Subgroups — C₁₃₇×#36833 #46886219

Order 35072.

1782 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2850×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#2773×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2732×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2714×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2710×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2698×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2692×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2688×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2672×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2651×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#2610×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#2605×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#2598×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#2560×C₁₃₇	C₂	1	2	yes	maximal, complemented
15	#2540×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#2471×C₁₃₇	C₂	1	2	yes	maximal, complemented
17	#2337×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#2319×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₃₇	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₇	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×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×#117×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
33	#400×C₁₃₇	C₂²	1	1	yes	characteristic
34	#400×C₁₃₇	C₂²	1	2	yes	—
35	#399×C₁₃₇	C₂²	1	2	yes	—
36	#399×C₁₃₇	C₂²	1	1	yes	characteristic
37	#399×C₁₃₇	C₂²	1	2	yes	—
38	#399×C₁₃₇	C₂²	1	2	yes	—
39	#398×C₁₃₇	C₂²	1	2	yes	—
40	#398×C₁₃₇	C₂²	1	2	yes	—
41	#398×C₁₃₇	C₂²	1	2	yes	—
42	#397×C₁₃₇	C₂²	1	2	yes	—
43	#397×C₁₃₇	C₂²	1	2	yes	—
44	#397×C₁₃₇	C₂²	1	2	yes	—
45	#397×C₁₃₇	C₂²	1	2	yes	—
46	#396×C₁₃₇	C₂²	1	2	yes	—
47	#396×C₁₃₇	C₂²	1	2	yes	—
48	#395×C₁₃₇	C₂²	1	2	yes	—
49	#395×C₁₃₇	C₂²	1	1	yes	characteristic
50	#394×C₁₃₇	C₂²	1	2	yes	—
51	#394×C₁₃₇	C₂²	1	1	yes	characteristic
52	#394×C₁₃₇	C₂²	1	1	yes	characteristic
53	#394×C₁₃₇	C₂²	1	2	yes	—
54	#394×C₁₃₇	C₂²	1	2	yes	—
55	#393×C₁₃₇	C₂²	1	2	yes	—
56	#393×C₁₃₇	C₂²	1	1	yes	characteristic
57	#392×C₁₃₇	C₂²	1	2	yes	—
58	#392×C₁₃₇	C₂²	1	1	yes	characteristic
59	#392×C₁₃₇	C₂²	1	1	yes	characteristic
60	#392×C₁₃₇	C₂²	1	2	yes	—
61	#391×C₁₃₇	C₂²	1	2	yes	—
