Subgroups — C₁₃₇×#28768 #46878154

Order 35072.

780 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#496×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#3140×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#3138×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2961×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#2046×C₁₃₇	C₂	1	2	yes	maximal, complemented
6	#2045×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#1978×C₁₃₇	C₂	1	2	yes	maximal, complemented
8	#1977×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	#1967×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#1965×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#1778×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₁₃₇	C₂²	1	1	yes	characteristic
16	#533×C₁₃₇	C₂²	1	1	yes	characteristic
17	C₂×#127×C₁₃₇	C₂²	1	1	yes	characteristic
18	C₂×#124×C₁₃₇	C₂²	1	1	yes	characteristic
19	#496×C₁₃₇	—	2	4	no	—
20	#490×C₁₃₇	—	2	2	no	—
21	#489×C₁₃₇	—	2	2	no	—
22	#488×C₁₃₇	—	2	2	no	—
23	#486×C₁₃₇	—	2	2	no	—
24	#446×C₁₃₇	—	2	4	no	—
25	C₂×#108×C₁₃₇	C₂²	1	2	yes	—
26	#424×C₁₃₇	C₂²	1	2	yes	—
27	#423×C₁₃₇	C₂²	1	1	yes	characteristic
28	#419×C₁₃₇	C₂²	1	2	yes	—
29	#418×C₁₃₇	C₂²	1	2	yes	—
30	#418×C₁₃₇	C₂²	1	2	yes	—
31	#418×C₁₃₇	C₂²	1	2	yes	—
32	C₂×#101×C₁₃₇	C₂²	1	2	yes	—
33	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
34	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
35	C₂×#100×C₁₃₇	C₂²	1	2	yes	—
36	#405×C₁₃₇	C₂²	1	2	yes	—
37	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₁₃₇	C₂²	1	1	yes	characteristic
40	#341×C₁₃₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₇	—	2	2	no	—
43	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₇	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
47	C₂×SD₁₆×C₁₃₇	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₇	—	2	4	no	—
49	C₂×SD₁₆×C₁₃₇	—	4	2	no	—
50	C₂×D₈×C₁₃₇	—	2	2	no	—
51	C₂×D₈×C₁₃₇	—	2	2	no	—
52	C₂×D₈×C₁₃₇	—	2	4	no	—
53	C₂×D₈×C₁₃₇	—	4	2	no	—
54	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₁₃₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₃₇	D₄	1	2	yes	—
60	#127×C₁₃₇	—	2	1	no	—
61	#127×C₁₃₇	—	2	1	no	—
62	#127×C₁₃₇	—	2	2	no	—
63	#125×C₁₃₇	D₄	1	2	yes	—
64	#124×C₁₃₇	—	2	1	no	—
65	#124×C₁₃₇	—	2	1	no	—
66	#124×C₁₃₇	—	2	2	no	—
67	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
68	C₄×Q₈×C₁₃₇	—	2	2	no	—
69	#117×C₁₃₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₃₇	—	2	2	no	—
71	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
72	#108×C₁₃₇	—	2	4	no	—
73	C₄⋊C₈×C₁₃₇	—	2	4	no	—
74	C₄⋊C₈×C₁₃₇	—	2	2	no	—
75	#103×C₁₃₇	—	2	4	no	—
76	#102×C₁₃₇	—	2	4	no	—
77	#102×C₁₃₇	—	2	4	no	—
78	#102×C₁₃₇	—	2	4	no	—
79	#101×C₁₃₇	—	4	2	no	—
80	#100×C₁₃₇	—	4	2	no	—
81	#100×C₁₃₇	—	4	2	no	—
82	#100×C₁₃₇	—	4	2	no	—
83	#97×C₁₃₇	—	2	2	no	—
