Subgroups — C₁₃₇×#28636 #46878022

Order 35072.

780 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3153×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3141×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#489×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2932×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2052×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2051×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1997×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#1967×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#1908×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	#1907×C₁₃₇	C₂	1	2	yes	maximal, complemented
11	#1778×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₇	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₁₃₇	C₂²	1	2	yes	—
14	C₂×#131×C₁₃₇	C₂²	1	2	yes	—
15	#532×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
18	#497×C₁₃₇	—	2	1	no	—
19	#496×C₁₃₇	—	2	1	no	—
20	#495×C₁₃₇	—	2	2	no	—
21	#489×C₁₃₇	—	2	2	no	—
22	#489×C₁₃₇	—	2	2	no	—
23	#489×C₁₃₇	—	2	2	no	—
24	#487×C₁₃₇	—	2	1	no	—
25	#486×C₁₃₇	—	2	1	no	—
26	#435×C₁₃₇	—	2	2	no	—
27	#435×C₁₃₇	—	2	2	no	—
28	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
29	#423×C₁₃₇	C₂²	1	1	yes	characteristic
30	#417×C₁₃₇	C₂²	1	2	yes	—
31	#417×C₁₃₇	C₂²	1	2	yes	—
32	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₁₃₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
35	C₂×#102×C₁₃₇	C₂²	1	1	yes	characteristic
36	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
37	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
38	#408×C₁₃₇	C₂²	1	2	yes	—
39	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
42	#343×C₁₃₇	C₂²	1	2	yes	—
43	#343×C₁₃₇	C₂²	1	2	yes	—
44	#341×C₁₃₇	C₂²	1	2	yes	—
45	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃₇	—	2	1	no	—
47	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
49	#137×C₁₃₇	—	2	4	no	—
50	#137×C₁₃₇	—	4	2	no	—
51	AGL(1,ℤ/8)×C₁₃₇	—	2	4	no	—
52	AGL(1,ℤ/8)×C₁₃₇	—	4	2	no	—
53	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
54	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
55	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
56	C₂×D₈×C₁₃₇	—	2	2	no	—
57	#131×C₁₃₇	—	4	2	no	—
58	#131×C₁₃₇	—	4	2	no	—
59	C₂×M₁₆×C₁₃₇	—	2	2	no	—
60	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
61	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
62	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃₇	—	2	2	no	—
64	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
67	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
68	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
69	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
70	C₄⋊Q₈×C₁₃₇	D₄	1	1	yes	characteristic
71	#127×C₁₃₇	D₄	1	1	yes	characteristic
72	#124×C₁₃₇	—	2	1	no	—
73	#124×C₁₃₇	—	2	1	no	—
74	#124×C₁₃₇	—	2	1	no	—
75	#124×C₁₃₇	—	2	1	no	—
76	#124×C₁₃₇	D₄	1	2	yes	—
77	#121×C₁₃₇	—	2	1	no	—
78	#121×C₁₃₇	—	2	1	no	—
79	C₄×D₄×C₁₃₇	—	2	1	no	—
80	C₄×D₄×C₁₃₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
86	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
87	#108×C₁₃₇	—	2	4	no	—
88	C₄⋊C₈×C₁₃₇	—	2	1	no	—
89	C₄⋊C₈×C₁₃₇	—	2	1	no	—
90	#103×C₁₃₇	—	2	2	no	—
