Subgroups — C₁₃₇×#26274 #46875660

Order 35072.

796 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3155×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3096×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2952×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2051×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2037×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1978×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1975×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1972×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1951×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1883×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1773×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₃₇	C₂²	1	2	yes	—
13	C₂×#135×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	#535×C₁₃₇	C₂²	1	2	yes	—
16	#520×C₁₃₇	C₂²	1	2	yes	—
17	#496×C₁₃₇	—	2	2	no	—
18	#495×C₁₃₇	—	2	1	no	—
19	#493×C₁₃₇	—	2	1	no	—
20	#482×C₁₃₇	—	2	2	no	—
21	#482×C₁₃₇	—	2	2	no	—
22	#481×C₁₃₇	—	2	2	no	—
23	#480×C₁₃₇	—	2	2	no	—
24	#442×C₁₃₇	—	2	1	no	—
25	#441×C₁₃₇	—	2	1	no	—
26	C₄×SD₁₆×C₁₃₇	—	2	2	no	—
27	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×#108×C₁₃₇	C₂²	1	1	yes	characteristic
29	#428×C₁₃₇	C₂²	1	2	yes	—
30	#427×C₁₃₇	C₂²	1	1	yes	characteristic
31	C₂×#106×C₁₃₇	C₂²	1	1	yes	characteristic
32	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
33	#418×C₁₃₇	C₂²	1	2	yes	—
34	#417×C₁₃₇	C₂²	1	2	yes	—
35	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
36	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
37	#408×C₁₃₇	C₂²	1	2	yes	—
38	#405×C₁₃₇	C₂²	1	1	yes	characteristic
39	#405×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
41	#390×C₁₃₇	C₂²	1	2	yes	—
42	#343×C₁₃₇	C₂²	1	2	yes	—
43	#339×C₁₃₇	C₂²	1	1	yes	characteristic
44	#339×C₁₃₇	C₂²	1	1	yes	characteristic
45	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
47	AGL(1,ℤ/8)×C₁₃₇	—	2	4	no	—
48	AGL(1,ℤ/8)×C₁₃₇	—	4	2	no	—
49	#135×C₁₃₇	—	2	2	no	—
50	#135×C₁₃₇	—	2	2	no	—
51	C₂×Q₁₆×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
53	C₂×SD₁₆×C₁₃₇	D₄	1	2	yes	—
54	C₂×D₈×C₁₃₇	—	2	2	no	—
55	C₂×D₈×C₁₃₇	—	2	1	no	—
56	C₂×D₈×C₁₃₇	—	2	1	no	—
57	C₂×D₈×C₁₃₇	—	2	2	no	—
58	C₂×D₈×C₁₃₇	—	2	2	no	—
59	C₂×D₈×C₁₃₇	D₄	1	1	yes	characteristic
60	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
65	#127×C₁₃₇	—	2	2	no	—
66	#124×C₁₃₇	—	2	2	no	—
67	#121×C₁₃₇	—	2	2	no	—
68	#121×C₁₃₇	—	2	2	no	—
69	#120×C₁₃₇	—	4	2	no	—
70	C₄×Q₈×C₁₃₇	—	2	2	no	—
71	C₄×D₄×C₁₃₇	—	2	2	no	—
72	C₄×D₄×C₁₃₇	—	4	2	no	—
73	#117×C₁₃₇	—	2	2	no	—
74	#117×C₁₃₇	C₂³	1	1	yes	characteristic
75	#117×C₁₃₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₃₇	—	4	2	no	—
79	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
80	#108×C₁₃₇	—	2	2	no	—
81	#108×C₁₃₇	—	2	2	no	—
82	#107×C₁₃₇	—	2	2	no	—
83	#107×C₁₃₇	D₄	1	2	yes	—
84	#106×C₁₃₇	—	2	1	no	—
85	#106×C₁₃₇	—	2	1	no	—
86	#106×C₁₃₇	—	2	2	no	—
87	#106×C₁₃₇	D₄	1	2	yes	—
88	#104×C₁₃₇	—	4	2	no	—
89	#103×C₁₃₇	—	2	2	no	—
90	#102×C₁₃₇	—	2	2	no	—
91	#102×C₁₃₇	—	2	2	no	—
92	#102×C₁₃₇	—	2	2	no	—
93	#102×C₁₃₇	—	2	2	no	—
94	#102×C₁₃₇	—	2	2	no	—
95	#100×C₁₃₇	—	4	2	no	—
