Subgroups — C₁₃₇×#36834 #46886220

Order 35072.

1454 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2851×C₁₃₇	C₂	1	2	yes	maximal
2	#2788×C₁₃₇	C₂	1	2	yes	maximal
3	#2787×C₁₃₇	C₂	1	2	yes	maximal
4	#2774×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2770×C₁₃₇	C₂	1	2	yes	maximal
6	#2768×C₁₃₇	C₂	1	2	yes	maximal
7	#2766×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#2726×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#2719×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#2655×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#2611×C₁₃₇	C₂	1	1	yes	maximal, characteristic
12	#2606×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#2599×C₁₃₇	C₂	1	1	yes	maximal, characteristic
14	#2590×C₁₃₇	C₂	1	2	yes	maximal, complemented
15	#2584×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#2475×C₁₃₇	C₂	1	2	yes	maximal
17	#2336×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#2320×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#2296×C₁₃₇	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₇	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
27	#401×C₁₃₇	C₂²	1	2	yes	—
28	#400×C₁₃₇	C₂²	1	2	yes	—
29	#400×C₁₃₇	C₂²	1	2	yes	—
30	#400×C₁₃₇	C₂²	1	2	yes	—
31	#400×C₁₃₇	C₂²	1	2	yes	—
32	#400×C₁₃₇	C₂²	1	1	yes	characteristic
33	#400×C₁₃₇	C₂²	1	2	yes	—
34	#400×C₁₃₇	C₂²	1	2	yes	—
35	#399×C₁₃₇	C₂²	1	1	yes	characteristic
36	#398×C₁₃₇	C₂²	1	2	yes	—
37	#398×C₁₃₇	C₂²	1	2	yes	—
38	#398×C₁₃₇	C₂²	1	2	yes	—
39	#398×C₁₃₇	C₂²	1	2	yes	—
40	#398×C₁₃₇	C₂²	1	1	yes	characteristic
41	#398×C₁₃₇	C₂²	1	2	yes	—
42	#398×C₁₃₇	C₂²	1	2	yes	—
43	#398×C₁₃₇	C₂²	1	1	yes	characteristic
44	#398×C₁₃₇	C₂²	1	2	yes	—
45	#398×C₁₃₇	C₂²	1	2	yes	—
46	#398×C₁₃₇	C₂²	1	2	yes	—
47	#398×C₁₃₇	C₂²	1	2	yes	—
48	#397×C₁₃₇	C₂²	1	1	yes	characteristic
49	#397×C₁₃₇	C₂²	1	2	yes	—
50	#397×C₁₃₇	C₂²	1	1	yes	characteristic
51	#396×C₁₃₇	C₂²	1	2	yes	—
52	#395×C₁₃₇	C₂²	1	2	yes	—
53	#395×C₁₃₇	C₂²	1	1	yes	characteristic
54	#393×C₁₃₇	C₂²	1	1	yes	characteristic
55	#391×C₁₃₇	C₂²	1	2	yes	—
56	#389×C₁₃₇	C₂²	1	2	yes	—
57	#389×C₁₃₇	C₂²	1	2	yes	—
58	#389×C₁₃₇	C₂²	1	2	yes	—
59	#389×C₁₃₇	C₂²	1	2	yes	—
60	#389×C₁₃₇	C₂²	1	2	yes	—
61	#389×C₁₃₇	C₂²	1	2	yes	—
62	#389×C₁₃₇	C₂²	1	2	yes	—
63	#389×C₁₃₇	C₂²	1	2	yes	—
64	#389×C₁₃₇	C₂²	1	2	yes	—
65	#389×C₁₃₇	C₂²	1	2	yes	—
66	#389×C₁₃₇	C₂²	1	2	yes	—