91	#103×C₁₃₇	—	2	2	no	—
92	#103×C₁₃₇	—	2	2	no	—
93	#103×C₁₃₇	—	2	2	no	—
94	#102×C₁₃₇	—	2	2	no	—
95	#102×C₁₃₇	—	2	2	no	—
96	#102×C₁₃₇	—	2	2	no	—
97	#102×C₁₃₇	—	2	2	no	—
98	#101×C₁₃₇	—	4	2	no	—
99	#100×C₁₃₇	—	4	2	no	—
100	C₂²⋊C₈×C₁₃₇	—	2	4	no	—
101	#97×C₁₃₇	—	2	1	no	—
102	#97×C₁₃₇	—	2	1	no	—
103	#97×C₁₃₇	D₄	1	2	yes	—
104	#97×C₁₃₇	D₄	1	2	yes	—
105	C₄×C₈×C₁₃₇	—	2	1	no	—
106	C₄×C₈×C₁₃₇	—	2	1	no	—
107	C₂⁴×C₁₃₇	—	2	1	no	—
108	#41×C₁₃₇	—	2	2	no	—
109	#41×C₁₃₇	—	2	2	no	—
110	#41×C₁₃₇	—	2	2	no	—
111	#41×C₁₃₇	—	2	2	no	—
112	C₂×Q₈×C₁₃₇	—	2	1	no	—
113	C₂×Q₈×C₁₃₇	—	2	1	no	—
114	C₂×Q₈×C₁₃₇	—	2	2	no	—
115	C₂×Q₈×C₁₃₇	—	2	2	no	—
116	C₂×Q₈×C₁₃₇	—	4	1	no	—
117	C₂×Q₈×C₁₃₇	—	4	1	no	—
118	C₂×Q₈×C₁₃₇	—	8	2	no	—
119	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₃₇	—	2	2	no	—
121	C₂×D₄×C₁₃₇	—	2	1	no	—
122	C₂×D₄×C₁₃₇	—	2	1	no	—
123	C₂×D₄×C₁₃₇	—	2	1	no	—
124	C₂×D₄×C₁₃₇	—	2	1	no	—
125	C₂×D₄×C₁₃₇	—	2	2	no	—
126	C₂×D₄×C₁₃₇	—	2	2	no	—
127	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₇	—	2	2	no	—
129	C₂²×C₄×C₁₃₇	—	2	1	no	—
130	C₂²×C₄×C₁₃₇	—	2	1	no	—
131	C₂²×C₄×C₁₃₇	—	2	1	no	—
132	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₁₃₇	—	4	4	no	—
136	SD₁₆×C₁₃₇	—	4	4	no	—
137	SD₁₆×C₁₃₇	—	4	4	no	—
138	D₈×C₁₃₇	—	4	4	no	—
139	M₁₆×C₁₃₇	—	2	2	no	—
140	M₁₆×C₁₃₇	—	2	2	no	—
141	M₁₆×C₁₃₇	—	2	2	no	—
142	M₁₆×C₁₃₇	—	2	2	no	—
143	M₁₆×C₁₃₇	—	2	2	no	—
144	M₁₆×C₁₃₇	—	4	4	no	—
145	M₁₆×C₁₃₇	#41	1	4	yes	—
146	C₂×C₈×C₁₃₇	—	2	2	no	—
147	C₂×C₈×C₁₃₇	—	2	2	no	—
148	C₂×C₈×C₁₃₇	—	2	2	no	—
149	C₂×C₈×C₁₃₇	—	2	2	no	—
150	C₂×C₈×C₁₃₇	—	2	2	no	—
151	C₂×C₈×C₁₃₇	—	4	4	no	—
152	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₁₃₇	—	2	1	no	—
155	C₄⋊C₄×C₁₃₇	—	2	1	no	—
156	C₄⋊C₄×C₁₃₇	—	2	1	no	—
157	C₄⋊C₄×C₁₃₇	—	2	1	no	—
158	C₄⋊C₄×C₁₃₇	—	2	1	no	—
159	C₄⋊C₄×C₁₃₇	—	2	1	no	—
160	C₄⋊C₄×C₁₃₇	—	4	1	no	—
161	C₄⋊C₄×C₁₃₇	—	4	1	no	—
162	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
163	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
164	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
165	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
166	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
167	C₂²⋊C₄×C₁₃₇	—	4	1	no	—
168	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₁₃₇	—	2	2	no	—
173	C₂³×C₁₃₇	—	4	1	no	—
174	C₂³×C₁₃₇	—	4	2	no	—
175	C₂³×C₁₃₇	—	8	1	no	—
176	C₂³×C₁₃₇	—	8	1	no	—
177	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
178	Q₈×C₁₃₇	—	2	2	no	—
179	Q₈×C₁₃₇	—	2	2	no	—
180	Q₈×C₁₃₇	—	4	1	no	—
181	Q₈×C₁₃₇	—	4	1	no	—
182	Q₈×C₁₃₇	—	4	2	no	—
183	Q₈×C₁₃₇	—	8	2	no	—
184	Q₈×C₁₃₇	—	8	2	no	—
185	D₄×C₁₃₇	—	2	2	no	—
186	D₄×C₁₃₇	—	2	2	no	—
187	D₄×C₁₃₇	—	4	2	no	—
188	D₄×C₁₃₇	—	4	2	no	—
189	D₄×C₁₃₇	—	4	1	no	—
190	D₄×C₁₃₇	—	4	1	no	—
191	D₄×C₁₃₇	—	4	2	no	—
192	D₄×C₁₃₇	—	8	1	no	—
193	D₄×C₁₃₇	—	8	1	no	—
194	C₂×C₄×C₁₃₇	—	2	2	no	—
195	C₂×C₄×C₁₃₇	—	4	1	no	—
196	C₂×C₄×C₁₃₇	—	4	1	no	—
197	C₂×C₄×C₁₃₇	—	4	2	no	—
198	C₂×C₄×C₁₃₇	—	4	2	no	—
199	C₂×C₄×C₁₃₇	—	4	1	no	—
200	C₂×C₄×C₁₃₇	—	4	1	no	—
201	C₂×C₄×C₁₃₇	—	4	1	no	—
202	C₂×C₄×C₁₃₇	—	4	2	no	—
203	C₂×C₄×C₁₃₇	—	8	1	no	—
204	C₂×C₄×C₁₃₇	—	8	1	no	—
205	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
206	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
207	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
