Subgroups — C₁₃₇×#28941 #46878327

Order 35072.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3137×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	#3063×C₁₃₇	C₂	1	2	yes	maximal
3	#2061×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2040×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	#2005×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#1960×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#1930×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1908×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1765×C₁₃₇	C₂	1	2	yes	maximal, complemented
10	C₂×#137×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	#536×C₁₃₇	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	#491×C₁₃₇	—	2	2	no	—
17	#489×C₁₃₇	—	2	2	no	—
18	#488×C₁₃₇	—	2	2	no	—
19	#487×C₁₃₇	—	2	2	no	—
20	#470×C₁₃₇	—	2	2	no	—
21	#468×C₁₃₇	—	2	2	no	—
22	#467×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	#419×C₁₃₇	C₂²	1	2	yes	—
27	#417×C₁₃₇	C₂²	1	2	yes	—
28	#416×C₁₃₇	C₂²	1	2	yes	—
29	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
30	C₂×#103×C₁₃₇	C₂²	1	2	yes	—
31	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
32	#405×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
34	#382×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×Q₈×C₁₃₇	C₂³	1	2	yes	—
41	#137×C₁₃₇	—	2	4	no	—
42	#137×C₁₃₇	—	4	2	no	—
43	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
44	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
45	#131×C₁₃₇	—	2	4	no	—
46	#131×C₁₃₇	—	4	2	no	—
47	C₂×M₁₆×C₁₃₇	—	2	2	no	—
48	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₇	—	2	2	no	—
51	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
54	C₄⋊Q₈×C₁₃₇	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₇	—	4	1	no	—
56	#125×C₁₃₇	—	2	2	no	—
57	#124×C₁₃₇	—	2	2	no	—
58	#123×C₁₃₇	—	4	2	no	—
59	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
60	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
61	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₇	—	4	1	no	—
63	#121×C₁₃₇	—	2	2	no	—
64	#121×C₁₃₇	—	4	1	no	—
65	#117×C₁₃₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₇	—	4	1	no	—
67	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
70	#107×C₁₃₇	—	2	2	no	—
71	#106×C₁₃₇	—	2	2	no	—
72	#104×C₁₃₇	—	2	4	no	—
73	#103×C₁₃₇	—	2	2	no	—
74	#103×C₁₃₇	—	2	2	no	—
75	#103×C₁₃₇	—	2	2	no	—
76	#103×C₁₃₇	—	2	2	no	—
77	#103×C₁₃₇	—	2	2	no	—
78	#103×C₁₃₇	—	2	2	no	—
79	#103×C₁₃₇	—	2	2	no	—
80	#103×C₁₃₇	D₄	1	2	yes	—
81	#103×C₁₃₇	D₄	1	2	yes	—
82	#102×C₁₃₇	—	2	2	no	—
83	#102×C₁₃₇	D₄	1	2	yes	—
84	#102×C₁₃₇	D₄	1	2	yes	—
85	#101×C₁₃₇	—	2	4	no	—
86	#97×C₁₃₇	—	2	2	no	—
87	#97×C₁₃₇	—	4	1	no	—
88	C₄×C₈×C₁₃₇	—	2	2	no	—
89	#95×C₁₃₇	—	4	1	no	—
90	#41×C₁₃₇	—	2	2	no	—
91	#41×C₁₃₇	—	2	2	no	—
92	#41×C₁₃₇	—	2	2	no	—
93	#41×C₁₃₇	—	2	2	no	—
94	C₂×Q₈×C₁₃₇	—	2	2	no	—
95	C₂×Q₈×C₁₃₇	—	2	2	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×Q₈×C₁₃₇	—	2	2	no	—
99	C₂×Q₈×C₁₃₇	—	2	2	no	—
100	C₂×Q₈×C₁₃₇	—	4	1	no	—
101	C₂×Q₈×C₁₃₇	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₁₃₇	—	2	2	no	—
103	C₂×D₄×C₁₃₇	—	4	1	no	—
104	C₂×D₄×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₇	—	2	1	no	—
106	C₂²×C₄×C₁₃₇	—	2	2	no	—
107	C₂²×C₄×C₁₃₇	—	2	2	no	—
108	C₂²×C₄×C₁₃₇	—	2	1	no	—
109	C₂²×C₄×C₁₃₇	—	2	1	no	—
110	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₁₃₇	—	4	4	no	—
112	SD₁₆×C₁₃₇	—	4	4	no	—
113	M₁₆×C₁₃₇	—	2	2	no	—
114	M₁₆×C₁₃₇	—	2	2	no	—