67	#389×C₁₃₇	C₂²	1	2	yes	—
68	#388×C₁₃₇	C₂²	1	2	yes	—
69	#388×C₁₃₇	C₂²	1	2	yes	—
70	#388×C₁₃₇	C₂²	1	2	yes	—
71	#388×C₁₃₇	C₂²	1	2	yes	—
72	#387×C₁₃₇	C₂²	1	2	yes	—
73	#387×C₁₃₇	C₂²	1	2	yes	—
74	#387×C₁₃₇	C₂²	1	2	yes	—
75	#387×C₁₃₇	C₂²	1	2	yes	—
76	#387×C₁₃₇	C₂²	1	2	yes	—
77	#387×C₁₃₇	C₂²	1	2	yes	—
78	#387×C₁₃₇	C₂²	1	2	yes	—
79	#387×C₁₃₇	C₂²	1	2	yes	—
80	#387×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	#387×C₁₃₇	C₂²	1	2	yes	—
86	#387×C₁₃₇	C₂²	1	2	yes	—
87	#387×C₁₃₇	C₂²	1	2	yes	—
88	#387×C₁₃₇	C₂²	1	2	yes	—
89	#385×C₁₃₇	C₂²	1	2	yes	—
90	#385×C₁₃₇	C₂²	1	2	yes	—
91	#385×C₁₃₇	C₂²	1	2	yes	—
92	#385×C₁₃₇	C₂²	1	2	yes	—
93	#385×C₁₃₇	C₂²	1	2	yes	—
94	#385×C₁₃₇	C₂²	1	2	yes	—
95	#383×C₁₃₇	C₂²	1	2	yes	—
96	#383×C₁₃₇	C₂²	1	1	yes	characteristic
97	#382×C₁₃₇	C₂²	1	2	yes	—
98	#382×C₁₃₇	C₂²	1	2	yes	—
99	#380×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×C₄⋊C₄×C₁₃₇	C₂²	1	2	yes	—
106	#376×C₁₃₇	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃₇	C₂³	1	2	yes	—
110	#125×C₁₃₇	—	2	4	no	—
111	#125×C₁₃₇	—	4	4	no	—
112	#125×C₁₃₇	—	4	4	no	—
113	C₄×Q₈×C₁₃₇	—	2	4	no	—
114	#117×C₁₃₇	—	2	4	no	—
115	#117×C₁₃₇	—	4	2	no	—
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×C₄⋊C₄×C₁₃₇	C₂³	1	2	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	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
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	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₇	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₇	—	4	2	no	—
155	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
166	#95×C₁₃₇	C₂³	1	1	yes	characteristic
167	#95×C₁₃₇	C₂³	1	1	yes	characteristic
168	#95×C₁₃₇	C₂³	1	2	yes	—
169	#95×C₁₃₇	C₂³	1	2	yes	—
170	#95×C₁₃₇	C₂³	1	2	yes	—
171	#95×C₁₃₇	C₂³	1	2	yes	—
172	#95×C₁₃₇	C₂³	1	2	yes	—
173	#95×C₁₃₇	C₂³	1	2	yes	—
174	#95×C₁₃₇	C₂³	1	2	yes	—
175	#95×C₁₃₇	C₂³	1	2	yes	—
176	#95×C₁₃₇	C₂³	1	2	yes	—
177	#95×C₁₃₇	C₂³	1	2	yes	—
178	#95×C₁₃₇	C₂³	1	2	yes	—
179	#95×C₁₃₇	C₂³	1	2	yes	—
180	#95×C₁₃₇	C₂³	1	2	yes	—
181	#95×C₁₃₇	C₂³	1	2	yes	—
182	#95×C₁₃₇	C₂³	1	2	yes	—
183	#95×C₁₃₇	C₂³	1	2	yes	—
184	#95×C₁₃₇	C₂³	1	1	yes	characteristic
185	#95×C₁₃₇	C₂³	1	2	yes	—
186	#95×C₁₃₇	C₂³	1	2	yes	—
187	#95×C₁₃₇	C₂³	1	2	yes	—
188	#95×C₁₃₇	C₂³	1	1	yes	characteristic
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	2	yes	—