96	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
97	C₂²⋊C₈×C₁₃₇	—	2	2	no	—
98	#97×C₁₃₇	—	2	1	no	—
99	#97×C₁₃₇	—	2	1	no	—
100	#97×C₁₃₇	—	2	2	no	—
101	C₄×C₈×C₁₃₇	—	2	1	no	—
102	C₄×C₈×C₁₃₇	—	2	1	no	—
103	C₂⁴×C₁₃₇	—	2	2	no	—
104	#41×C₁₃₇	—	2	2	no	—
105	#41×C₁₃₇	—	2	2	no	—
106	#41×C₁₃₇	—	2	2	no	—
107	#41×C₁₃₇	—	2	2	no	—
108	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	2	2	no	—
111	C₂×D₄×C₁₃₇	—	2	2	no	—
112	C₂×D₄×C₁₃₇	—	2	2	no	—
113	C₂×D₄×C₁₃₇	—	2	2	no	—
114	C₂×D₄×C₁₃₇	—	2	2	no	—
115	C₂×D₄×C₁₃₇	—	2	2	no	—
116	C₂×D₄×C₁₃₇	—	4	2	no	—
117	C₂×D₄×C₁₃₇	—	4	2	no	—
118	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃₇	—	2	2	no	—
120	C₂²×C₄×C₁₃₇	—	2	1	no	—
121	C₂²×C₄×C₁₃₇	—	2	2	no	—
122	C₂²×C₄×C₁₃₇	—	4	2	no	—
123	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₁₃₇	—	2	2	no	—
125	SD₁₆×C₁₃₇	—	2	4	no	—
126	SD₁₆×C₁₃₇	—	4	4	no	—
127	D₈×C₁₃₇	—	2	2	no	—
128	D₈×C₁₃₇	—	4	4	no	—
129	D₈×C₁₃₇	—	4	2	no	—
130	D₈×C₁₃₇	—	4	2	no	—
131	M₁₆×C₁₃₇	—	2	1	no	—
132	M₁₆×C₁₃₇	—	2	1	no	—
133	M₁₆×C₁₃₇	—	2	2	no	—
134	M₁₆×C₁₃₇	—	2	1	no	—
135	M₁₆×C₁₃₇	—	2	2	no	—
136	M₁₆×C₁₃₇	#41	1	2	yes	—
137	C₂×C₈×C₁₃₇	—	2	1	no	—
138	C₂×C₈×C₁₃₇	—	2	1	no	—
139	C₂×C₈×C₁₃₇	—	2	1	no	—
140	C₂×C₈×C₁₃₇	—	2	1	no	—
141	C₂×C₈×C₁₃₇	—	2	2	no	—
142	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃₇	#41	1	2	yes	—
147	C₂×C₈×C₁₃₇	#41	1	2	yes	—
148	C₄⋊C₄×C₁₃₇	—	2	2	no	—
149	C₄⋊C₄×C₁₃₇	—	2	2	no	—
150	C₄⋊C₄×C₁₃₇	—	4	2	no	—
151	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
154	C₂²⋊C₄×C₁₃₇	—	2	1	no	—
155	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
156	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
157	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
158	C₂²⋊C₄×C₁₃₇	—	8	4	no	—
159	C₄²×C₁₃₇	—	2	1	no	—
160	C₄²×C₁₃₇	—	2	1	no	—
161	C₄²×C₁₃₇	—	2	1	no	—
162	C₄²×C₁₃₇	—	2	1	no	—
163	C₄²×C₁₃₇	—	4	2	no	—
164	C₂³×C₁₃₇	—	2	2	no	—
165	C₂³×C₁₃₇	—	4	2	no	—
166	C₂³×C₁₃₇	—	4	2	no	—
167	C₂³×C₁₃₇	—	4	2	no	—
168	C₂³×C₁₃₇	—	8	2	no	—
169	C₂³×C₁₃₇	—	8	2	no	—
170	C₂³×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
171	Q₈×C₁₃₇	—	2	2	no	—
172	Q₈×C₁₃₇	—	2	2	no	—
173	D₄×C₁₃₇	—	2	2	no	—
174	D₄×C₁₃₇	—	2	2	no	—
175	D₄×C₁₃₇	—	4	2	no	—
176	D₄×C₁₃₇	—	4	2	no	—
177	D₄×C₁₃₇	—	4	2	no	—
178	D₄×C₁₃₇	—	4	2	no	—
179	D₄×C₁₃₇	—	4	2	no	—
180	D₄×C₁₃₇	—	4	2	no	—
181	D₄×C₁₃₇	—	16	2	no	—
182	D₄×C₁₃₇	—	16	2	no	—
183	C₂×C₄×C₁₃₇	—	2	2	no	—
184	C₂×C₄×C₁₃₇	—	2	2	no	—
185	C₂×C₄×C₁₃₇	—	2	2	no	—
186	C₂×C₄×C₁₃₇	—	4	2	no	—
187	C₂×C₄×C₁₃₇	—	4	2	no	—
188	C₂×C₄×C₁₃₇	—	4	2	no	—
189	C₂×C₄×C₁₃₇	—	4	1	no	—
190	C₂×C₄×C₁₃₇	—	4	2	no	—
191	C₂×C₄×C₁₃₇	—	8	2	no	—
192	C₂×C₄×C₁₃₇	—	16	2	no	—
193	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
199	C₈×C₁₃₇	—	2	1	no	—
200	C₈×C₁₃₇	—	2	1	no	—
201	C₈×C₁₃₇	—	2	2	no	—
202	C₈×C₁₃₇	—	4	1	no	—
203	C₈×C₁₃₇	—	4	2	no	—
204	C₈×C₁₃₇	#123	1	2	yes	—
205	C₈×C₁₃₇	#123	1	2	yes	—
206	C₂²×C₁₃₇	—	2	2	no	—
207	C₂²×C₁₃₇	—	4	2	no	—
208	C₂²×C₁₃₇	—	4	2	no	—
209	C₂²×C₁₃₇	—	4	2	no	—
210	C₂²×C₁₃₇	—	8	4	no	—
211	C₂²×C₁₃₇	—	8	2	no	—
212	C₂²×C₁₃₇	—	8	2	no	—
213	C₂²×C₁₃₇	—	8	2	no	—
214	C₂²×C₁₃₇	—	16	2	no	—
215	C₂²×C₁₃₇	#540	1	1	yes	characteristic
216	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