84	#97×C₁₃₇	—	2	1	no	—
85	#97×C₁₃₇	—	2	1	no	—
86	#97×C₁₃₇	D₄	1	4	yes	—
87	C₄×C₈×C₁₃₇	—	2	2	no	—
88	C₄×C₈×C₁₃₇	—	2	1	no	—
89	C₄×C₈×C₁₃₇	—	2	1	no	—
90	C₂⁴×C₁₃₇	—	2	1	no	—
91	C₂⁴×C₁₃₇	—	2	1	no	—
92	C₂⁴×C₁₃₇	—	2	1	no	—
93	C₂×Q₈×C₁₃₇	—	2	2	no	—
94	C₂×Q₈×C₁₃₇	—	2	1	no	—
95	C₂×Q₈×C₁₃₇	—	2	1	no	—
96	C₂×Q₈×C₁₃₇	—	2	2	no	—
97	C₂×Q₈×C₁₃₇	—	2	2	no	—
98	C₂×D₄×C₁₃₇	—	2	1	no	—
99	C₂×D₄×C₁₃₇	—	2	1	no	—
100	C₂×D₄×C₁₃₇	—	2	1	no	—
101	C₂×D₄×C₁₃₇	—	2	1	no	—
102	C₂×D₄×C₁₃₇	—	2	1	no	—
103	C₂×D₄×C₁₃₇	—	2	1	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	—	2	2	no	—
107	C₂×D₄×C₁₃₇	—	2	2	no	—
108	C₂×D₄×C₁₃₇	—	2	2	no	—
109	C₂×D₄×C₁₃₇	—	2	2	no	—
110	C₂×D₄×C₁₃₇	—	4	2	no	—
111	C₂×D₄×C₁₃₇	—	4	2	no	—
112	C₂×D₄×C₁₃₇	—	8	4	no	—
113	C₂²×C₄×C₁₃₇	—	2	1	no	—
114	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
115	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₁₃₇	—	4	4	no	—
117	SD₁₆×C₁₃₇	—	4	4	no	—
118	D₈×C₁₃₇	—	4	4	no	—
119	D₈×C₁₃₇	—	4	4	no	—
120	M₁₆×C₁₃₇	—	2	2	no	—
121	M₁₆×C₁₃₇	—	2	2	no	—
122	M₁₆×C₁₃₇	—	2	2	no	—
123	M₁₆×C₁₃₇	—	2	2	no	—
124	M₁₆×C₁₃₇	—	2	2	no	—
125	M₁₆×C₁₃₇	—	2	2	no	—
126	C₂×C₈×C₁₃₇	—	2	2	no	—
127	C₂×C₈×C₁₃₇	—	2	2	no	—
128	C₂×C₈×C₁₃₇	—	2	2	no	—
129	C₂×C₈×C₁₃₇	—	2	2	no	—
130	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃₇	#41	1	4	yes	—
133	C₄⋊C₄×C₁₃₇	—	2	4	no	—
134	C₄⋊C₄×C₁₃₇	—	2	2	no	—
135	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₁₃₇	—	2	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	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃₇	C₂×D₄	1	2	yes	—
143	C₂³×C₁₃₇	—	4	1	no	—
144	C₂³×C₁₃₇	—	4	1	no	—
145	C₂³×C₁₃₇	—	4	1	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	—	8	2	no	—
152	C₂³×C₁₃₇	C₂×#41	1	1	yes	characteristic
153	Q₈×C₁₃₇	—	4	1	no	—
154	Q₈×C₁₃₇	—	4	1	no	—
155	Q₈×C₁₃₇	—	4	2	no	—
156	Q₈×C₁₃₇	—	8	2	no	—
157	D₄×C₁₃₇	—	4	1	no	—
158	D₄×C₁₃₇	—	4	1	no	—
159	D₄×C₁₃₇	—	4	1	no	—
160	D₄×C₁₃₇	—	4	1	no	—
161	D₄×C₁₃₇	—	4	1	no	—
162	D₄×C₁₃₇	—	4	1	no	—
163	D₄×C₁₃₇	—	4	2	no	—
164	D₄×C₁₃₇	—	4	2	no	—
165	D₄×C₁₃₇	—	4	2	no	—
166	D₄×C₁₃₇	—	8	4	no	—
167	D₄×C₁₃₇	—	8	4	no	—
168	C₂×C₄×C₁₃₇	—	2	4	no	—
169	C₂×C₄×C₁₃₇	—	4	2	no	—
170	C₂×C₄×C₁₃₇	—	4	1	no	—
171	C₂×C₄×C₁₃₇	—	4	2	no	—
172	C₂×C₄×C₁₃₇	#121	1	2	yes	—
173	C₂×C₄×C₁₃₇	#121	1	2	yes	—
174	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₇	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃₇	H(5,𝔽₂)	1	2	yes	—
178	C₈×C₁₃₇	—	2	2	no	—
179	C₈×C₁₃₇	—	4	2	no	—
180	C₈×C₁₃₇	—	4	2	no	—
181	C₈×C₁₃₇	—	4	2	no	—
182	C₈×C₁₃₇	#124	1	4	yes	—
183	C₂²×C₁₃₇	—	2	2	no	—
184	C₂²×C₁₃₇	—	8	1	no	—
185	C₂²×C₁₃₇	—	8	1	no	—
186	C₂²×C₁₃₇	—	8	1	no	—
187	C₂²×C₁₃₇	—	8	2	no	—
188	C₂²×C₁₃₇	—	8	2	no	—
189	C₂²×C₁₃₇	—	8	2	no	—
190	C₂²×C₁₃₇	—	16	2	no	—
191	C₂²×C₁₃₇	—	16	2	no	—
192	C₂²×C₁₃₇	—	16	2	no	—
193	C₂²×C₁₃₇	C₂×#121	1	1	yes	characteristic