208	C₂×C₄×C₁₃₇	#121	1	1	yes	characteristic
209	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
213	C₈×C₁₃₇	—	2	2	no	—
214	C₈×C₁₃₇	—	2	2	no	—
215	C₈×C₁₃₇	—	2	4	no	—
216	C₈×C₁₃₇	—	4	2	no	—
217	C₈×C₁₃₇	—	4	2	no	—
218	C₂²×C₁₃₇	—	2	1	no	—
219	C₂²×C₁₃₇	—	2	1	no	—
220	C₂²×C₁₃₇	—	4	2	no	—
221	C₂²×C₁₃₇	—	4	2	no	—
222	C₂²×C₁₃₇	—	4	2	no	—
223	C₂²×C₁₃₇	—	8	1	no	—
224	C₂²×C₁₃₇	—	8	1	no	—
225	C₂²×C₁₃₇	—	8	1	no	—
226	C₂²×C₁₃₇	—	16	2	no	—
227	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
228	C₂²×C₁₃₇	#559	1	2	yes	—
229	C₄×C₁₃₇	—	2	1	no	—
230	C₄×C₁₃₇	—	2	1	no	—
231	C₄×C₁₃₇	—	2	1	no	—
232	C₄×C₁₃₇	—	2	1	no	—
233	C₄×C₁₃₇	—	4	2	no	—
234	C₄×C₁₃₇	—	8	1	no	—
235	C₄×C₁₃₇	—	8	1	no	—
236	C₄×C₁₃₇	—	8	1	no	—
237	C₄×C₁₃₇	#532	1	1	yes	characteristic
238	C₄×C₁₃₇	#535	1	1	yes	characteristic
239	C₄×C₁₃₇	#546	1	2	yes	—
240	C₂×C₁₃₇	—	2	2	no	—
241	C₂×C₁₃₇	—	8	2	no	—
242	C₂×C₁₃₇	—	16	1	no	—
243	C₂×C₁₃₇	#2544	1	1	yes	characteristic
244	C₂×C₁₃₇	#3068	1	1	yes	characteristic
245	C₂×C₁₃₇	#3069	1	1	yes	characteristic
246	#28636	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₃₇	#28636	1	1	yes	characteristic, direct product factor, Sylow
248	#3153	C₂×C₁₃₇	1	1	yes	characteristic
249	#3141	C₂×C₁₃₇	1	1	yes	characteristic, complemented
250	C₂×#489	C₂×C₁₃₇	1	1	yes	characteristic, complemented
251	#2932	C₂×C₁₃₇	1	1	yes	characteristic, complemented
252	#2052	C₂×C₁₃₇	1	2	yes	complemented
253	#2051	C₂×C₁₃₇	1	2	yes	complemented
254	#1997	C₂×C₁₃₇	1	1	yes	characteristic, complemented
255	#1967	C₂×C₁₃₇	1	1	yes	characteristic, complemented
256	#1908	C₂×C₁₃₇	1	2	yes	complemented
257	#1907	C₂×C₁₃₇	1	2	yes	complemented
258	#1778	C₂×C₁₃₇	1	1	yes	characteristic, complemented
259	C₂×#137	C₂²×C₁₃₇	1	2	yes	—
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₇	1	2	yes	—
261	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
262	#532	C₂²×C₁₃₇	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
264	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
265	#497	—	2	1	no	—
266	#496	—	2	1	no	—
267	#495	—	2	2	no	—
268	#489	—	2	2	no	—
269	#489	—	2	2	no	—
270	#489	—	2	2	no	—
271	#487	—	2	1	no	—
272	#486	—	2	1	no	—
273	#435	—	2	2	no	—
274	#435	—	2	2	no	—
275	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
276	#423	C₂²×C₁₃₇	1	1	yes	characteristic
277	#417	C₂²×C₁₃₇	1	2	yes	—
278	#417	C₂²×C₁₃₇	1	2	yes	—
279	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
280	C₂×#103	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₂×#102	C₂²×C₁₃₇	1	1	yes	characteristic
283	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
284	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
285	#408	C₂²×C₁₃₇	1	2	yes	—
286	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
287	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
289	#343	C₂²×C₁₃₇	1	2	yes	—
290	#343	C₂²×C₁₃₇	1	2	yes	—
291	#341	C₂²×C₁₃₇	1	2	yes	—
292	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
296	#137	—	2	4	no	—
297	#137	—	4	2	no	—
298	AGL(1,ℤ/8)	—	2	4	no	—
299	AGL(1,ℤ/8)	—	4	2	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×D₈	—	2	2	no	—
304	#131	—	4	2	no	—
305	#131	—	4	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
308	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