62	#391×C₁₃₇	C₂²	1	2	yes	—
63	#391×C₁₃₇	C₂²	1	2	yes	—
64	#390×C₁₃₇	C₂²	1	2	yes	—
65	#390×C₁₃₇	C₂²	1	2	yes	—
66	#390×C₁₃₇	C₂²	1	2	yes	—
67	#390×C₁₃₇	C₂²	1	2	yes	—
68	#390×C₁₃₇	C₂²	1	2	yes	—
69	#389×C₁₃₇	C₂²	1	2	yes	—
70	#389×C₁₃₇	C₂²	1	2	yes	—
71	#389×C₁₃₇	C₂²	1	2	yes	—
72	#388×C₁₃₇	C₂²	1	2	yes	—
73	#388×C₁₃₇	C₂²	1	2	yes	—
74	#388×C₁₃₇	C₂²	1	2	yes	—
75	#388×C₁₃₇	C₂²	1	2	yes	—
76	#388×C₁₃₇	C₂²	1	2	yes	—
77	#388×C₁₃₇	C₂²	1	2	yes	—
78	#388×C₁₃₇	C₂²	1	2	yes	—
79	#388×C₁₃₇	C₂²	1	2	yes	—
80	#388×C₁₃₇	C₂²	1	2	yes	—
81	#387×C₁₃₇	C₂²	1	2	yes	—
82	#387×C₁₃₇	C₂²	1	2	yes	—
83	#387×C₁₃₇	C₂²	1	2	yes	—
84	#387×C₁₃₇	C₂²	1	2	yes	—
85	#386×C₁₃₇	C₂²	1	2	yes	—
86	#386×C₁₃₇	C₂²	1	2	yes	—
87	#386×C₁₃₇	C₂²	1	2	yes	—
88	#386×C₁₃₇	C₂²	1	2	yes	—
89	#386×C₁₃₇	C₂²	1	2	yes	—
90	#386×C₁₃₇	C₂²	1	2	yes	—
91	#386×C₁₃₇	C₂²	1	2	yes	—
92	#386×C₁₃₇	C₂²	1	2	yes	—
93	#385×C₁₃₇	C₂²	1	2	yes	—
94	#385×C₁₃₇	C₂²	1	2	yes	—
95	#385×C₁₃₇	C₂²	1	2	yes	—
96	#385×C₁₃₇	C₂²	1	2	yes	—
97	#383×C₁₃₇	C₂²	1	1	yes	characteristic
98	#382×C₁₃₇	C₂²	1	2	yes	—
99	#381×C₁₃₇	C₂²	1	2	yes	—
100	#380×C₁₃₇	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
105	C₄×C₂²⋊C₄×C₁₃₇	C₂²	1	2	yes	—
106	#376×C₁₃₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
119	#126×C₁₃₇	—	4	4	no	—
120	#124×C₁₃₇	—	2	4	no	—
121	#124×C₁₃₇	—	4	4	no	—
122	#123×C₁₃₇	—	4	4	no	—
123	C₂²⋊Q₈×C₁₃₇	—	4	4	no	—
124	C₂²⋊Q₈×C₁₃₇	—	4	4	no	—
125	C₂²⋊Q₈×C₁₃₇	—	4	4	no	—
126	#121×C₁₃₇	—	4	4	no	—
127	#121×C₁₃₇	—	4	4	no	—
128	C₄×D₄×C₁₃₇	—	2	4	no	—
129	#117×C₁₃₇	—	2	4	no	—
130	#117×C₁₃₇	—	4	2	no	—
131	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊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×C₄²×C₁₃₇	—	4	2	no	—
175	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
184	#95×C₁₃₇	C₂³	1	1	yes	characteristic
185	#95×C₁₃₇	C₂³	1	1	yes	characteristic
186	#95×C₁₃₇	C₂³	1	2	yes	—
187	#95×C₁₃₇	C₂³	1	2	yes	—
188	#95×C₁₃₇	C₂³	1	2	yes	—
189	#95×C₁₃₇	C₂³	1	2	yes	—
190	#95×C₁₃₇	C₂³	1	2	yes	—
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	1	yes	characteristic
199	#95×C₁₃₇	C₂³	1	2	yes	—
200	#95×C₁₃₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₇	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
210	C₂×Q₈×C₁₃₇	—	2	2	no	—
211	C₂×Q₈×C₁₃₇	—	2	4	no	—
212	C₂×Q₈×C₁₃₇	—	4	2	no	—
213	C₂×Q₈×C₁₃₇	—	4	2	no	—