199	#95×C₁₃₇	C₂³	1	2	yes	—
200	#95×C₁₃₇	C₂³	1	2	yes	—
201	C₂⁴×C₁₃₇	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₁₃₇	—	2	2	no	—
203	C₂×Q₈×C₁₃₇	—	4	2	no	—
204	C₂²×C₄×C₁₃₇	—	2	2	no	—
205	C₂²×C₄×C₁₃₇	—	2	2	no	—
206	C₂²×C₄×C₁₃₇	—	2	2	no	—
207	C₂²×C₄×C₁₃₇	—	2	4	no	—
208	C₂²×C₄×C₁₃₇	—	4	2	no	—
209	C₂²×C₄×C₁₃₇	—	4	2	no	—
210	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₇	C₂⁴	1	2	yes	—
228	C₄⋊C₄×C₁₃₇	—	2	2	no	—
229	C₄⋊C₄×C₁₃₇	—	2	2	no	—
230	C₄⋊C₄×C₁₃₇	—	2	2	no	—
231	C₄⋊C₄×C₁₃₇	—	2	4	no	—
232	C₄⋊C₄×C₁₃₇	—	2	2	no	—
233	C₄⋊C₄×C₁₃₇	—	2	2	no	—
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	4	no	—
241	C₄⋊C₄×C₁₃₇	—	2	4	no	—
242	C₄⋊C₄×C₁₃₇	—	2	4	no	—
243	C₄⋊C₄×C₁₃₇	—	4	2	no	—
244	C₄⋊C₄×C₁₃₇	—	4	2	no	—
245	C₄⋊C₄×C₁₃₇	—	4	2	no	—
246	C₄⋊C₄×C₁₃₇	—	4	2	no	—
247	C₄⋊C₄×C₁₃₇	—	4	2	no	—
248	C₄⋊C₄×C₁₃₇	—	4	2	no	—
249	C₄⋊C₄×C₁₃₇	—	4	2	no	—
250	C₄⋊C₄×C₁₃₇	—	4	2	no	—
251	C₄⋊C₄×C₁₃₇	—	4	2	no	—
252	C₄⋊C₄×C₁₃₇	—	4	2	no	—
253	C₄⋊C₄×C₁₃₇	—	4	2	no	—
254	C₄⋊C₄×C₁₃₇	—	4	2	no	—
255	C₄⋊C₄×C₁₃₇	—	4	2	no	—
256	C₄⋊C₄×C₁₃₇	—	4	2	no	—
257	C₄⋊C₄×C₁₃₇	—	4	2	no	—
258	C₄⋊C₄×C₁₃₇	—	4	2	no	—
259	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₇	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
262	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
263	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
264	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
265	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
266	C₄²×C₁₃₇	—	2	2	no	—
267	C₄²×C₁₃₇	—	2	4	no	—
268	C₄²×C₁₃₇	—	2	4	no	—
269	C₄²×C₁₃₇	—	4	1	no	—
270	C₄²×C₁₃₇	—	4	1	no	—
271	C₄²×C₁₃₇	—	4	2	no	—
272	C₄²×C₁₃₇	—	4	2	no	—
273	C₄²×C₁₃₇	—	4	1	no	—
274	C₄²×C₁₃₇	—	4	1	no	—
275	C₄²×C₁₃₇	—	4	2	no	—
276	C₄²×C₁₃₇	#41	1	4	yes	—
277	C₂³×C₁₃₇	—	2	1	no	—
278	C₂³×C₁₃₇	—	2	1	no	—
279	C₂³×C₁₃₇	—	2	2	no	—
280	C₂³×C₁₃₇	—	2	2	no	—
281	C₂³×C₁₃₇	2₋¹⁺⁴	1	2	yes	—
282	C₂³×C₁₃₇	C₂⁵	1	1	yes	characteristic
283	Q₈×C₁₃₇	—	4	4	no	—
284	C₂×C₄×C₁₃₇	—	2	8	no	—
285	C₂×C₄×C₁₃₇	—	2	1	no	—
286	C₂×C₄×C₁₃₇	—	2	2	no	—
287	C₂×C₄×C₁₃₇	—	2	1	no	—
288	C₂×C₄×C₁₃₇	—	2	2	no	—
289	C₂×C₄×C₁₃₇	—	2	1	no	—
290	C₂×C₄×C₁₃₇	—	2	1	no	—
291	C₂×C₄×C₁₃₇	—	2	2	no	—
292	C₂×C₄×C₁₃₇	—	2	2	no	—
293	C₂×C₄×C₁₃₇	—	2	1	no	—
294	C₂×C₄×C₁₃₇	—	2	1	no	—
295	C₂×C₄×C₁₃₇	—	2	2	no	—
296	C₂×C₄×C₁₃₇	—	2	2	no	—