217	C₂²×C₁₃₇	#559	1	1	yes	characteristic
218	C₄×C₁₃₇	—	4	2	no	—
219	C₄×C₁₃₇	—	4	2	no	—
220	C₄×C₁₃₇	—	4	2	no	—
221	C₄×C₁₃₇	—	8	1	no	—
222	C₄×C₁₃₇	—	8	2	no	—
223	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
224	C₄×C₁₃₇	#532	1	1	yes	characteristic
225	C₄×C₁₃₇	#546	1	1	yes	characteristic
226	C₄×C₁₃₇	#550	1	1	yes	characteristic
227	C₂×C₁₃₇	—	2	1	no	—
228	C₂×C₁₃₇	—	2	1	no	—
229	C₂×C₁₃₇	—	8	2	no	—
230	C₂×C₁₃₇	—	16	2	no	—
231	C₂×C₁₃₇	#2445	1	1	yes	characteristic
232	C₂×C₁₃₇	#3288	1	2	yes	—
233	#26274	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₁₃₇	#26274	1	1	yes	characteristic, direct product factor, Sylow
235	#3155	C₂×C₁₃₇	1	1	yes	characteristic
236	#3096	C₂×C₁₃₇	1	2	yes	complemented
237	#2952	C₂×C₁₃₇	1	1	yes	characteristic, complemented
238	#2051	C₂×C₁₃₇	1	2	yes	complemented
239	#2037	C₂×C₁₃₇	1	2	yes	complemented
240	#1978	C₂×C₁₃₇	1	1	yes	characteristic, complemented
241	#1975	C₂×C₁₃₇	1	1	yes	characteristic, complemented
242	#1972	C₂×C₁₃₇	1	1	yes	characteristic, complemented
243	#1951	C₂×C₁₃₇	1	1	yes	characteristic, complemented
244	#1883	C₂×C₁₃₇	1	2	yes	complemented
245	#1773	C₂×C₁₃₇	1	1	yes	characteristic, complemented
246	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₇	1	2	yes	—
247	C₂×#135	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
249	#535	C₂²×C₁₃₇	1	2	yes	—
250	#520	C₂²×C₁₃₇	1	2	yes	—
251	#496	—	2	2	no	—
252	#495	—	2	1	no	—
253	#493	—	2	1	no	—
254	#482	—	2	2	no	—
255	#482	—	2	2	no	—
256	#481	—	2	2	no	—
257	#480	—	2	2	no	—
258	#442	—	2	1	no	—
259	#441	—	2	1	no	—
260	C₄×SD₁₆	—	2	2	no	—
261	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
262	C₂×#108	C₂²×C₁₃₇	1	1	yes	characteristic
263	#428	C₂²×C₁₃₇	1	2	yes	—
264	#427	C₂²×C₁₃₇	1	1	yes	characteristic
265	C₂×#106	C₂²×C₁₃₇	1	1	yes	characteristic
266	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
267	#418	C₂²×C₁₃₇	1	2	yes	—
268	#417	C₂²×C₁₃₇	1	2	yes	—
269	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
270	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
271	#408	C₂²×C₁₃₇	1	2	yes	—
272	#405	C₂²×C₁₃₇	1	1	yes	characteristic
273	#405	C₂²×C₁₃₇	1	1	yes	characteristic
274	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
275	#390	C₂²×C₁₃₇	1	2	yes	—
276	#343	C₂²×C₁₃₇	1	2	yes	—
277	#339	C₂²×C₁₃₇	1	1	yes	characteristic
278	#339	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
280	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
281	AGL(1,ℤ/8)	—	2	4	no	—
282	AGL(1,ℤ/8)	—	4	2	no	—
283	#135	—	2	2	no	—
284	#135	—	2	2	no	—
285	C₂×Q₁₆	D₄×C₁₃₇	1	1	yes	characteristic
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	D₄×C₁₃₇	1	2	yes	—
288	C₂×D₈	—	2	2	no	—
289	C₂×D₈	—	2	1	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂×D₈	D₄×C₁₃₇	1	1	yes	characteristic
294	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
296	C₂×M₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
299	#127	—	2	2	no	—
300	#124	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	2	2	no	—
303	#120	—	4	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	4	2	no	—
307	#117	—	2	2	no	—
308	#117	C₂³×C₁₃₇	1	1	yes	characteristic
309	#117	C₂³×C₁₃₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