214	C₂×Q₈×C₁₃₇	—	4	2	no	—
215	C₂×D₄×C₁₃₇	—	2	4	no	—
216	C₂×D₄×C₁₃₇	—	2	4	no	—
217	C₂×D₄×C₁₃₇	—	2	2	no	—
218	C₂×D₄×C₁₃₇	—	2	2	no	—
219	C₂×D₄×C₁₃₇	—	2	4	no	—
220	C₂×D₄×C₁₃₇	—	4	2	no	—
221	C₂×D₄×C₁₃₇	—	4	2	no	—
222	C₂×D₄×C₁₃₇	—	4	2	no	—
223	C₂×D₄×C₁₃₇	—	4	2	no	—
224	C₂×D₄×C₁₃₇	—	4	2	no	—
225	C₂×D₄×C₁₃₇	—	4	2	no	—
226	C₂×D₄×C₁₃₇	—	4	2	no	—
227	C₂×D₄×C₁₃₇	—	4	2	no	—
228	C₂×D₄×C₁₃₇	—	4	2	no	—
229	C₂×D₄×C₁₃₇	—	4	2	no	—
230	C₂×D₄×C₁₃₇	—	4	2	no	—
231	C₂²×C₄×C₁₃₇	—	2	2	no	—
232	C₂²×C₄×C₁₃₇	—	2	2	no	—
233	C₂²×C₄×C₁₃₇	—	2	2	no	—
234	C₂²×C₄×C₁₃₇	—	2	4	no	—
235	C₂²×C₄×C₁₃₇	—	2	4	no	—
236	C₂²×C₄×C₁₃₇	—	4	2	no	—
237	C₂²×C₄×C₁₃₇	—	4	2	no	—
238	C₂²×C₄×C₁₃₇	—	4	2	no	—
239	C₂²×C₄×C₁₃₇	—	4	2	no	—
240	C₂²×C₄×C₁₃₇	—	4	2	no	—
241	C₂²×C₄×C₁₃₇	—	4	2	no	—
242	C₂²×C₄×C₁₃₇	—	4	2	no	—
243	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₁₃₇	—	2	2	no	—
260	C₄⋊C₄×C₁₃₇	—	2	2	no	—
261	C₄⋊C₄×C₁₃₇	—	2	2	no	—
262	C₄⋊C₄×C₁₃₇	—	2	4	no	—
263	C₄⋊C₄×C₁₃₇	—	2	4	no	—
264	C₄⋊C₄×C₁₃₇	—	2	4	no	—
265	C₄⋊C₄×C₁₃₇	—	2	4	no	—
266	C₄⋊C₄×C₁₃₇	—	2	4	no	—
267	C₄⋊C₄×C₁₃₇	—	4	2	no	—
268	C₄⋊C₄×C₁₃₇	—	4	2	no	—
269	C₄⋊C₄×C₁₃₇	—	4	2	no	—
270	C₄⋊C₄×C₁₃₇	—	4	2	no	—
271	C₄⋊C₄×C₁₃₇	—	4	2	no	—
272	C₄⋊C₄×C₁₃₇	—	4	2	no	—
273	C₄⋊C₄×C₁₃₇	—	4	2	no	—
274	C₄⋊C₄×C₁₃₇	—	4	2	no	—
275	C₄⋊C₄×C₁₃₇	—	4	2	no	—
276	C₄⋊C₄×C₁₃₇	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
278	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
279	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
290	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
292	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
293	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
294	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
295	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
296	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
298	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
299	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
300	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
301	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
302	C₄²×C₁₃₇	—	2	2	no	—
303	C₄²×C₁₃₇	—	2	4	no	—
304	C₄²×C₁₃₇	—	4	1	no	—
305	C₄²×C₁₃₇	—	4	1	no	—
306	C₄²×C₁₃₇	—	4	2	no	—
307	C₄²×C₁₃₇	—	4	1	no	—
308	C₄²×C₁₃₇	—	4	1	no	—
309	C₄²×C₁₃₇	—	4	2	no	—
310	C₄²×C₁₃₇	#41	1	4	yes	—
311	C₂³×C₁₃₇	—	2	1	no	—