297	C₂×C₄×C₁₃₇	—	2	2	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	2	no	—
308	C₂×C₄×C₁₃₇	—	2	2	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	2	no	—
314	C₂×C₄×C₁₃₇	—	2	2	no	—
315	C₂×C₄×C₁₃₇	—	2	2	no	—
316	C₂×C₄×C₁₃₇	—	2	2	no	—
317	C₂×C₄×C₁₃₇	—	2	2	no	—
318	C₂×C₄×C₁₃₇	—	2	2	no	—
319	C₂×C₄×C₁₃₇	—	2	2	no	—
320	C₂×C₄×C₁₃₇	—	2	2	no	—
321	C₂×C₄×C₁₃₇	—	2	2	no	—
322	C₂×C₄×C₁₃₇	—	2	2	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	—	4	8	no	—
331	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
332	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
334	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	4	yes	—
336	C₂²×C₁₃₇	—	2	2	no	—
337	C₂²×C₁₃₇	—	2	4	no	—
338	C₂²×C₁₃₇	—	4	1	no	—
339	C₂²×C₁₃₇	—	4	1	no	—
340	C₂²×C₁₃₇	—	4	2	no	—
341	C₂²×C₁₃₇	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₁₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₁₃₇	C₂×2₋¹⁺⁴	1	2	yes	—
345	C₂²×C₁₃₇	#585	1	2	yes	—
346	C₄×C₁₃₇	—	2	2	no	—
347	C₄×C₁₃₇	—	2	2	no	—
348	C₄×C₁₃₇	—	2	2	no	—
349	C₄×C₁₃₇	—	2	2	no	—
350	C₄×C₁₃₇	—	2	4	no	—
351	C₄×C₁₃₇	—	4	1	no	—
352	C₄×C₁₃₇	—	4	2	no	—
353	C₄×C₁₃₇	—	4	2	no	—
354	C₄×C₁₃₇	—	4	2	no	—
355	C₄×C₁₃₇	—	4	2	no	—
356	C₄×C₁₃₇	—	4	1	no	—
357	C₄×C₁₃₇	—	4	2	no	—
358	C₄×C₁₃₇	—	4	2	no	—
359	C₄×C₁₃₇	—	4	2	no	—
360	C₄×C₁₃₇	—	4	2	no	—
361	C₄×C₁₃₇	—	4	2	no	—
362	C₄×C₁₃₇	—	4	2	no	—
363	C₄×C₁₃₇	—	4	2	no	—
364	C₂×C₁₃₇	—	4	2	no	—
365	C₂×C₁₃₇	#3455	1	1	yes	characteristic
366	C₂×C₁₃₇	#3492	1	1	yes	characteristic
367	C₂×C₁₃₇	#3509	1	1	yes	characteristic
368	C₂×C₁₃₇	#3541	1	2	yes	—
369	C₂×C₁₃₇	#3563	1	2	yes	—
370	#36834	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₁₃₇	#36834	1	1	yes	characteristic, direct product factor, Sylow
372	#2851	C₂×C₁₃₇	1	2	yes	—
373	#2788	C₂×C₁₃₇	1	2	yes	—
374	#2787	C₂×C₁₃₇	1	2	yes	—
375	#2774	C₂×C₁₃₇	1	2	yes	complemented
376	#2770	C₂×C₁₃₇	1	2	yes	—
377	#2768	C₂×C₁₃₇	1	2	yes	—
378	#2766	C₂×C₁₃₇	1	2	yes	complemented
379	#2726	C₂×C₁₃₇	1	2	yes	complemented
380	#2719	C₂×C₁₃₇	1	2	yes	complemented
381	#2655	C₂×C₁₃₇	1	2	yes	complemented
382	#2611	C₂×C₁₃₇	1	1	yes	characteristic
383	#2606	C₂×C₁₃₇	1	1	yes	characteristic, complemented
384	#2599	C₂×C₁₃₇	1	1	yes	characteristic
385	#2590	C₂×C₁₃₇	1	2	yes	complemented
386	#2584	C₂×C₁₃₇	1	1	yes	characteristic, complemented
387	#2475	C₂×C₁₃₇	1	2	yes	—