312	C₂×C₂²⋊C₄	—	4	2	no	—
313	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
314	#108	—	2	2	no	—
315	#108	—	2	2	no	—
316	#107	—	2	2	no	—
317	#107	D₄×C₁₃₇	1	2	yes	—
318	#106	—	2	1	no	—
319	#106	—	2	1	no	—
320	#106	—	2	2	no	—
321	#106	D₄×C₁₃₇	1	2	yes	—
322	#104	—	4	2	no	—
323	#103	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	2	no	—
327	#102	—	2	2	no	—
328	#102	—	2	2	no	—
329	#100	—	4	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	—	2	2	no	—
332	#97	—	2	1	no	—
333	#97	—	2	1	no	—
334	#97	—	2	2	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₂⁴	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
358	Q₁₆	—	2	2	no	—
359	SD₁₆	—	2	4	no	—
360	SD₁₆	—	4	4	no	—
361	D₈	—	2	2	no	—
362	D₈	—	4	4	no	—
363	D₈	—	4	2	no	—
364	D₈	—	4	2	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	#41×C₁₃₇	1	2	yes	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
380	C₂×C₈	#41×C₁₃₇	1	2	yes	—
381	C₂×C₈	#41×C₁₃₇	1	2	yes	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
386	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	8	4	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	4	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	8	2	no	—
403	C₂³	—	8	2	no	—
404	C₂³	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	Q₈	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	16	2	no	—
416	D₄	—	16	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	16	2	no	—
427	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
432	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	#123×C₁₃₇	1	2	yes	—
439	C₈	#123×C₁₃₇	1	2	yes	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	#540×C₁₃₇	1	1	yes	characteristic
450	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
451	C₂²	#559×C₁₃₇	1	1	yes	characteristic
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
458	C₄	#532×C₁₃₇	1	1	yes	characteristic
459	C₄	#546×C₁₃₇	1	1	yes	characteristic
460	C₄	#550×C₁₃₇	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	8	2	no	—
464	C₂	—	16	2	no	—
465	C₂	#2445×C₁₃₇	1	1	yes	characteristic
466	C₂	#3288×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#3155×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
2. #3096×C₁₃₇	C₂	semidirect
3. #2952×C₁₃₇	C₂	semidirect
4. #2051×C₁₃₇	C₂	semidirect
5. #2037×C₁₃₇	C₂	semidirect
6. #1978×C₁₃₇	C₂	semidirect
7. #1975×C₁₃₇	C₂	semidirect
8. #1972×C₁₃₇	C₂	semidirect
9. #1951×C₁₃₇	C₂	semidirect
10. #1883×C₁₃₇	C₂	semidirect
11. #1773×C₁₃₇	C₂	semidirect
233. #26274	C₁₃₇	direct (N × H)
234. C₁₃₇	#26274	direct (N × H)
236. #3096	C₂×C₁₃₇	semidirect
237. #2952	C₂×C₁₃₇	semidirect
238. #2051	C₂×C₁₃₇	semidirect
239. #2037	C₂×C₁₃₇	semidirect
240. #1978	C₂×C₁₃₇	semidirect
241. #1975	C₂×C₁₃₇	semidirect
242. #1972	C₂×C₁₃₇	semidirect
243. #1951	C₂×C₁₃₇	semidirect
244. #1883	C₂×C₁₃₇	semidirect
245. #1773	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3155×C₁₃₇	2
#3096×C₁₃₇	2
#2952×C₁₃₇	2
#2051×C₁₃₇	2
#2037×C₁₃₇	2
#1978×C₁₃₇	2
#1975×C₁₃₇	2
#1972×C₁₃₇	2
#1951×C₁₃₇	2
#1883×C₁₃₇	2
#1773×C₁₃₇	2
#26274	137

Subgroups — C137×#26274 #46875660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#26274 #46875660