312	C₂³×C₁₃₇	—	2	1	no	—
313	C₂³×C₁₃₇	—	2	2	no	—
314	C₂³×C₁₃₇	—	2	2	no	—
315	C₂³×C₁₃₇	—	2	2	no	—
316	C₂³×C₁₃₇	—	2	2	no	—
317	C₂³×C₁₃₇	—	2	2	no	—
318	C₂³×C₁₃₇	—	2	2	no	—
319	C₂³×C₁₃₇	—	2	2	no	—
320	C₂³×C₁₃₇	—	2	2	no	—
321	C₂³×C₁₃₇	—	2	2	no	—
322	C₂³×C₁₃₇	—	2	2	no	—
323	C₂³×C₁₃₇	—	2	2	no	—
324	C₂³×C₁₃₇	—	2	2	no	—
325	C₂³×C₁₃₇	—	2	2	no	—
326	C₂³×C₁₃₇	—	2	2	no	—
327	C₂³×C₁₃₇	—	2	2	no	—
328	C₂³×C₁₃₇	—	2	2	no	—
329	C₂³×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
330	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
331	Q₈×C₁₃₇	—	8	2	no	—
332	Q₈×C₁₃₇	—	8	4	no	—
333	D₄×C₁₃₇	—	4	4	no	—
334	D₄×C₁₃₇	—	8	2	no	—
335	D₄×C₁₃₇	—	8	4	no	—
336	D₄×C₁₃₇	—	8	4	no	—
337	D₄×C₁₃₇	—	8	4	no	—
338	D₄×C₁₃₇	—	8	4	no	—
339	C₂×C₄×C₁₃₇	—	2	8	no	—
340	C₂×C₄×C₁₃₇	—	2	1	no	—
341	C₂×C₄×C₁₃₇	—	2	2	no	—
342	C₂×C₄×C₁₃₇	—	2	1	no	—
343	C₂×C₄×C₁₃₇	—	2	2	no	—
344	C₂×C₄×C₁₃₇	—	2	1	no	—
345	C₂×C₄×C₁₃₇	—	2	1	no	—
346	C₂×C₄×C₁₃₇	—	2	2	no	—
347	C₂×C₄×C₁₃₇	—	2	2	no	—
348	C₂×C₄×C₁₃₇	—	2	1	no	—
349	C₂×C₄×C₁₃₇	—	2	1	no	—
350	C₂×C₄×C₁₃₇	—	2	2	no	—
351	C₂×C₄×C₁₃₇	—	2	2	no	—
352	C₂×C₄×C₁₃₇	—	2	2	no	—
353	C₂×C₄×C₁₃₇	—	2	2	no	—
354	C₂×C₄×C₁₃₇	—	2	2	no	—
355	C₂×C₄×C₁₃₇	—	2	2	no	—
356	C₂×C₄×C₁₃₇	—	2	2	no	—
357	C₂×C₄×C₁₃₇	—	2	2	no	—
358	C₂×C₄×C₁₃₇	—	2	2	no	—
359	C₂×C₄×C₁₃₇	—	2	2	no	—
360	C₂×C₄×C₁₃₇	—	2	2	no	—
361	C₂×C₄×C₁₃₇	—	2	2	no	—
362	C₂×C₄×C₁₃₇	—	2	2	no	—
363	C₂×C₄×C₁₃₇	—	2	2	no	—
364	C₂×C₄×C₁₃₇	—	2	2	no	—
365	C₂×C₄×C₁₃₇	—	2	2	no	—
366	C₂×C₄×C₁₃₇	—	2	2	no	—
367	C₂×C₄×C₁₃₇	—	2	2	no	—
368	C₂×C₄×C₁₃₇	—	2	2	no	—
369	C₂×C₄×C₁₃₇	—	2	2	no	—
370	C₂×C₄×C₁₃₇	—	2	2	no	—
371	C₂×C₄×C₁₃₇	—	2	2	no	—
372	C₂×C₄×C₁₃₇	—	2	2	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	—	4	8	no	—
380	C₂×C₄×C₁₃₇	—	8	4	no	—
381	C₂×C₄×C₁₃₇	—	8	4	no	—
382	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
383	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
385	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	4	yes	—
387	C₂²×C₁₃₇	—	2	2	no	—
388	C₂²×C₁₃₇	—	2	4	no	—
389	C₂²×C₁₃₇	—	4	1	no	—
390	C₂²×C₁₃₇	—	4	1	no	—
391	C₂²×C₁₃₇	—	4	2	no	—
392	C₂²×C₁₃₇	—	4	2	no	—
393	C₂²×C₁₃₇	—	4	2	no	—
394	C₂²×C₁₃₇	—	4	2	no	—
395	C₂²×C₁₃₇	—	4	2	no	—
396	C₂²×C₁₃₇	—	4	2	no	—
397	C₂²×C₁₃₇	—	4	2	no	—
398	C₂²×C₁₃₇	—	4	2	no	—
399	C₂²×C₁₃₇	—	4	2	no	—
400	C₂²×C₁₃₇	—	4	2	no	—
401	C₂²×C₁₃₇	—	4	2	no	—
