Subgroups — C₁₃₇×#28938 #46878324

Order 35072.

826 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3136×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3062×C₁₃₇	C₂	1	2	yes	maximal, complemented
3	#2060×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2039×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2002×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1957×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1931×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1907×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1764×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₂×AGL(1,ℤ/8)×C₁₃₇	C₂²	1	2	yes	—
11	C₂×#131×C₁₃₇	C₂²	1	2	yes	—
12	#544×C₁₃₇	C₂²	1	1	yes	characteristic
13	#537×C₁₃₇	C₂²	1	1	yes	characteristic
14	#535×C₁₃₇	C₂²	1	2	yes	—
15	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
16	#490×C₁₃₇	—	2	2	no	—
17	#489×C₁₃₇	—	2	2	no	—
18	#488×C₁₃₇	—	2	2	no	—
19	#486×C₁₃₇	—	2	2	no	—
20	#469×C₁₃₇	—	2	2	no	—
21	#468×C₁₃₇	—	2	2	no	—
22	#466×C₁₃₇	—	2	2	no	—
23	#465×C₁₃₇	—	2	2	no	—
24	#428×C₁₃₇	C₂²	1	2	yes	—
25	C₂×#104×C₁₃₇	C₂²	1	2	yes	—
26	#418×C₁₃₇	C₂²	1	2	yes	—
27	#417×C₁₃₇	C₂²	1	2	yes	—
28	#416×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#102×C₁₃₇	C₂²	1	2	yes	—
31	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
32	#405×C₁₃₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
34	#384×C₁₃₇	C₂²	1	1	yes	characteristic
35	#343×C₁₃₇	C₂²	1	1	yes	characteristic
36	#343×C₁₃₇	C₂²	1	1	yes	characteristic
37	#341×C₁₃₇	C₂²	1	2	yes	—
38	#339×C₁₃₇	C₂²	1	2	yes	—
39	C₂×#41×C₁₃₇	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃₇	—	4	1	no	—
41	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
42	AGL(1,ℤ/8)×C₁₃₇	—	2	4	no	—
43	AGL(1,ℤ/8)×C₁₃₇	—	4	2	no	—
44	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
45	C₂×D₈×C₁₃₇	—	2	2	no	—
46	#131×C₁₃₇	—	2	4	no	—
47	#131×C₁₃₇	—	4	2	no	—
48	C₂×M₁₆×C₁₃₇	—	2	2	no	—
49	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
50	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃₇	—	2	2	no	—
52	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
54	#127×C₁₃₇	—	2	2	no	—
55	#127×C₁₃₇	—	2	2	no	—
56	#127×C₁₃₇	—	4	1	no	—
57	#125×C₁₃₇	—	2	2	no	—
58	#124×C₁₃₇	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
61	#121×C₁₃₇	—	2	2	no	—
62	#121×C₁₃₇	—	2	2	no	—
63	#121×C₁₃₇	—	2	2	no	—
64	#121×C₁₃₇	—	4	1	no	—
65	#120×C₁₃₇	—	4	2	no	—
66	#117×C₁₃₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₇	—	4	1	no	—
68	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
71	#107×C₁₃₇	—	2	2	no	—
72	#106×C₁₃₇	—	2	2	no	—
73	#104×C₁₃₇	—	2	4	no	—
74	#103×C₁₃₇	—	2	2	no	—
75	#103×C₁₃₇	D₄	1	2	yes	complemented
76	#103×C₁₃₇	D₄	1	2	yes	complemented
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	#102×C₁₃₇	—	2	2	no	—
83	#102×C₁₃₇	—	2	2	no	—
84	#102×C₁₃₇	D₄	1	2	yes	complemented
85	#102×C₁₃₇	D₄	1	2	yes	complemented
86	#100×C₁₃₇	—	2	4	no	—