115	M₁₆×C₁₃₇	—	2	2	no	—
116	M₁₆×C₁₃₇	—	4	4	no	—
117	M₁₆×C₁₃₇	#41	1	4	yes	—
118	C₂×C₈×C₁₃₇	—	2	2	no	—
119	C₂×C₈×C₁₃₇	—	2	2	no	—
120	C₂×C₈×C₁₃₇	—	2	2	no	—
121	C₂×C₈×C₁₃₇	—	2	2	no	—
122	C₂×C₈×C₁₃₇	—	4	4	no	—
123	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₁₃₇	—	2	2	no	—
126	C₄⋊C₄×C₁₃₇	—	2	2	no	—
127	C₄⋊C₄×C₁₃₇	—	4	1	no	—
128	C₄⋊C₄×C₁₃₇	—	4	2	no	—
129	C₄⋊C₄×C₁₃₇	—	4	2	no	—
130	C₄⋊C₄×C₁₃₇	—	4	1	no	—
131	C₄⋊C₄×C₁₃₇	—	4	2	no	—
132	C₄⋊C₄×C₁₃₇	—	4	4	no	—
133	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₃₇	C₂×D₄	1	2	yes	—
135	C₂²⋊C₄×C₁₃₇	—	2	2	no	—
136	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
137	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
138	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
139	C₄²×C₁₃₇	—	2	2	no	—
140	C₄²×C₁₃₇	—	2	1	no	—
141	C₄²×C₁₃₇	#41	1	2	yes	—
142	C₂³×C₁₃₇	—	2	2	no	—
143	C₂³×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
144	Q₈×C₁₃₇	—	2	2	no	—
145	Q₈×C₁₃₇	—	2	2	no	—
146	Q₈×C₁₃₇	—	4	2	no	—
147	Q₈×C₁₃₇	—	4	2	no	—
148	Q₈×C₁₃₇	—	4	2	no	—
149	Q₈×C₁₃₇	—	4	2	no	—
150	Q₈×C₁₃₇	—	16	1	no	—
151	D₄×C₁₃₇	—	2	2	no	—
152	D₄×C₁₃₇	—	2	2	no	—
153	D₄×C₁₃₇	—	4	2	no	—
154	D₄×C₁₃₇	—	4	2	no	—
155	D₄×C₁₃₇	—	16	1	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	—	4	1	no	—
161	C₂×C₄×C₁₃₇	—	4	1	no	—
162	C₂×C₄×C₁₃₇	—	4	2	no	—
163	C₂×C₄×C₁₃₇	—	4	2	no	—
164	C₂×C₄×C₁₃₇	—	4	2	no	—
165	C₂×C₄×C₁₃₇	—	4	1	no	—
166	C₂×C₄×C₁₃₇	—	4	2	no	—
167	C₂×C₄×C₁₃₇	—	4	1	no	—
168	C₂×C₄×C₁₃₇	—	4	2	no	—
169	C₂×C₄×C₁₃₇	—	8	1	no	—
170	C₂×C₄×C₁₃₇	—	8	1	no	—
171	C₂×C₄×C₁₃₇	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
174	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₈×C₁₃₇	—	2	2	no	—
176	C₈×C₁₃₇	—	2	2	no	—
177	C₈×C₁₃₇	—	2	4	no	—
178	C₈×C₁₃₇	—	4	2	no	—
179	C₂²×C₁₃₇	—	2	1	no	—
180	C₂²×C₁₃₇	—	2	1	no	—
181	C₂²×C₁₃₇	—	4	2	no	—
182	C₂²×C₁₃₇	—	4	2	no	—
183	C₂²×C₁₃₇	—	4	2	no	—
184	C₂²×C₁₃₇	#538	1	1	yes	characteristic
185	C₂²×C₁₃₇	D₄²	1	1	yes	characteristic
186	C₂²×C₁₃₇	#555	1	1	yes	characteristic
187	C₄×C₁₃₇	—	4	2	no	—
188	C₄×C₁₃₇	—	4	2	no	—
189	C₄×C₁₃₇	—	4	2	no	—
190	C₄×C₁₃₇	—	4	2	no	—
191	C₄×C₁₃₇	—	8	1	no	—
192	C₄×C₁₃₇	—	8	1	no	—
193	C₄×C₁₃₇	—	8	2	no	—
194	C₄×C₁₃₇	#532	1	2	yes	—
195	C₄×C₁₃₇	#546	1	2	yes	—
196	C₂×C₁₃₇	—	2	1	no	—
197	C₂×C₁₃₇	—	2	1	no	—
198	C₂×C₁₃₇	—	8	2	no	—
199	C₂×C₁₃₇	#2555	1	1	yes	characteristic
200	C₂×C₁₃₇	#3289	1	1	yes	characteristic
201	C₂×C₁₃₇	#3289	1	1	yes	characteristic
202	#28941	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₇	#28941	1	1	yes	characteristic, direct product factor, Sylow
204	#3137	C₂×C₁₃₇	1	2	yes	complemented
205	#3063	C₂×C₁₃₇	1	2	yes	—
206	#2061	C₂×C₁₃₇	1	1	yes	characteristic, complemented
207	#2040	C₂×C₁₃₇	1	1	yes	characteristic
208	#2005	C₂×C₁₃₇	1	2	yes	complemented
209	#1960	C₂×C₁₃₇	1	1	yes	characteristic, complemented
210	#1930	C₂×C₁₃₇	1	2	yes	complemented
211	#1908	C₂×C₁₃₇	1	2	yes	complemented
212	#1765	C₂×C₁₃₇	1	2	yes	complemented
213	C₂×#137	C₂²×C₁₃₇	1	2	yes	—
214	C₂×#131	C₂²×C₁₃₇	1	2	yes	—
215	#544	C₂²×C₁₃₇	1	1	yes	characteristic
216	#537	C₂²×C₁₃₇	1	1	yes	characteristic
217	#536	C₂²×C₁₃₇	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₁₃₇	1	1	yes	characteristic
219	#491	—	2	2	no	—
220	#489	—	2	2	no	—
221	#488	—	2	2	no	—
222	#487	—	2	2	no	—
223	#470	—	2	2	no	—
224	#468	—	2	2	no	—
225	#467	—	2	2	no	—
226	#465	—	2	2	no	—
227	#428	C₂²×C₁₃₇	1	2	yes	—
228	C₂×#104	C₂²×C₁₃₇	1	2	yes	—
229	#419	C₂²×C₁₃₇	1	2	yes	—