402	C₂²×C₁₃₇	—	4	2	no	—
403	C₂²×C₁₃₇	—	4	2	no	—
404	C₂²×C₁₃₇	—	4	2	no	—
405	C₂²×C₁₃₇	—	4	2	no	—
406	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂²×C₁₃₇	#585	1	2	yes	—
411	C₄×C₁₃₇	—	2	2	no	—
412	C₄×C₁₃₇	—	2	2	no	—
413	C₄×C₁₃₇	—	2	2	no	—
414	C₄×C₁₃₇	—	2	2	no	—
415	C₄×C₁₃₇	—	2	4	no	—
416	C₄×C₁₃₇	—	4	1	no	—
417	C₄×C₁₃₇	—	4	1	no	—
418	C₄×C₁₃₇	—	4	2	no	—
419	C₄×C₁₃₇	—	4	2	no	—
420	C₄×C₁₃₇	—	4	2	no	—
421	C₄×C₁₃₇	—	4	2	no	—
422	C₄×C₁₃₇	—	4	2	no	—
423	C₄×C₁₃₇	—	4	2	no	—
424	C₄×C₁₃₇	—	4	2	no	—
425	C₄×C₁₃₇	—	4	2	no	—
426	C₄×C₁₃₇	—	4	2	no	—
427	C₂×C₁₃₇	—	4	2	no	—
428	C₂×C₁₃₇	—	8	2	no	—
429	C₂×C₁₃₇	—	8	2	no	—
430	C₂×C₁₃₇	#3455	1	1	yes	characteristic
431	C₂×C₁₃₇	#3492	1	1	yes	characteristic
432	C₂×C₁₃₇	#3508	1	1	yes	characteristic
433	C₂×C₁₃₇	#3542	1	2	yes	—
434	C₂×C₁₃₇	#3561	1	2	yes	—
435	#36833	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₁₃₇	#36833	1	1	yes	characteristic, direct product factor, Sylow
437	#2850	C₂×C₁₃₇	1	2	yes	complemented
438	#2773	C₂×C₁₃₇	1	2	yes	complemented
439	#2732	C₂×C₁₃₇	1	2	yes	complemented
440	#2714	C₂×C₁₃₇	1	2	yes	complemented
441	#2710	C₂×C₁₃₇	1	2	yes	complemented
442	#2698	C₂×C₁₃₇	1	2	yes	complemented
443	#2692	C₂×C₁₃₇	1	2	yes	complemented
444	#2688	C₂×C₁₃₇	1	2	yes	complemented
445	#2672	C₂×C₁₃₇	1	2	yes	complemented
446	#2651	C₂×C₁₃₇	1	2	yes	complemented
447	#2610	C₂×C₁₃₇	1	1	yes	characteristic, complemented
448	#2605	C₂×C₁₃₇	1	1	yes	characteristic, complemented
449	#2598	C₂×C₁₃₇	1	1	yes	characteristic, complemented
450	#2560	C₂×C₁₃₇	1	2	yes	complemented
451	#2540	C₂×C₁₃₇	1	1	yes	characteristic, complemented
452	#2471	C₂×C₁₃₇	1	2	yes	complemented
453	#2337	C₂×C₁₃₇	1	1	yes	characteristic, complemented
454	#2319	C₂×C₁₃₇	1	1	yes	characteristic, complemented
455	#2296	C₂×C₁₃₇	1	1	yes	characteristic, complemented
456	C₂×#126	C₂²×C₁₃₇	1	2	yes	—
457	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
458	C₂×#124	C₂²×C₁₃₇	1	2	yes	—
459	C₂×#123	C₂²×C₁₃₇	1	2	yes	—
460	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
461	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₁₃₇	1	2	yes	—
463	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
464	C₂×#121	C₂²×C₁₃₇	1	2	yes	—
465	C₂×C₄×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
466	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