194	C₂²×C₁₃₇	#559	1	2	yes	—
195	C₄×C₁₃₇	—	2	2	no	—
196	C₄×C₁₃₇	—	2	2	no	—
197	C₄×C₁₃₇	—	4	4	no	—
198	C₄×C₁₃₇	—	8	1	no	—
199	C₄×C₁₃₇	C₂×#124	1	1	yes	characteristic
200	C₄×C₁₃₇	#535	1	1	yes	characteristic
201	C₄×C₁₃₇	#550	1	2	yes	—
202	C₂×C₁₃₇	—	2	2	no	—
203	C₂×C₁₃₇	—	16	1	no	—
204	C₂×C₁₃₇	—	16	1	no	—
205	C₂×C₁₃₇	—	16	1	no	—
206	C₂×C₁₃₇	#2548	1	1	yes	characteristic
207	C₂×C₁₃₇	#3068	1	2	yes	—
208	#28768	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₁₃₇	#28768	1	1	yes	characteristic, direct product factor, Sylow
210	C₂×#496	C₂×C₁₃₇	1	1	yes	characteristic
211	#3140	C₂×C₁₃₇	1	1	yes	characteristic, complemented
212	#3138	C₂×C₁₃₇	1	1	yes	characteristic, complemented
213	#2961	C₂×C₁₃₇	1	1	yes	characteristic, complemented
214	#2046	C₂×C₁₃₇	1	2	yes	complemented
215	#2045	C₂×C₁₃₇	1	2	yes	complemented
216	#1978	C₂×C₁₃₇	1	2	yes	complemented
217	#1977	C₂×C₁₃₇	1	2	yes	complemented
218	#1967	C₂×C₁₃₇	1	1	yes	characteristic, complemented
219	#1965	C₂×C₁₃₇	1	1	yes	characteristic, complemented
220	#1778	C₂×C₁₃₇	1	1	yes	characteristic, complemented
221	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
222	C₂²×SD₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
223	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₁₃₇	1	1	yes	characteristic
225	#533	C₂²×C₁₃₇	1	1	yes	characteristic
226	C₂×#127	C₂²×C₁₃₇	1	1	yes	characteristic
227	C₂×#124	C₂²×C₁₃₇	1	1	yes	characteristic
228	#496	—	2	4	no	—
229	#490	—	2	2	no	—
230	#489	—	2	2	no	—
231	#488	—	2	2	no	—
232	#486	—	2	2	no	—
233	#446	—	2	4	no	—
234	C₂×#108	C₂²×C₁₃₇	1	2	yes	—
235	#424	C₂²×C₁₃₇	1	2	yes	—
236	#423	C₂²×C₁₃₇	1	1	yes	characteristic
237	#419	C₂²×C₁₃₇	1	2	yes	—
238	#418	C₂²×C₁₃₇	1	2	yes	—
239	#418	C₂²×C₁₃₇	1	2	yes	—
240	#418	C₂²×C₁₃₇	1	2	yes	—
241	C₂×#101	C₂²×C₁₃₇	1	2	yes	—
242	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
243	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
244	C₂×#100	C₂²×C₁₃₇	1	2	yes	—
245	#405	C₂²×C₁₃₇	1	2	yes	—
246	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
247	C₄×M₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
248	C₂×#97	C₂²×C₁₃₇	1	1	yes	characteristic
249	#341	C₂²×C₁₃₇	1	2	yes	—
250	C₂²×Q₈	C₂³×C₁₃₇	1	1	yes	characteristic
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
253	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
254	C₂²×D₄	C₂³×C₁₃₇	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	4	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
264	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
265	C₂×M₁₆	C₂³×C₁₃₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
268	C₄⋊Q₈	D₄×C₁₃₇	1	2	yes	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	2	no	—
272	#125	D₄×C₁₃₇	1	2	yes	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	2	no	—