87	#97×C₁₃₇	—	2	2	no	—
88	C₄×C₈×C₁₃₇	—	2	2	no	—
89	C₄×C₈×C₁₃₇	—	4	1	no	—
90	C₂⁴×C₁₃₇	—	2	2	no	—
91	#41×C₁₃₇	—	2	2	no	—
92	#41×C₁₃₇	—	2	2	no	—
93	#41×C₁₃₇	—	2	2	no	—
94	#41×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	4	1	no	—
96	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	2	2	no	—
99	C₂×D₄×C₁₃₇	—	2	2	no	—
100	C₂×D₄×C₁₃₇	—	2	2	no	—
101	C₂×D₄×C₁₃₇	—	2	2	no	—
102	C₂×D₄×C₁₃₇	—	2	2	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	4	4	no	—
105	C₂×D₄×C₁₃₇	—	4	2	no	—
106	C₂×D₄×C₁₃₇	—	4	2	no	—
107	C₂×D₄×C₁₃₇	—	4	1	no	—
108	C₂×D₄×C₁₃₇	—	8	2	no	—
109	C₂×D₄×C₁₃₇	—	8	2	no	—
110	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₇	—	2	1	no	—
112	C₂²×C₄×C₁₃₇	—	2	2	no	—
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	—	2	1	no	—
115	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₁₃₇	—	4	4	no	—
117	D₈×C₁₃₇	—	4	4	no	—
118	M₁₆×C₁₃₇	—	2	2	no	—
119	M₁₆×C₁₃₇	—	2	2	no	—
120	M₁₆×C₁₃₇	—	2	2	no	—
121	M₁₆×C₁₃₇	—	4	4	no	—
122	M₁₆×C₁₃₇	#41	1	4	yes	—
123	C₂×C₈×C₁₃₇	—	2	2	no	—
124	C₂×C₈×C₁₃₇	—	2	2	no	—
125	C₂×C₈×C₁₃₇	—	2	2	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	4	4	no	—
128	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₁₃₇	—	2	2	no	—
131	C₄⋊C₄×C₁₃₇	—	2	2	no	—
132	C₄⋊C₄×C₁₃₇	—	4	1	no	—
133	C₄⋊C₄×C₁₃₇	—	4	1	no	—
134	C₄⋊C₄×C₁₃₇	—	4	2	no	—
135	C₄⋊C₄×C₁₃₇	—	8	2	no	—
136	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
139	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
140	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
141	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
142	C₄²×C₁₃₇	—	2	2	no	—
143	C₄²×C₁₃₇	—	2	1	no	—
144	C₄²×C₁₃₇	#41	1	2	yes	—
145	C₂³×C₁₃₇	—	2	2	no	—
146	C₂³×C₁₃₇	—	4	2	no	—
147	C₂³×C₁₃₇	—	4	2	no	—
148	C₂³×C₁₃₇	—	4	2	no	—
149	C₂³×C₁₃₇	—	8	2	no	—
150	C₂³×C₁₃₇	—	8	2	no	—
151	C₂³×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
152	Q₈×C₁₃₇	—	2	2	no	—
153	Q₈×C₁₃₇	—	2	2	no	—
154	Q₈×C₁₃₇	—	16	1	no	—
155	D₄×C₁₃₇	—	2	2	no	—
156	D₄×C₁₃₇	—	2	2	no	—
157	D₄×C₁₃₇	—	4	2	no	—
158	D₄×C₁₃₇	—	4	2	no	—
159	D₄×C₁₃₇	—	4	2	no	—
160	D₄×C₁₃₇	—	4	2	no	—
161	D₄×C₁₃₇	—	4	2	no	—
162	D₄×C₁₃₇	—	4	2	no	—
163	D₄×C₁₃₇	—	8	8	no	—
164	D₄×C₁₃₇	—	16	2	no	—
165	D₄×C₁₃₇	—	16	2	no	—
166	D₄×C₁₃₇	—	16	1	no	—
167	C₂×C₄×C₁₃₇	—	2	2	no	—
168	C₂×C₄×C₁₃₇	—	2	2	no	—
169	C₂×C₄×C₁₃₇	—	2	2	no	—
170	C₂×C₄×C₁₃₇	—	2	2	no	—
171	C₂×C₄×C₁₃₇	—	2	2	no	—
172	C₂×C₄×C₁₃₇	—	2	2	no	—
173	C₂×C₄×C₁₃₇	—	4	2	no	—
174	C₂×C₄×C₁₃₇	—	4	2	no	—
175	C₂×C₄×C₁₃₇	—	4	1	no	—
176	C₂×C₄×C₁₃₇	—	4	1	no	—
177	C₂×C₄×C₁₃₇	—	8	1	no	—
178	C₂×C₄×C₁₃₇	—	8	1	no	—
179	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
183	C₈×C₁₃₇	—	2	2	no	—
184	C₈×C₁₃₇	—	2	2	no	—
185	C₈×C₁₃₇	—	2	4	no	—
186	C₈×C₁₃₇	—	4	2	no	—
187	C₂²×C₁₃₇	—	2	1	no	—
188	C₂²×C₁₃₇	—	2	1	no	—
189	C₂²×C₁₃₇	—	4	2	no	—
190	C₂²×C₁₃₇	—	4	2	no	—
191	C₂²×C₁₃₇	—	4	2	no	—
192	C₂²×C₁₃₇	—	8	4	no	—
193	C₂²×C₁₃₇	—	8	2	no	—
194	C₂²×C₁₃₇	—	8	2	no	—