467	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
468	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
469	#400	C₂²×C₁₃₇	1	1	yes	characteristic
470	#400	C₂²×C₁₃₇	1	2	yes	—
471	#399	C₂²×C₁₃₇	1	1	yes	characteristic
472	#399	C₂²×C₁₃₇	1	2	yes	—
473	#399	C₂²×C₁₃₇	1	2	yes	—
474	#399	C₂²×C₁₃₇	1	2	yes	—
475	#398	C₂²×C₁₃₇	1	2	yes	—
476	#398	C₂²×C₁₃₇	1	2	yes	—
477	#398	C₂²×C₁₃₇	1	2	yes	—
478	#397	C₂²×C₁₃₇	1	2	yes	—
479	#397	C₂²×C₁₃₇	1	2	yes	—
480	#397	C₂²×C₁₃₇	1	2	yes	—
481	#397	C₂²×C₁₃₇	1	2	yes	—
482	#396	C₂²×C₁₃₇	1	2	yes	—
483	#396	C₂²×C₁₃₇	1	2	yes	—
484	#395	C₂²×C₁₃₇	1	2	yes	—
485	#395	C₂²×C₁₃₇	1	1	yes	characteristic
486	#394	C₂²×C₁₃₇	1	2	yes	—
487	#394	C₂²×C₁₃₇	1	1	yes	characteristic
488	#394	C₂²×C₁₃₇	1	1	yes	characteristic
489	#394	C₂²×C₁₃₇	1	2	yes	—
490	#394	C₂²×C₁₃₇	1	2	yes	—
491	#393	C₂²×C₁₃₇	1	2	yes	—
492	#393	C₂²×C₁₃₇	1	1	yes	characteristic
493	#392	C₂²×C₁₃₇	1	1	yes	characteristic
494	#392	C₂²×C₁₃₇	1	1	yes	characteristic
495	#392	C₂²×C₁₃₇	1	2	yes	—
496	#392	C₂²×C₁₃₇	1	2	yes	—
497	#391	C₂²×C₁₃₇	1	2	yes	—
498	#391	C₂²×C₁₃₇	1	2	yes	—
499	#391	C₂²×C₁₃₇	1	2	yes	—
500	#390	C₂²×C₁₃₇	1	2	yes	—
501	#390	C₂²×C₁₃₇	1	2	yes	—
502	#390	C₂²×C₁₃₇	1	2	yes	—
503	#390	C₂²×C₁₃₇	1	2	yes	—
504	#390	C₂²×C₁₃₇	1	2	yes	—
505	#389	C₂²×C₁₃₇	1	2	yes	—
506	#389	C₂²×C₁₃₇	1	2	yes	—
507	#389	C₂²×C₁₃₇	1	2	yes	—
508	#388	C₂²×C₁₃₇	1	2	yes	—
509	#388	C₂²×C₁₃₇	1	2	yes	—
510	#388	C₂²×C₁₃₇	1	2	yes	—
511	#388	C₂²×C₁₃₇	1	2	yes	—
512	#388	C₂²×C₁₃₇	1	2	yes	—
513	#388	C₂²×C₁₃₇	1	2	yes	—
514	#388	C₂²×C₁₃₇	1	2	yes	—
515	#388	C₂²×C₁₃₇	1	2	yes	—
516	#388	C₂²×C₁₃₇	1	2	yes	—
517	#387	C₂²×C₁₃₇	1	2	yes	—
518	#387	C₂²×C₁₃₇	1	2	yes	—
519	#387	C₂²×C₁₃₇	1	2	yes	—
520	#387	C₂²×C₁₃₇	1	2	yes	—
521	#386	C₂²×C₁₃₇	1	2	yes	—
522	#386	C₂²×C₁₃₇	1	2	yes	—
523	#386	C₂²×C₁₃₇	1	2	yes	—
524	#386	C₂²×C₁₃₇	1	2	yes	—
525	#386	C₂²×C₁₃₇	1	2	yes	—
526	#386	C₂²×C₁₃₇	1	2	yes	—
527	#386	C₂²×C₁₃₇	1	2	yes	—
528	#386	C₂²×C₁₃₇	1	2	yes	—
529	#385	C₂²×C₁₃₇	1	2	yes	—
530	#385	C₂²×C₁₃₇	1	2	yes	—
531	#385	C₂²×C₁₃₇	1	2	yes	—
532	#385	C₂²×C₁₃₇	1	2	yes	—
533	#383	C₂²×C₁₃₇	1	1	yes	characteristic
534	#382	C₂²×C₁₃₇	1	2	yes	—
535	#381	C₂²×C₁₃₇	1	2	yes	—
536	#380	C₂²×C₁₃₇	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₁₃₇	1	2	yes	—
542	#376	C₂²×C₁₃₇	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
