	1	2	yes	—
664	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
665	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
666	C₂³	C₂×#41×C₁₃₇	1	4	yes	—
667	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
668	Q₈	—	2	8	no	—
669	D₄	—	2	8	no	—
670	D₄	—	2	16	no	—
671	D₄	—	4	16	no	—
672	C₂×C₄	—	2	16	no	—
673	C₂×C₄	—	2	8	no	—
674	C₂×C₄	—	2	16	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
712	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
713	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
714	C₂×C₄	C₂×#41×C₁₃₇	1	4	yes	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	4	16	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	#525×C₁₃₇	1	4	yes	—
730	C₂²	C₂³×D₄×C₁₃₇	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
732	C₂²	C₂²×#41×C₁₃₇	1	2	yes	—
733	C₂²	#585×C₁₃₇	1	2	yes	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	4	no	—
747	C₄	#525×C₁₃₇	1	4	yes	—
748	C₂	—	2	4	no	—
749	C₂	—	4	4	no	—
750	C₂	—	4	4	no	—
751	C₂	C₂×#525×C₁₃₇	1	1	yes	characteristic
752	C₂	C₂×#525×C₁₃₇	1	1	yes	characteristic
753	C₂	#3449×C₁₃₇	1	1	yes	characteristic
754	C₂	#3475×C₁₃₇	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
socle	C₂³×C₁₃₇	C₂⁵
prime radical	#2404×C₁₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₁₃₇	C₂	semidirect
2. C₂²×#117×C₁₃₇	C₂	semidirect
3. #2609×C₁₃₇	C₂	semidirect
4. #2599×C₁₃₇	C₂	semidirect
5. #2598×C₁₃₇	C₂	semidirect
6. #2579×C₁₃₇	C₂	semidirect
7. #2534×C₁₃₇	C₂	semidirect
8. #2484×C₁₃₇	C₂	semidirect
9. #2482×C₁₃₇	C₂	semidirect
10. #2406×C₁₃₇	C₂	semidirect
12. #2396×C₁₃₇	C₂	semidirect
13. #2392×C₁₃₇	C₂	semidirect
14. C₄×#123×C₁₃₇	C₂	semidirect
15. C₄×#120×C₁₃₇	C₂	semidirect
16. #2290×C₁₃₇	C₂	semidirect
17. #2283×C₁₃₇	C₂	semidirect
23. C₂×C₄×Q₈×C₁₃₇	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃₇	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃₇	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃₇	C₂²	semidirect
36. C₂×#117×C₁₃₇	C₂²	semidirect
43. C₂²×C₄²×C₁₃₇	C₂²	semidirect
44. #400×C₁₃₇	C₂²	semidirect
46. #398×C₁₃₇	C₂²	semidirect
47. #398×C₁₃₇	C₂²	semidirect
50. #396×C₁₃₇	C₂²	semidirect
51. #395×C₁₃₇	C₂²	semidirect
53. #394×C₁₃₇	C₂²	semidirect
58. #388×C₁₃₇	C₂²	semidirect
59. #387×C₁₃₇	C₂²	semidirect
60. #387×C₁₃₇	C₂²	semidirect
61. #387×C₁₃₇	C₂²	semidirect
70. #385×C₁₃₇	C₂²	semidirect
71. #385×C₁₃₇	C₂²	semidirect
72. #383×C₁₃₇	C₂²	semidirect
73. #382×C₁₃₇	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₇	C₂²	semidirect
83. C₄×C₂²⋊C₄×C₁₃₇	C₂²	semidirect
84. #376×C₁₃₇	C₂²	semidirect
153. C₂×C₄²×C₁₃₇	D₄	semidirect
219. C₂²×C₄×C₁₃₇	#41	semidirect
377. #34875	C₁₃₇	direct (N × H)
378. C₁₃₇	#34875	direct (N × H)
379. C₂×C₄×#41	C₂×C₁₃₇	semidirect
380. C₂²×#117	C₂×C₁₃₇	semidirect
381. #2609	C₂×C₁₃₇	semidirect
382. #2599	C₂×C₁₃₇	semidirect
383. #2598	C₂×C₁₃₇	semidirect
384. #2579	C₂×C₁₃₇	semidirect
385. #2534	C₂×C₁₃₇	semidirect
386. #2484	C₂×C₁₃₇	semidirect
387. #2482	C₂×C₁₃₇	semidirect
388. #2406	C₂×C₁₃₇	semidirect
390. #2396	C₂×C₁₃₇	semidirect
391. #2392	C₂×C₁₃₇	semidirect
392. C₄×#123	C₂×C₁₃₇	semidirect
393. C₄×#120	C₂×C₁₃₇	semidirect
394. #2290	C₂×C₁₃₇	semidirect
395. #2283	C₂×C₁₃₇	semidirect
401. C₂×C₄×Q₈	C₂²×C₁₃₇	semidirect
402. C₂×C₄×Q₈	C₂²×C₁₃₇	semidirect
406. C₂×C₄×D₄	C₂²×C₁₃₇	semidirect
407. C₂×C₄×D₄	C₂²×C₁₃₇	semidirect
414. C₂×#117	C₂²×C₁₃₇	semidirect
421. C₂²×C₄²	C₂²×C₁₃₇	semidirect
422. #400	C₂²×C₁₃₇	semidirect
424. #398	C₂²×C₁₃₇	semidirect
425. #398	C₂²×C₁₃₇	semidirect
428. #396	C₂²×C₁₃₇	semidirect
429. #395	C₂²×C₁₃₇	semidirect
431. #394	C₂²×C₁₃₇	semidirect
436. #388	C₂²×C₁₃₇	semidirect
437. #387	C₂²×C₁₃₇	semidirect
438. #387	C₂²×C₁₃₇	semidirect
439. #387	C₂²×C₁₃₇	semidirect
448. #385	C₂²×C₁₃₇	semidirect
449. #385	C₂²×C₁₃₇	semidirect
450. #383	C₂²×C₁₃₇	semidirect
451. #382	C₂²×C₁₃₇	semidirect
457. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
458. C₄×C₄⋊C₄	C₂²×C₁₃₇	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₁₃₇	semidirect
462. #376	C₂²×C₁₃₇	semidirect
531. C₂×C₄²	D₄×C₁₃₇	semidirect
597. C₂²×C₄	#41×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₃₇	2
C₂²×#117×C₁₃₇	2
#2609×C₁₃₇	2
#2599×C₁₃₇	2
#2598×C₁₃₇	2
#2579×C₁₃₇	2
#2534×C₁₃₇	2
#2484×C₁₃₇	2
#2482×C₁₃₇	2
#2406×C₁₃₇	2
#2404×C₁₃₇	2
#2396×C₁₃₇	2
#2392×C₁₃₇	2
C₄×#123×C₁₃₇	2
C₄×#120×C₁₃₇	2
#2290×C₁₃₇	2
#2283×C₁₃₇	2
#34875	137

Subgroups — C137×#34875 #46884261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#34875 #46884261