Subgroups — C₂×#1864×C₁₃₇ #46870255

Order 35072.

1974 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₁₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#389×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#1864×C₁₃₇	C₂	1	8	yes	maximal, direct product factor
7	C₂×#340×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#336×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃₇	—	2	1	no	—
11	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃₇	—	2	4	no	—
14	C₂×C₄×D₄×C₁₃₇	—	2	4	no	—
15	C₂×C₄×D₄×C₁₃₇	—	2	2	no	—
16	C₂×C₄×D₄×C₁₃₇	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₃₇	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₃₇	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₃₇	—	2	1	no	—
22	C₂²×C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
23	C₂×#106×C₁₃₇	—	2	4	no	—
24	C₂×#106×C₁₃₇	C₂²	1	4	yes	complemented
25	C₂×#102×C₁₃₇	—	2	4	no	—
26	C₂×#102×C₁₃₇	C₄	1	8	yes	complemented
27	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
28	C₂×#102×C₁₃₇	C₂²	1	4	yes	—
29	#389×C₁₃₇	—	2	2	no	—
30	#389×C₁₃₇	C₂²	1	4	yes	complemented
31	C₂×#95×C₁₃₇	—	2	1	no	—
32	#340×C₁₃₇	C₂²	1	4	yes	complemented
33	#336×C₁₃₇	C₂²	1	4	yes	complemented
34	C₂⁵×C₁₃₇	—	2	1	no	—
35	C₂²×D₄×C₁₃₇	—	2	1	no	—
36	C₂²×D₄×C₁₃₇	—	2	2	no	—
37	C₂²×D₄×C₁₃₇	—	2	2	no	—
38	C₂²×D₄×C₁₃₇	—	2	2	no	—
39	C₂²×D₄×C₁₃₇	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₃₇	D₄	1	4	yes	—
41	C₂²×D₄×C₁₃₇	Q₈	1	4	yes	—
42	C₂²×D₄×C₁₃₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃₇	—	2	8	no	—
44	C₂³×C₄×C₁₃₇	—	2	1	no	—
45	C₂³×C₄×C₁₃₇	—	2	1	no	—
46	C₂³×C₄×C₁₃₇	—	2	4	no	—
47	C₂³×C₄×C₁₃₇	—	2	1	no	—
48	C₂³×C₄×C₁₃₇	—	4	4	no	—
49	C₂³×C₄×C₁₃₇	—	4	4	no	—
50	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃₇	—	2	2	no	—
54	C₂²×C₈×C₁₃₇	—	2	2	no	—
55	C₂²×C₈×C₁₃₇	—	2	2	no	—
56	C₂²×C₈×C₁₃₇	—	2	2	no	—
57	C₂²×C₈×C₁₃₇	—	2	2	no	—
58	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	complemented
59	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
61	C₄×D₄×C₁₃₇	—	2	16	no	—
62	C₄×D₄×C₁₃₇	—	2	8	no	—
63	C₄×D₄×C₁₃₇	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₃₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₃₇	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₃₇	—	4	4	no	—
73	C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	1	4	yes	complemented
74	C₂×C₄⋊C₄×C₁₃₇	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₃₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₃₇	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₁₃₇	—	2	4	no	—
80	C₂×C₄²×C₁₃₇	—	2	2	no	—
81	C₂×C₄²×C₁₃₇	—	2	2	no	—
82	C₂×C₄²×C₁₃₇	D₄	1	2	yes	—
83	C₂×C₄²×C₁₃₇	C₂³	1	2	yes	—
84	#106×C₁₃₇	—	2	8	no	—
85	#102×C₁₃₇	—	2	8	no	—
86	#102×C₁₃₇	C₂×C₄	1	16	yes	complemented
87	#95×C₁₃₇	—	2	4	no	—
88	C₂⁴×C₁₃₇	—	2	4	no	—
89	C₂⁴×C₁₃₇	—	2	4	no	—
90	C₂⁴×C₁₃₇	—	2	4	no	—
91	C₂⁴×C₁₃₇	—	2	2	no	—
92	C₂⁴×C₁₃₇	—	4	2	no	—
93	C₂⁴×C₁₃₇	—	4	2	no	—
94	C₂⁴×C₁₃₇	—	4	2	no	—