388	#2336	C₂×C₁₃₇	1	1	yes	characteristic, complemented
389	#2320	C₂×C₁₃₇	1	1	yes	characteristic, complemented
390	#2296	C₂×C₁₃₇	1	1	yes	characteristic
391	C₂×#125	C₂²×C₁₃₇	1	1	yes	characteristic
392	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
393	C₂×#125	C₂²×C₁₃₇	1	2	yes	—
394	C₂×C₄×Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
395	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
396	C₂×#117	C₂²×C₁₃₇	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
398	#401	C₂²×C₁₃₇	1	2	yes	—
399	#400	C₂²×C₁₃₇	1	2	yes	—
400	#400	C₂²×C₁₃₇	1	1	yes	characteristic
401	#400	C₂²×C₁₃₇	1	2	yes	—
402	#400	C₂²×C₁₃₇	1	2	yes	—
403	#400	C₂²×C₁₃₇	1	2	yes	—
404	#400	C₂²×C₁₃₇	1	2	yes	—
405	#400	C₂²×C₁₃₇	1	2	yes	—
406	#399	C₂²×C₁₃₇	1	1	yes	characteristic
407	#398	C₂²×C₁₃₇	1	2	yes	—
408	#398	C₂²×C₁₃₇	1	2	yes	—
409	#398	C₂²×C₁₃₇	1	2	yes	—
410	#398	C₂²×C₁₃₇	1	2	yes	—
411	#398	C₂²×C₁₃₇	1	1	yes	characteristic
412	#398	C₂²×C₁₃₇	1	2	yes	—
413	#398	C₂²×C₁₃₇	1	2	yes	—
414	#398	C₂²×C₁₃₇	1	1	yes	characteristic
415	#398	C₂²×C₁₃₇	1	2	yes	—
416	#398	C₂²×C₁₃₇	1	2	yes	—
417	#398	C₂²×C₁₃₇	1	2	yes	—
418	#398	C₂²×C₁₃₇	1	2	yes	—
419	#397	C₂²×C₁₃₇	1	1	yes	characteristic
420	#397	C₂²×C₁₃₇	1	1	yes	characteristic
421	#397	C₂²×C₁₃₇	1	2	yes	—
422	#396	C₂²×C₁₃₇	1	2	yes	—
423	#395	C₂²×C₁₃₇	1	2	yes	—
424	#395	C₂²×C₁₃₇	1	1	yes	characteristic
425	#393	C₂²×C₁₃₇	1	1	yes	characteristic
426	#391	C₂²×C₁₃₇	1	2	yes	—
427	#389	C₂²×C₁₃₇	1	2	yes	—
428	#389	C₂²×C₁₃₇	1	2	yes	—
429	#389	C₂²×C₁₃₇	1	2	yes	—
430	#389	C₂²×C₁₃₇	1	2	yes	—
431	#389	C₂²×C₁₃₇	1	2	yes	—
432	#389	C₂²×C₁₃₇	1	2	yes	—
433	#389	C₂²×C₁₃₇	1	2	yes	—
434	#389	C₂²×C₁₃₇	1	2	yes	—
435	#389	C₂²×C₁₃₇	1	2	yes	—
436	#389	C₂²×C₁₃₇	1	2	yes	—
437	#389	C₂²×C₁₃₇	1	2	yes	—
438	#389	C₂²×C₁₃₇	1	2	yes	—
439	#388	C₂²×C₁₃₇	1	2	yes	—
440	#388	C₂²×C₁₃₇	1	2	yes	—
441	#388	C₂²×C₁₃₇	1	2	yes	—
442	#388	C₂²×C₁₃₇	1	2	yes	—
443	#387	C₂²×C₁₃₇	1	2	yes	—
444	#387	C₂²×C₁₃₇	1	2	yes	—
445	#387	C₂²×C₁₃₇	1	2	yes	—
446	#387	C₂²×C₁₃₇	1	2	yes	—
447	#387	C₂²×C₁₃₇	1	2	yes	—
448	#387	C₂²×C₁₃₇	1	2	yes	—
449	#387	C₂²×C₁₃₇	1	2	yes	—
450	#387	C₂²×C₁₃₇	1	2	yes	—
451	#387	C₂²×C₁₃₇	1	2	yes	—
452	#387	C₂²×C₁₃₇	1	2	yes	—
453	#387	C₂²×C₁₃₇	1	2	yes	—
454	#387	C₂²×C₁₃₇	1	2	yes	—
455	#387	C₂²×C₁₃₇	1	2	yes	—
456	#387	C₂²×C₁₃₇	1	2	yes	—
457	#387	C₂²×C₁₃₇	1	2	yes	—
458	#387	C₂²×C₁₃₇	1	2	yes	—