544	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
548	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
549	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
550	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
555	#126	—	4	4	no	—
556	#124	—	2	4	no	—
557	#124	—	4	4	no	—
558	#123	—	4	4	no	—
559	C₂²⋊Q₈	—	4	4	no	—
560	C₂²⋊Q₈	—	4	4	no	—
561	C₂²⋊Q₈	—	4	4	no	—
562	#121	—	4	4	no	—
563	#121	—	4	4	no	—
564	C₄×D₄	—	2	4	no	—
565	#117	—	2	4	no	—
566	#117	—	4	2	no	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
610	C₂×C₄²	—	4	2	no	—
611	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
620	#95	C₂³×C₁₃₇	1	1	yes	characteristic
621	#95	C₂³×C₁₃₇	1	1	yes	characteristic
622	#95	C₂³×C₁₃₇	1	2	yes	—
623	#95	C₂³×C₁₃₇	1	2	yes	—
624	#95	C₂³×C₁₃₇	1	2	yes	—
625	#95	C₂³×C₁₃₇	1	2	yes	—
626	#95	C₂³×C₁₃₇	1	2	yes	—
627	#95	C₂³×C₁₃₇	1	2	yes	—
628	#95	C₂³×C₁₃₇	1	2	yes	—
629	#95	C₂³×C₁₃₇	1	2	yes	—
630	#95	C₂³×C₁₃₇	1	2	yes	—
631	#95	C₂³×C₁₃₇	1	2	yes	—
632	#95	C₂³×C₁₃₇	1	2	yes	—
633	#95	C₂³×C₁₃₇	1	2	yes	—
634	#95	C₂³×C₁₃₇	1	1	yes	characteristic
635	#95	C₂³×C₁₃₇	1	2	yes	—
636	#95	C₂³×C₁₃₇	1	1	yes	characteristic
637	#95	C₂³×C₁₃₇	1	2	yes	—
638	#95	C₂³×C₁₃₇	1	2	yes	—
639	#95	C₂³×C₁₃₇	1	2	yes	—
640	#95	C₂³×C₁₃₇	1	2	yes	—
641	#95	C₂³×C₁₃₇	1	2	yes	—
642	#95	C₂³×C₁₃₇	1	2	yes	—
643	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
644	C₂⁴	C₂⁴×C₁₃₇	1	2	yes	—
645	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	2	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	1	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	1	no	—
744	C₄²	—	4	1	no	—
745	C₄²	—	4	2	no	—
746	C₄²	#41×C₁₃₇	1	4	yes	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
766	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
767	Q₈	—	8	2	no	—
768	Q₈	—	8	4	no	—
769	D₄	—	4	4	no	—
770	D₄	—	8	2	no	—
771	D₄	—	8	4	no	—
772	D₄	—	8	4	no	—
773	D₄	—	8	4	no	—
774	D₄	—	8	4	no	—
775	C₂×C₄	—	2	8	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	8	4	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
819	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
820	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
821	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
822	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	4	yes	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
