Subgroups — C₁₃₇×#26920 #46876306

Order 35072.

808 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3081×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#2948×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2045×C₁₃₇	C₂	1	2	yes	maximal, complemented
4	#2027×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2011×C₁₃₇	C₂	1	1	yes	maximal, characteristic
6	#1931×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1922×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1887×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1856×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₃₇	C₂²	1	2	yes	—
11	#544×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
13	#518×C₁₃₇	C₂²	1	2	yes	—
14	#518×C₁₃₇	C₂²	1	1	yes	characteristic
15	#478×C₁₃₇	—	2	2	no	—
16	#478×C₁₃₇	—	2	2	no	—
17	#476×C₁₃₇	—	2	2	no	—
18	#474×C₁₃₇	—	2	2	no	—
19	#442×C₁₃₇	—	2	2	no	—
20	#442×C₁₃₇	—	2	2	no	—
21	C₄×D₈×C₁₃₇	—	2	2	no	—
22	C₄×D₈×C₁₃₇	—	2	2	no	—
23	#428×C₁₃₇	C₂²	1	2	yes	—
24	#427×C₁₃₇	C₂²	1	2	yes	—
25	#424×C₁₃₇	C₂²	1	2	yes	—
26	#418×C₁₃₇	C₂²	1	2	yes	—
27	#418×C₁₃₇	C₂²	1	2	yes	—
28	#418×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#100×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
32	#405×C₁₃₇	C₂²	1	2	yes	—
33	#390×C₁₃₇	C₂²	1	1	yes	characteristic
34	#343×C₁₃₇	C₂²	1	1	yes	characteristic
35	#341×C₁₃₇	C₂²	1	2	yes	—
36	#339×C₁₃₇	C₂²	1	2	yes	—
37	#339×C₁₃₇	C₂²	1	2	yes	—
38	#336×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂²×D₄×C₁₃₇	—	4	1	no	—
40	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
42	C₂×D₈×C₁₃₇	—	2	4	no	—
43	C₂×D₈×C₁₃₇	—	2	4	no	—
44	C₂×D₈×C₁₃₇	—	2	2	no	—
45	C₂×D₈×C₁₃₇	—	2	2	no	—
46	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
47	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
50	#127×C₁₃₇	—	2	4	no	—
51	#125×C₁₃₇	—	2	2	no	—
52	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
53	C₄×D₄×C₁₃₇	—	2	2	no	—
54	C₄×D₄×C₁₃₇	—	2	2	no	—
55	C₄×D₄×C₁₃₇	—	2	2	no	—
56	C₄×D₄×C₁₃₇	—	2	2	no	—
57	C₄×D₄×C₁₃₇	—	2	2	no	—
58	C₄×D₄×C₁₃₇	—	2	2	no	—
59	#117×C₁₃₇	C₂³	1	2	yes	—
60	#117×C₁₃₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₇	—	4	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₇	—	4	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₇	—	4	1	no	—
65	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
66	#107×C₁₃₇	—	2	2	no	—
67	#107×C₁₃₇	D₄	1	2	yes	complemented
68	#107×C₁₃₇	D₄	1	2	yes	complemented
69	#106×C₁₃₇	—	2	2	no	—
70	#106×C₁₃₇	D₄	1	2	yes	complemented
71	#106×C₁₃₇	D₄	1	2	yes	complemented
72	C₄⋊C₈×C₁₃₇	—	2	2	no	—
73	C₄⋊C₈×C₁₃₇	—	2	2	no	—
74	#102×C₁₃₇	—	2	2	no	—
75	#102×C₁₃₇	—	2	2	no	—
76	#102×C₁₃₇	—	2	2	no	—
77	#102×C₁₃₇	—	2	2	no	—
78	#102×C₁₃₇	—	2	2	no	—
79	#102×C₁₃₇	—	2	2	no	—
80	#102×C₁₃₇	—	2	2	no	—