459	#387	C₂²×C₁₃₇	1	2	yes	—
460	#385	C₂²×C₁₃₇	1	2	yes	—
461	#385	C₂²×C₁₃₇	1	2	yes	—
462	#385	C₂²×C₁₃₇	1	2	yes	—
463	#385	C₂²×C₁₃₇	1	2	yes	—
464	#385	C₂²×C₁₃₇	1	2	yes	—
465	#385	C₂²×C₁₃₇	1	2	yes	—
466	#383	C₂²×C₁₃₇	1	2	yes	—
467	#383	C₂²×C₁₃₇	1	1	yes	characteristic
468	#382	C₂²×C₁₃₇	1	2	yes	—
469	#382	C₂²×C₁₃₇	1	2	yes	—
470	#380	C₂²×C₁₃₇	1	2	yes	—
471	#380	C₂²×C₁₃₇	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
477	#376	C₂²×C₁₃₇	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃₇	1	2	yes	—
481	#125	—	2	4	no	—
482	#125	—	4	4	no	—
483	#125	—	4	4	no	—
484	C₄×Q₈	—	2	4	no	—
485	#117	—	2	4	no	—
486	#117	—	4	2	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
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	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
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	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₇	1	2	yes	—
525	C₂×C₄²	—	4	2	no	—
526	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
537	#95	C₂³×C₁₃₇	1	1	yes	characteristic
538	#95	C₂³×C₁₃₇	1	1	yes	characteristic
539	#95	C₂³×C₁₃₇	1	2	yes	—
540	#95	C₂³×C₁₃₇	1	2	yes	—
541	#95	C₂³×C₁₃₇	1	2	yes	—
542	#95	C₂³×C₁₃₇	1	2	yes	—
543	#95	C₂³×C₁₃₇	1	2	yes	—
544	#95	C₂³×C₁₃₇	1	2	yes	—
545	#95	C₂³×C₁₃₇	1	2	yes	—
546	#95	C₂³×C₁₃₇	1	2	yes	—
547	#95	C₂³×C₁₃₇	1	2	yes	—
548	#95	C₂³×C₁₃₇	1	2	yes	—
549	#95	C₂³×C₁₃₇	1	2	yes	—
550	#95	C₂³×C₁₃₇	1	2	yes	—
551	#95	C₂³×C₁₃₇	1	2	yes	—
552	#95	C₂³×C₁₃₇	1	2	yes	—
553	#95	C₂³×C₁₃₇	1	2	yes	—
554	#95	C₂³×C₁₃₇	1	2	yes	—
555	#95	C₂³×C₁₃₇	1	1	yes	characteristic
556	#95	C₂³×C₁₃₇	1	2	yes	—
557	#95	C₂³×C₁₃₇	1	2	yes	—
558	#95	C₂³×C₁₃₇	1	2	yes	—
559	#95	C₂³×C₁₃₇	1	1	yes	characteristic
560	#95	C₂³×C₁₃₇	1	2	yes	—
561	#95	C₂³×C₁₃₇	1	2	yes	—
562	#95	C₂³×C₁₃₇	1	2	yes	—
563	#95	C₂³×C₁₃₇	1	2	yes	—
564	#95	C₂³×C₁₃₇	1	2	yes	—
565	#95	C₂³×C₁₃₇	1	2	yes	—
566	#95	C₂³×C₁₃₇	1	2	yes	—
567	#95	C₂³×C₁₃₇	1	2	yes	—
568	#95	C₂³×C₁₃₇	1	2	yes	—
569	#95	C₂³×C₁₃₇	1	2	yes	—
570	#95	C₂³×C₁₃₇	1	2	yes	—
571	#95	C₂³×C₁₃₇	1	2	yes	—
572	C₂⁴	C₂⁴×C₁₃₇	1	1	yes	characteristic
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃₇	1	2	yes	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	2	no	—
644	C₄²	—	4	1	no	—
645	C₄²	—	4	1	no	—
646	C₄²	—	4	2	no	—
647	C₄²	#41×C₁₃₇	1	4	yes	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	2₋¹⁺⁴×C₁₃₇	1	2	yes	—