309	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	D₄×C₁₃₇	1	1	yes	characteristic
318	#127	D₄×C₁₃₇	1	1	yes	characteristic
319	#124	—	2	1	no	—
320	#124	—	2	1	no	—
321	#124	—	2	1	no	—
322	#124	—	2	1	no	—
323	#124	D₄×C₁₃₇	1	2	yes	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
334	#108	—	2	4	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	#103	—	2	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#101	—	4	2	no	—
346	#100	—	4	2	no	—
347	C₂²⋊C₈	—	2	4	no	—
348	#97	—	2	1	no	—
349	#97	—	2	1	no	—
350	#97	D₄×C₁₃₇	1	2	yes	—
351	#97	D₄×C₁₃₇	1	2	yes	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₂⁴	—	2	1	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	4	1	no	—
364	C₂×Q₈	—	4	1	no	—
365	C₂×Q₈	—	8	2	no	—
366	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
380	C₂²×C₄	#41×C₁₃₇	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
382	Q₁₆	—	4	4	no	—
383	SD₁₆	—	4	4	no	—
384	SD₁₆	—	4	4	no	—
385	D₈	—	4	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	4	4	no	—
392	M₁₆	#41×C₁₃₇	1	4	yes	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	4	no	—
399	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
400	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	8	1	no	—
423	C₂³	—	8	1	no	—
424	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	8	2	no	—
431	Q₈	—	8	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	1	no	—
440	D₄	—	8	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
453	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
454	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
455	C₂×C₄	#121×C₁₃₇	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
459	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	16	2	no	—
474	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
475	C₂²	#559×C₁₃₇	1	2	yes	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	#532×C₁₃₇	1	1	yes	characteristic
485	C₄	#535×C₁₃₇	1	1	yes	characteristic
486	C₄	#546×C₁₃₇	1	2	yes	—
487	C₂	—	2	2	no	—
488	C₂	—	8	2	no	—
489	C₂	—	16	1	no	—
490	C₂	#2544×C₁₃₇	1	1	yes	characteristic
491	C₂	#3068×C₁₃₇	1	1	yes	characteristic
492	C₂	#3069×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#3153×C₁₃₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. #3141×C₁₃₇	C₂	semidirect
3. C₂×#489×C₁₃₇	C₂	semidirect
4. #2932×C₁₃₇	C₂	semidirect
5. #2052×C₁₃₇	C₂	semidirect
6. #2051×C₁₃₇	C₂	semidirect
7. #1997×C₁₃₇	C₂	semidirect
8. #1967×C₁₃₇	C₂	semidirect
9. #1908×C₁₃₇	C₂	semidirect
10. #1907×C₁₃₇	C₂	semidirect
11. #1778×C₁₃₇	C₂	semidirect
246. #28636	C₁₃₇	direct (N × H)
247. C₁₃₇	#28636	direct (N × H)
249. #3141	C₂×C₁₃₇	semidirect
250. C₂×#489	C₂×C₁₃₇	semidirect
251. #2932	C₂×C₁₃₇	semidirect
252. #2052	C₂×C₁₃₇	semidirect
253. #2051	C₂×C₁₃₇	semidirect
254. #1997	C₂×C₁₃₇	semidirect
255. #1967	C₂×C₁₃₇	semidirect
256. #1908	C₂×C₁₃₇	semidirect
257. #1907	C₂×C₁₃₇	semidirect
258. #1778	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3153×C₁₃₇	2
#3141×C₁₃₇	2
C₂×#489×C₁₃₇	2
#2932×C₁₃₇	2
#2052×C₁₃₇	2
#2051×C₁₃₇	2
#1997×C₁₃₇	2
#1967×C₁₃₇	2
#1908×C₁₃₇	2
#1907×C₁₃₇	2
#1778×C₁₃₇	2
#28636	137

Subgroups — C137×#28636 #46878022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28636 #46878022