843	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	2	yes	—
844	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
845	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
846	C₂²	#585×C₁₃₇	1	2	yes	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	4	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₂	—	4	2	no	—
864	C₂	—	8	2	no	—
865	C₂	—	8	2	no	—
866	C₂	#3455×C₁₃₇	1	1	yes	characteristic
867	C₂	#3492×C₁₃₇	1	1	yes	characteristic
868	C₂	#3508×C₁₃₇	1	1	yes	characteristic
869	C₂	#3542×C₁₃₇	1	2	yes	—
870	C₂	#3561×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
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. #2850×C₁₃₇	C₂	semidirect
2. #2773×C₁₃₇	C₂	semidirect
3. #2732×C₁₃₇	C₂	semidirect
4. #2714×C₁₃₇	C₂	semidirect
5. #2710×C₁₃₇	C₂	semidirect
6. #2698×C₁₃₇	C₂	semidirect
7. #2692×C₁₃₇	C₂	semidirect
8. #2688×C₁₃₇	C₂	semidirect
9. #2672×C₁₃₇	C₂	semidirect
10. #2651×C₁₃₇	C₂	semidirect
11. #2610×C₁₃₇	C₂	semidirect
12. #2605×C₁₃₇	C₂	semidirect
13. #2598×C₁₃₇	C₂	semidirect
14. #2560×C₁₃₇	C₂	semidirect
15. #2540×C₁₃₇	C₂	semidirect
16. #2471×C₁₃₇	C₂	semidirect
17. #2337×C₁₃₇	C₂	semidirect
18. #2319×C₁₃₇	C₂	semidirect
19. #2296×C₁₃₇	C₂	semidirect
435. #36833	C₁₃₇	direct (N × H)
436. C₁₃₇	#36833	direct (N × H)
437. #2850	C₂×C₁₃₇	semidirect
438. #2773	C₂×C₁₃₇	semidirect
439. #2732	C₂×C₁₃₇	semidirect
440. #2714	C₂×C₁₃₇	semidirect
441. #2710	C₂×C₁₃₇	semidirect
442. #2698	C₂×C₁₃₇	semidirect
443. #2692	C₂×C₁₃₇	semidirect
444. #2688	C₂×C₁₃₇	semidirect
445. #2672	C₂×C₁₃₇	semidirect
446. #2651	C₂×C₁₃₇	semidirect
447. #2610	C₂×C₁₃₇	semidirect
448. #2605	C₂×C₁₃₇	semidirect
449. #2598	C₂×C₁₃₇	semidirect
450. #2560	C₂×C₁₃₇	semidirect
451. #2540	C₂×C₁₃₇	semidirect
452. #2471	C₂×C₁₃₇	semidirect
453. #2337	C₂×C₁₃₇	semidirect
454. #2319	C₂×C₁₃₇	semidirect
455. #2296	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2850×C₁₃₇	2
#2773×C₁₃₇	2
#2732×C₁₃₇	2
#2714×C₁₃₇	2
#2710×C₁₃₇	2
#2698×C₁₃₇	2
#2692×C₁₃₇	2
#2688×C₁₃₇	2
#2672×C₁₃₇	2
#2651×C₁₃₇	2
#2610×C₁₃₇	2
#2605×C₁₃₇	2
#2598×C₁₃₇	2
#2560×C₁₃₇	2
#2540×C₁₃₇	2
#2471×C₁₃₇	2
#2337×C₁₃₇	2
#2319×C₁₃₇	2
#2296×C₁₃₇	2
#36833	137

Subgroups — C137×#36833 #46886219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#36833 #46886219