653	C₂³	C₂⁵×C₁₃₇	1	1	yes	characteristic
654	Q₈	—	4	4	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	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	2	no	—
686	C₂×C₄	—	2	2	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	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
703	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
704	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
705	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
706	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	4	yes	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	2	no	—
712	C₂²	C₂²×#41×C₁₃₇	1	1	yes	characteristic
713	C₂²	C₂×H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
714	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
715	C₂²	C₂×2₋¹⁺⁴×C₁₃₇	1	2	yes	—
716	C₂²	#585×C₁₃₇	1	2	yes	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₂	—	4	2	no	—
736	C₂	#3455×C₁₃₇	1	1	yes	characteristic
737	C₂	#3492×C₁₃₇	1	1	yes	characteristic
738	C₂	#3509×C₁₃₇	1	1	yes	characteristic
739	C₂	#3541×C₁₃₇	1	2	yes	—
740	C₂	#3563×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₇
prime radical	C₂⁴×C₁₃₇	C₂⁴
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
4. #2774×C₁₃₇	C₂	semidirect
7. #2766×C₁₃₇	C₂	semidirect
8. #2726×C₁₃₇	C₂	semidirect
9. #2719×C₁₃₇	C₂	semidirect
10. #2655×C₁₃₇	C₂	semidirect
12. #2606×C₁₃₇	C₂	semidirect
14. #2590×C₁₃₇	C₂	semidirect
15. #2584×C₁₃₇	C₂	semidirect
17. #2336×C₁₃₇	C₂	semidirect
18. #2320×C₁₃₇	C₂	semidirect
370. #36834	C₁₃₇	direct (N × H)
371. C₁₃₇	#36834	direct (N × H)
375. #2774	C₂×C₁₃₇	semidirect
378. #2766	C₂×C₁₃₇	semidirect
379. #2726	C₂×C₁₃₇	semidirect
380. #2719	C₂×C₁₃₇	semidirect
381. #2655	C₂×C₁₃₇	semidirect
383. #2606	C₂×C₁₃₇	semidirect
385. #2590	C₂×C₁₃₇	semidirect
386. #2584	C₂×C₁₃₇	semidirect
388. #2336	C₂×C₁₃₇	semidirect
389. #2320	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#2851×C₁₃₇	2
#2788×C₁₃₇	2
#2787×C₁₃₇	2
#2774×C₁₃₇	2
#2770×C₁₃₇	2
#2768×C₁₃₇	2
#2766×C₁₃₇	2
#2726×C₁₃₇	2
#2719×C₁₃₇	2
#2655×C₁₃₇	2
#2611×C₁₃₇	2
#2606×C₁₃₇	2
#2599×C₁₃₇	2
#2590×C₁₃₇	2
#2584×C₁₃₇	2
#2475×C₁₃₇	2
#2336×C₁₃₇	2
#2320×C₁₃₇	2
#2296×C₁₃₇	2
#36834	137

Subgroups — C137×#36834 #46886220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#36834 #46886220