276	C₂²⋊Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	#117	C₂³×C₁₃₇	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
281	#108	—	2	4	no	—
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	2	4	no	—
287	#102	—	2	4	no	—
288	#101	—	4	2	no	—
289	#100	—	4	2	no	—
290	#100	—	4	2	no	—
291	#100	—	4	2	no	—
292	#97	—	2	2	no	—
293	#97	—	2	1	no	—
294	#97	—	2	1	no	—
295	#97	D₄×C₁₃₇	1	4	yes	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₂⁴	—	2	1	no	—
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	2	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
325	SD₁₆	—	4	4	no	—
326	SD₁₆	—	4	4	no	—
327	D₈	—	4	4	no	—
328	D₈	—	4	4	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
341	C₂×C₈	#41×C₁₃₇	1	4	yes	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₁₃₇	1	2	yes	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₂×#41×C₁₃₇	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	4	no	—
376	D₄	—	8	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	#121×C₁₃₇	1	2	yes	—
382	C₂×C₄	#121×C₁₃₇	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₁₃₇	1	2	yes	—
386	C₂×C₄	H(5,𝔽₂)×C₁₃₇	1	2	yes	—
387	C₈	—	2	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	#124×C₁₃₇	1	4	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	16	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	C₂×#121×C₁₃₇	1	1	yes	characteristic
403	C₂²	#559×C₁₃₇	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	8	1	no	—
408	C₄	C₂×#124×C₁₃₇	1	1	yes	characteristic
409	C₄	#535×C₁₃₇	1	1	yes	characteristic
410	C₄	#550×C₁₃₇	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	16	1	no	—
413	C₂	—	16	1	no	—
414	C₂	—	16	1	no	—
415	C₂	#2548×C₁₃₇	1	1	yes	characteristic
416	C₂	#3068×C₁₃₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂×#496×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. #3140×C₁₃₇	C₂	semidirect
3. #3138×C₁₃₇	C₂	semidirect
4. #2961×C₁₃₇	C₂	semidirect
5. #2046×C₁₃₇	C₂	semidirect
6. #2045×C₁₃₇	C₂	semidirect
7. #1978×C₁₃₇	C₂	semidirect
8. #1977×C₁₃₇	C₂	semidirect
9. #1967×C₁₃₇	C₂	semidirect
10. #1965×C₁₃₇	C₂	semidirect
11. #1778×C₁₃₇	C₂	semidirect
208. #28768	C₁₃₇	direct (N × H)
209. C₁₃₇	#28768	direct (N × H)
211. #3140	C₂×C₁₃₇	semidirect
212. #3138	C₂×C₁₃₇	semidirect
213. #2961	C₂×C₁₃₇	semidirect
214. #2046	C₂×C₁₃₇	semidirect
215. #2045	C₂×C₁₃₇	semidirect
216. #1978	C₂×C₁₃₇	semidirect
217. #1977	C₂×C₁₃₇	semidirect
218. #1967	C₂×C₁₃₇	semidirect
219. #1965	C₂×C₁₃₇	semidirect
220. #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
C₂×#496×C₁₃₇	2
#3140×C₁₃₇	2
#3138×C₁₃₇	2
#2961×C₁₃₇	2
#2046×C₁₃₇	2
#2045×C₁₃₇	2
#1978×C₁₃₇	2
#1977×C₁₃₇	2
#1967×C₁₃₇	2
#1965×C₁₃₇	2
#1778×C₁₃₇	2
#28768	137

Subgroups — C137×#28768 #46878154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#28768 #46878154