81	#102×C₁₃₇	—	2	2	no	—
82	#100×C₁₃₇	—	2	4	no	—
83	#100×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	2	no	—
85	C₄×C₈×C₁₃₇	—	2	2	no	—
86	C₂⁴×C₁₃₇	—	2	1	no	—
87	C₂⁴×C₁₃₇	—	2	2	no	—
88	C₂×Q₈×C₁₃₇	—	4	1	no	—
89	C₂×D₄×C₁₃₇	—	2	2	no	—
90	C₂×D₄×C₁₃₇	—	2	2	no	—
91	C₂×D₄×C₁₃₇	—	2	2	no	—
92	C₂×D₄×C₁₃₇	—	2	2	no	—
93	C₂×D₄×C₁₃₇	—	2	2	no	—
94	C₂×D₄×C₁₃₇	—	2	2	no	—
95	C₂×D₄×C₁₃₇	—	2	2	no	—
96	C₂×D₄×C₁₃₇	—	2	1	no	—
97	C₂×D₄×C₁₃₇	—	4	4	no	—
98	C₂×D₄×C₁₃₇	—	8	2	no	—
99	C₂×D₄×C₁₃₇	—	8	2	no	—
100	C₂×D₄×C₁₃₇	#41	1	4	yes	—
101	C₂×D₄×C₁₃₇	#41	1	2	yes	—
102	C₂²×C₄×C₁₃₇	—	2	1	no	—
103	C₂²×C₄×C₁₃₇	—	2	1	no	—
104	C₂²×C₄×C₁₃₇	—	4	1	no	—
105	C₂²×C₄×C₁₃₇	—	4	1	no	—
106	C₂²×C₄×C₁₃₇	—	4	2	no	—
107	C₂²×C₄×C₁₃₇	—	4	2	no	—
108	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
109	D₈×C₁₃₇	—	2	8	no	—
110	D₈×C₁₃₇	—	2	8	no	—
111	M₁₆×C₁₃₇	—	2	2	no	—
112	M₁₆×C₁₃₇	—	2	2	no	—
113	M₁₆×C₁₃₇	—	2	2	no	—
114	M₁₆×C₁₃₇	—	2	2	no	—
115	C₂×C₈×C₁₃₇	—	2	2	no	—
116	C₂×C₈×C₁₃₇	—	2	2	no	—
117	C₂×C₈×C₁₃₇	—	2	2	no	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₁₃₇	—	2	2	no	—
122	C₄⋊C₄×C₁₃₇	—	4	1	no	—
123	C₄⋊C₄×C₁₃₇	—	4	2	no	—
124	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
129	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
130	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
132	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₇	—	8	2	no	—
134	C₄²×C₁₃₇	—	2	2	no	—
135	C₄²×C₁₃₇	—	2	2	no	—
136	C₄²×C₁₃₇	—	2	2	no	—
137	C₂³×C₁₃₇	—	2	2	no	—
138	C₂³×C₁₃₇	—	2	4	no	—
139	C₂³×C₁₃₇	—	4	2	no	—
140	C₂³×C₁₃₇	—	4	1	no	—
141	C₂³×C₁₃₇	—	4	2	no	—
142	C₂³×C₁₃₇	—	4	1	no	—
143	C₂³×C₁₃₇	—	8	1	no	—
144	C₂³×C₁₃₇	—	8	2	no	—
145	C₂³×C₁₃₇	—	8	2	no	—
146	C₂³×C₁₃₇	—	8	1	no	—
147	C₂³×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
148	Q₈×C₁₃₇	—	16	1	no	—
149	D₄×C₁₃₇	—	2	4	no	—
150	D₄×C₁₃₇	—	2	4	no	—
151	D₄×C₁₃₇	—	2	4	no	—
152	D₄×C₁₃₇	—	4	2	no	—
153	D₄×C₁₃₇	—	4	2	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	D₄×C₁₃₇	—	8	8	no	—
156	C₂×C₄×C₁₃₇	—	2	2	no	—
157	C₂×C₄×C₁₃₇	—	2	2	no	—
158	C₂×C₄×C₁₃₇	—	2	2	no	—
159	C₂×C₄×C₁₃₇	—	2	2	no	—
160	C₂×C₄×C₁₃₇	—	2	2	no	—
161	C₂×C₄×C₁₃₇	—	4	1	no	—
162	C₂×C₄×C₁₃₇	—	4	1	no	—
163	C₂×C₄×C₁₃₇	—	4	1	no	—
164	C₂×C₄×C₁₃₇	—	8	1	no	—
165	C₂×C₄×C₁₃₇	—	16	2	no	—
166	C₂×C₄×C₁₃₇	—	16	1	no	—
167	C₂×C₄×C₁₃₇	—	16	1	no	—
168	C₂×C₄×C₁₃₇	—	16	2	no	—
169	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₁₃₇	—	2	2	no	—
174	C₈×C₁₃₇	—	2	2	no	—
175	C₈×C₁₃₇	—	4	2	no	—
176	C₈×C₁₃₇	—	4	2	no	—
177	C₂²×C₁₃₇	—	2	1	no	—
178	C₂²×C₁₃₇	—	2	1	no	—
179	C₂²×C₁₃₇	—	4	2	no	—
180	C₂²×C₁₃₇	—	4	4	no	—
181	C₂²×C₁₃₇	—	8	4	no	—
182	C₂²×C₁₃₇	—	8	2	no	—
183	C₂²×C₁₃₇	—	8	2	no	—
184	C₂²×C₁₃₇	—	8	1	no	—
185	C₂²×C₁₃₇	—	8	1	no	—
186	C₂²×C₁₃₇	—	8	2	no	—
187	C₂²×C₁₃₇	—	16	1	no	—
188	C₂²×C₁₃₇	—	16	2	no	—