195	C₂²×C₁₃₇	—	8	2	no	—
196	C₂²×C₁₃₇	—	16	2	no	—
197	C₂²×C₁₃₇	#538	1	1	yes	characteristic
198	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
199	C₂²×C₁₃₇	#555	1	1	yes	characteristic
200	C₄×C₁₃₇	—	2	4	no	—
201	C₄×C₁₃₇	—	4	2	no	—
202	C₄×C₁₃₇	—	4	2	no	—
203	C₄×C₁₃₇	—	4	2	no	—
204	C₄×C₁₃₇	—	8	1	no	—
205	C₄×C₁₃₇	—	8	1	no	—
206	C₄×C₁₃₇	#532	1	2	yes	—
207	C₄×C₁₃₇	#546	1	2	yes	—
208	C₂×C₁₃₇	—	2	1	no	—
209	C₂×C₁₃₇	—	2	1	no	—
210	C₂×C₁₃₇	—	8	2	no	—
211	C₂×C₁₃₇	—	16	2	no	—
212	C₂×C₁₃₇	#2555	1	1	yes	characteristic
213	C₂×C₁₃₇	#3291	1	1	yes	characteristic
214	C₂×C₁₃₇	#3292	1	1	yes	characteristic
215	#28938	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₇	#28938	1	1	yes	characteristic, direct product factor, Sylow
217	#3136	C₂×C₁₃₇	1	2	yes	complemented
218	#3062	C₂×C₁₃₇	1	2	yes	complemented
219	#2060	C₂×C₁₃₇	1	1	yes	characteristic, complemented
220	#2039	C₂×C₁₃₇	1	1	yes	characteristic, complemented
221	#2002	C₂×C₁₃₇	1	2	yes	complemented
222	#1957	C₂×C₁₃₇	1	1	yes	characteristic, complemented
223	#1931	C₂×C₁₃₇	1	2	yes	complemented
224	#1907	C₂×C₁₃₇	1	2	yes	complemented
225	#1764	C₂×C₁₃₇	1	2	yes	complemented
226	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₇	1	2	yes	—
227	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
228	#544	C₂²×C₁₃₇	1	1	yes	characteristic
229	#537	C₂²×C₁₃₇	1	1	yes	characteristic
230	#535	C₂²×C₁₃₇	1	2	yes	—
231	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
232	#490	—	2	2	no	—
233	#489	—	2	2	no	—
234	#488	—	2	2	no	—
235	#486	—	2	2	no	—
236	#469	—	2	2	no	—
237	#468	—	2	2	no	—
238	#466	—	2	2	no	—
239	#465	—	2	2	no	—
240	#428	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
242	#418	C₂²×C₁₃₇	1	2	yes	—
243	#417	C₂²×C₁₃₇	1	2	yes	—
244	#416	C₂²×C₁₃₇	1	2	yes	—
245	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
246	C₂×#102	C₂²×C₁₃₇	1	2	yes	—
247	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
248	#405	C₂²×C₁₃₇	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
250	#384	C₂²×C₁₃₇	1	1	yes	characteristic
251	#343	C₂²×C₁₃₇	1	1	yes	characteristic
252	#343	C₂²×C₁₃₇	1	1	yes	characteristic
253	#341	C₂²×C₁₃₇	1	2	yes	—
254	#339	C₂²×C₁₃₇	1	2	yes	—
255	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
256	C₂²×D₄	—	4	1	no	—
257	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
258	AGL(1,ℤ/8)	—	2	4	no	—
259	AGL(1,ℤ/8)	—	4	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×D₈	—	2	2	no	—
262	#131	—	2	4	no	—
263	#131	—	4	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
266	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
269	C₄⋊Q₈	—	2	2	no	—
270	#127	—	2	2	no	—
271	#127	—	2	2	no	—
272	#127	—	4	1	no	—
273	#125	—	2	2	no	—
274	#124	—	2	2	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	—	4	1	no	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	#121	—	2	2	no	—
280	#121	—	4	1	no	—
281	#120	—	4	2	no	—
282	#117	C₂³×C₁₃₇	1	2	yes	—