230	#417	C₂²×C₁₃₇	1	2	yes	—
231	#416	C₂²×C₁₃₇	1	2	yes	—
232	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
233	C₂×#103	C₂²×C₁₃₇	1	2	yes	—
234	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
235	#405	C₂²×C₁₃₇	1	2	yes	—
236	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
237	#382	C₂²×C₁₃₇	1	1	yes	characteristic
238	#343	C₂²×C₁₃₇	1	1	yes	characteristic
239	#343	C₂²×C₁₃₇	1	1	yes	characteristic
240	#341	C₂²×C₁₃₇	1	2	yes	—
241	#339	C₂²×C₁₃₇	1	2	yes	—
242	C₂×#41	C₂³×C₁₃₇	1	2	yes	—
243	C₂²×Q₈	C₂³×C₁₃₇	1	2	yes	—
244	#137	—	2	4	no	—
245	#137	—	4	2	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	#131	—	2	4	no	—
249	#131	—	4	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
252	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	4	1	no	—
259	#125	—	2	2	no	—
260	#124	—	2	2	no	—
261	#123	—	4	2	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	C₂²⋊Q₈	—	4	1	no	—
266	#121	—	2	2	no	—
267	#121	—	4	1	no	—
268	#117	C₂³×C₁₃₇	1	2	yes	—
269	C₂×C₄⋊C₄	—	4	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
273	#107	—	2	2	no	—
274	#106	—	2	2	no	—
275	#104	—	2	4	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#103	D₄×C₁₃₇	1	2	yes	—
284	#103	D₄×C₁₃₇	1	2	yes	—
285	#102	—	2	2	no	—
286	#102	D₄×C₁₃₇	1	2	yes	—
287	#102	D₄×C₁₃₇	1	2	yes	—
288	#101	—	2	4	no	—
289	#97	—	2	2	no	—
290	#97	—	4	1	no	—
291	C₄×C₈	—	2	2	no	—
292	#95	—	4	1	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	C₂×D₄×C₁₃₇	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	C₂×D₄×C₁₃₇	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
314	Q₁₆	—	4	4	no	—
315	SD₁₆	—	4	4	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	4	4	no	—
320	M₁₆	#41×C₁₃₇	1	4	yes	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
337	C₄⋊C₄	C₂×D₄×C₁₃₇	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	#41×C₁₃₇	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	16	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	16	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	C₂²×D₄×C₁₃₇	1	2	yes	—
375	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
377	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	#538×C₁₃₇	1	1	yes	characteristic
388	C₂²	D₄²×C₁₃₇	1	1	yes	characteristic
389	C₂²	#555×C₁₃₇	1	1	yes	characteristic
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	#532×C₁₃₇	1	2	yes	—
398	C₄	#546×C₁₃₇	1	2	yes	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	8	2	no	—
402	C₂	#2555×C₁₃₇	1	1	yes	characteristic
403	C₂	#3289×C₁₃₇	1	1	yes	characteristic
404	C₂	#3289×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	#537×C₁₃₇	C₂²
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. #3137×C₁₃₇	C₂	semidirect
3. #2061×C₁₃₇	C₂	semidirect
5. #2005×C₁₃₇	C₂	semidirect
6. #1960×C₁₃₇	C₂	semidirect
7. #1930×C₁₃₇	C₂	semidirect
8. #1908×C₁₃₇	C₂	semidirect
9. #1765×C₁₃₇	C₂	semidirect
202. #28941	C₁₃₇	direct (N × H)
203. C₁₃₇	#28941	direct (N × H)
204. #3137	C₂×C₁₃₇	semidirect
206. #2061	C₂×C₁₃₇	semidirect
208. #2005	C₂×C₁₃₇	semidirect
209. #1960	C₂×C₁₃₇	semidirect
210. #1930	C₂×C₁₃₇	semidirect
211. #1908	C₂×C₁₃₇	semidirect
212. #1765	C₂×C₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
#3137×C₁₃₇	2
#3063×C₁₃₇	2
#2061×C₁₃₇	2
#2040×C₁₃₇	2
#2005×C₁₃₇	2
#1960×C₁₃₇	2
#1930×C₁₃₇	2
#1908×C₁₃₇	2
#1765×C₁₃₇	2
#28941	137

Subgroups — C137×#28941 #46878327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28941 #46878327