189	C₂²×C₁₃₇	#539	1	1	yes	characteristic
190	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
191	C₂²×C₁₃₇	#551	1	1	yes	characteristic
192	C₄×C₁₃₇	—	4	2	no	—
193	C₄×C₁₃₇	—	4	2	no	—
194	C₄×C₁₃₇	—	4	2	no	—
195	C₄×C₁₃₇	—	4	2	no	—
196	C₄×C₁₃₇	—	4	2	no	—
197	C₄×C₁₃₇	—	8	1	no	—
198	C₄×C₁₃₇	#525	1	2	yes	—
199	C₄×C₁₃₇	#548	1	2	yes	—
200	C₂×C₁₃₇	—	2	1	no	—
201	C₂×C₁₃₇	—	2	1	no	—
202	C₂×C₁₃₇	—	8	4	no	—
203	C₂×C₁₃₇	—	8	2	no	—
204	C₂×C₁₃₇	#2463	1	1	yes	characteristic
205	C₂×C₁₃₇	#3288	1	1	yes	characteristic
206	C₂×C₁₃₇	#3292	1	1	yes	characteristic
207	#26920	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₇	#26920	1	1	yes	characteristic, direct product factor, Sylow
209	#3081	C₂×C₁₃₇	1	2	yes	complemented
210	#2948	C₂×C₁₃₇	1	2	yes	complemented
211	#2045	C₂×C₁₃₇	1	2	yes	complemented
212	#2027	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	#2011	C₂×C₁₃₇	1	1	yes	characteristic
214	#1931	C₂×C₁₃₇	1	2	yes	complemented
215	#1922	C₂×C₁₃₇	1	2	yes	complemented
216	#1887	C₂×C₁₃₇	1	2	yes	complemented
217	#1856	C₂×C₁₃₇	1	1	yes	characteristic, complemented
218	C₂²×D₈	C₂²×C₁₃₇	1	2	yes	—
219	#544	C₂²×C₁₃₇	1	1	yes	characteristic
220	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
221	#518	C₂²×C₁₃₇	1	2	yes	—
222	#518	C₂²×C₁₃₇	1	1	yes	characteristic
223	#478	—	2	2	no	—
224	#478	—	2	2	no	—
225	#476	—	2	2	no	—
226	#474	—	2	2	no	—
227	#442	—	2	2	no	—
228	#442	—	2	2	no	—
229	C₄×D₈	—	2	2	no	—
230	C₄×D₈	—	2	2	no	—
231	#428	C₂²×C₁₃₇	1	2	yes	—
232	#427	C₂²×C₁₃₇	1	2	yes	—
233	#424	C₂²×C₁₃₇	1	2	yes	—
234	#418	C₂²×C₁₃₇	1	2	yes	—
235	#418	C₂²×C₁₃₇	1	2	yes	—
236	#418	C₂²×C₁₃₇	1	2	yes	—
237	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
238	C₂×#100	C₂²×C₁₃₇	1	1	yes	characteristic
239	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
240	#405	C₂²×C₁₃₇	1	2	yes	—
241	#390	C₂²×C₁₃₇	1	1	yes	characteristic
242	#343	C₂²×C₁₃₇	1	1	yes	characteristic
243	#341	C₂²×C₁₃₇	1	2	yes	—
244	#339	C₂²×C₁₃₇	1	2	yes	—
245	#339	C₂²×C₁₃₇	1	2	yes	—
246	#336	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₂²×D₄	—	4	1	no	—
248	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
249	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₂×D₈	—	2	4	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
255	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
257	C₄⋊Q₈	—	2	2	no	—
258	#127	—	2	4	no	—
259	#125	—	2	2	no	—
260	C₂²⋊Q₈	—	4	1	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	#117	C₂³×C₁₃₇	1	2	yes	—
268	#117	C₂³×C₁₃₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	4	1	no	—
271	C₂×C₂²⋊C₄	—	4	2	no	—
272	C₂×C₂²⋊C₄	—	4	1	no	—
273	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	D₄×C₁₃₇	1	2	yes	complemented
276	#107	D₄×C₁₃₇	1	2	yes	complemented
277	#106	—	2	2	no	—