283	C₂×C₄⋊C₄	—	4	1	no	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#106	—	2	2	no	—
289	#104	—	2	4	no	—
290	#103	—	2	2	no	—
291	#103	D₄×C₁₃₇	1	2	yes	complemented
292	#103	D₄×C₁₃₇	1	2	yes	complemented
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	—	2	2	no	—
296	#102	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	D₄×C₁₃₇	1	2	yes	complemented
301	#102	D₄×C₁₃₇	1	2	yes	complemented
302	#100	—	2	4	no	—
303	#97	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	4	1	no	—
306	C₂⁴	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
332	SD₁₆	—	4	4	no	—
333	D₈	—	4	4	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	4	4	no	—
338	M₁₆	#41×C₁₃₇	1	4	yes	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	4	no	—
344	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
353	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	#41×C₁₃₇	1	2	yes	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	16	1	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	8	8	no	—
380	D₄	—	16	2	no	—
381	D₄	—	16	2	no	—
382	D₄	—	16	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
396	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
398	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	2	4	no	—
402	C₈	—	4	2	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	16	2	no	—
413	C₂²	#538×C₁₃₇	1	1	yes	characteristic
414	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
415	C₂²	#555×C₁₃₇	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	#532×C₁₃₇	1	2	yes	—
423	C₄	#546×C₁₃₇	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	16	2	no	—
428	C₂	#2555×C₁₃₇	1	1	yes	characteristic
429	C₂	#3291×C₁₃₇	1	1	yes	characteristic
430	C₂	#3292×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
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. #3136×C₁₃₇	C₂	semidirect
2. #3062×C₁₃₇	C₂	semidirect
3. #2060×C₁₃₇	C₂	semidirect
4. #2039×C₁₃₇	C₂	semidirect
5. #2002×C₁₃₇	C₂	semidirect
6. #1957×C₁₃₇	C₂	semidirect
7. #1931×C₁₃₇	C₂	semidirect
8. #1907×C₁₃₇	C₂	semidirect
9. #1764×C₁₃₇	C₂	semidirect
75. #103×C₁₃₇	D₄	semidirect
76. #103×C₁₃₇	D₄	semidirect
84. #102×C₁₃₇	D₄	semidirect
85. #102×C₁₃₇	D₄	semidirect
215. #28938	C₁₃₇	direct (N × H)
216. C₁₃₇	#28938	direct (N × H)
217. #3136	C₂×C₁₃₇	semidirect
218. #3062	C₂×C₁₃₇	semidirect
219. #2060	C₂×C₁₃₇	semidirect
220. #2039	C₂×C₁₃₇	semidirect
221. #2002	C₂×C₁₃₇	semidirect
222. #1957	C₂×C₁₃₇	semidirect
223. #1931	C₂×C₁₃₇	semidirect
224. #1907	C₂×C₁₃₇	semidirect
225. #1764	C₂×C₁₃₇	semidirect
291. #103	D₄×C₁₃₇	semidirect
292. #103	D₄×C₁₃₇	semidirect
300. #102	D₄×C₁₃₇	semidirect
301. #102	D₄×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3136×C₁₃₇	2
#3062×C₁₃₇	2
#2060×C₁₃₇	2
#2039×C₁₃₇	2
#2002×C₁₃₇	2
#1957×C₁₃₇	2
#1931×C₁₃₇	2
#1907×C₁₃₇	2
#1764×C₁₃₇	2
#28938	137

Subgroups — C137×#28938 #46878324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28938 #46878324