278	#106	D₄×C₁₃₇	1	2	yes	complemented
279	#106	D₄×C₁₃₇	1	2	yes	complemented
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#100	—	2	4	no	—
291	#100	—	2	2	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	2	2	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	#41×C₁₃₇	1	4	yes	—
309	C₂×D₄	#41×C₁₃₇	1	2	yes	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
317	D₈	—	2	8	no	—
318	D₈	—	2	8	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
328	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
333	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
334	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
335	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	1	no	—
355	C₂³	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
356	Q₈	—	16	1	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	8	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	16	1	no	—
374	C₂×C₄	—	16	2	no	—
375	C₂×C₄	—	16	1	no	—
376	C₂×C₄	—	16	2	no	—
377	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
380	C₂×C₄	2₋¹⁺⁴×C₁₃₇	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	1	no	—
396	C₂²	—	16	2	no	—
397	C₂²	#539×C₁₃₇	1	1	yes	characteristic
398	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
399	C₂²	#551×C₁₃₇	1	1	yes	characteristic
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	#525×C₁₃₇	1	2	yes	—
407	C₄	#548×C₁₃₇	1	2	yes	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	8	4	no	—
411	C₂	—	8	2	no	—
412	C₂	#2463×C₁₃₇	1	1	yes	characteristic
413	C₂	#3288×C₁₃₇	1	1	yes	characteristic
414	C₂	#3292×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#2011×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂²×C₄×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3081×C₁₃₇	C₂	semidirect
2. #2948×C₁₃₇	C₂	semidirect
3. #2045×C₁₃₇	C₂	semidirect
4. #2027×C₁₃₇	C₂	semidirect
6. #1931×C₁₃₇	C₂	semidirect
7. #1922×C₁₃₇	C₂	semidirect
8. #1887×C₁₃₇	C₂	semidirect
9. #1856×C₁₃₇	C₂	semidirect
67. #107×C₁₃₇	D₄	semidirect
68. #107×C₁₃₇	D₄	semidirect
70. #106×C₁₃₇	D₄	semidirect
71. #106×C₁₃₇	D₄	semidirect
207. #26920	C₁₃₇	direct (N × H)
208. C₁₃₇	#26920	direct (N × H)
209. #3081	C₂×C₁₃₇	semidirect
210. #2948	C₂×C₁₃₇	semidirect
211. #2045	C₂×C₁₃₇	semidirect
212. #2027	C₂×C₁₃₇	semidirect
214. #1931	C₂×C₁₃₇	semidirect
215. #1922	C₂×C₁₃₇	semidirect
216. #1887	C₂×C₁₃₇	semidirect
217. #1856	C₂×C₁₃₇	semidirect
275. #107	D₄×C₁₃₇	semidirect
276. #107	D₄×C₁₃₇	semidirect
278. #106	D₄×C₁₃₇	semidirect
279. #106	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3081×C₁₃₇	2
#2948×C₁₃₇	2
#2045×C₁₃₇	2
#2027×C₁₃₇	2
#2011×C₁₃₇	2
#1931×C₁₃₇	2
#1922×C₁₃₇	2
#1887×C₁₃₇	2
#1856×C₁₃₇	2
#26920	137

Subgroups — C137×#26920 #46876306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26920 #46876306