95	C₂⁴×C₁₃₇	—	4	2	no	—
96	C₂⁴×C₁₃₇	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃₇	—	2	8	no	—
98	C₂×D₄×C₁₃₇	—	2	4	no	—
99	C₂×D₄×C₁₃₇	—	2	4	no	—
100	C₂×D₄×C₁₃₇	—	2	8	no	—
101	C₂×D₄×C₁₃₇	—	2	4	no	—
102	C₂×D₄×C₁₃₇	—	2	8	no	—
103	C₂×D₄×C₁₃₇	—	2	2	no	—
104	C₂×D₄×C₁₃₇	—	2	2	no	—
105	C₂×D₄×C₁₃₇	—	2	2	no	—
106	C₂×D₄×C₁₃₇	C₄⋊C₄	1	16	yes	complemented
107	C₂×D₄×C₁₃₇	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₁₃₇	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₁₃₇	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₁₃₇	—	2	2	no	—
111	C₂²×C₄×C₁₃₇	—	2	2	no	—
112	C₂²×C₄×C₁₃₇	—	2	16	no	—
113	C₂²×C₄×C₁₃₇	—	2	4	no	—
114	C₂²×C₄×C₁₃₇	—	2	2	no	—
115	C₂²×C₄×C₁₃₇	—	2	4	no	—
116	C₂²×C₄×C₁₃₇	—	2	2	no	—
117	C₂²×C₄×C₁₃₇	—	2	2	no	—
118	C₂²×C₄×C₁₃₇	—	2	2	no	—
119	C₂²×C₄×C₁₃₇	—	2	2	no	—
120	C₂²×C₄×C₁₃₇	—	2	2	no	—
121	C₂²×C₄×C₁₃₇	—	4	8	no	—
122	C₂²×C₄×C₁₃₇	—	4	32	no	—
123	C₂²×C₄×C₁₃₇	—	4	2	no	—
124	C₂²×C₄×C₁₃₇	—	4	2	no	—
125	C₂²×C₄×C₁₃₇	—	4	2	no	—
126	C₂²×C₄×C₁₃₇	—	4	2	no	—
127	C₂²×C₄×C₁₃₇	—	4	8	no	—
128	C₂²×C₄×C₁₃₇	—	4	2	no	—
129	C₂²×C₄×C₁₃₇	—	4	2	no	—
130	C₂²×C₄×C₁₃₇	—	4	2	no	—
131	C₂²×C₄×C₁₃₇	SD₁₆	1	4	yes	—
132	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃₇	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
140	C₂²×C₄×C₁₃₇	#41	1	2	yes	—
141	C₂²×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₁₃₇	—	2	8	no	—
143	C₂×C₈×C₁₃₇	—	2	2	no	—
144	C₂×C₈×C₁₃₇	—	2	2	no	—
145	C₂×C₈×C₁₃₇	—	2	2	no	—
146	C₂×C₈×C₁₃₇	—	2	2	no	—
147	C₂×C₈×C₁₃₇	—	2	2	no	—
148	C₂×C₈×C₁₃₇	—	4	4	no	—
149	C₂×C₈×C₁₃₇	C₂²×C₄	1	4	yes	complemented
150	C₄⋊C₄×C₁₃₇	—	2	4	no	—
151	C₄⋊C₄×C₁₃₇	—	2	4	no	—
152	C₄⋊C₄×C₁₃₇	—	2	2	no	—
153	C₄⋊C₄×C₁₃₇	—	2	2	no	—
154	C₄⋊C₄×C₁₃₇	—	2	2	no	—
155	C₄⋊C₄×C₁₃₇	—	2	2	no	—
156	C₄⋊C₄×C₁₃₇	—	4	8	no	—
157	C₄⋊C₄×C₁₃₇	—	4	2	no	—
158	C₄⋊C₄×C₁₃₇	C₂²×C₄	1	4	yes	complemented
159	C₄⋊C₄×C₁₃₇	C₂×D₄	1	4	yes	—
160	C₂²⋊C₄×C₁₃₇	—	2	16	no	—
161	C₄²×C₁₃₇	—	2	4	no	—
162	C₄²×C₁₃₇	—	2	2	no	—
163	C₄²×C₁₃₇	—	2	2	no	—
164	C₂³×C₁₃₇	—	2	4	no	—
165	C₂³×C₁₃₇	—	2	4	no	—
166	C₂³×C₁₃₇	—	2	4	no	—
167	C₂³×C₁₃₇	—	2	16	no	—
168	C₂³×C₁₃₇	—	4	2	no	—
169	C₂³×C₁₃₇	—	4	2	no	—
170	C₂³×C₁₃₇	—	4	2	no	—
171	C₂³×C₁₃₇	—	4	2	no	—
172	C₂³×C₁₃₇	—	4	8	no	—
173	C₂³×C₁₃₇	—	4	8	no	—
174	C₂³×C₁₃₇	—	4	8	no	—
175	C₂³×C₁₃₇	—	4	8	no	—
176	C₂³×C₁₃₇	—	4	8	no	—
177	C₂³×C₁₃₇	—	4	8	no	—
178	C₂³×C₁₃₇	C₄×D₄	1	2	yes	—
179	C₂³×C₁₃₇	#120	1	2	yes	—
180	C₂³×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
181	C₂³×C₁₃₇	C₂×SD₁₆	1	2	yes	—
182	C₂³×C₁₃₇	#135	1	2	yes	—
183	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₁₃₇	AGL(1,ℤ/8)	1	2	yes	—
185	C₂³×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
186	D₄×C₁₃₇	—	2	4	no	—
187	D₄×C₁₃₇	—	2	4	no	—
188	D₄×C₁₃₇	—	2	4	no	—
189	D₄×C₁₃₇	—	2	16	no	—
190	D₄×C₁₃₇	C₂×C₄⋊C₄	1	8	yes	complemented
191	C₂×C₄×C₁₃₇	—	2	2	no	—
192	C₂×C₄×C₁₃₇	—	2	2	no	—
193	C₂×C₄×C₁₃₇	—	2	8	no	—
194	C₂×C₄×C₁₃₇	—	2	4	no	—
195	C₂×C₄×C₁₃₇	—	2	2	no	—
196	C₂×C₄×C₁₃₇	—	2	4	no	—
197	C₂×C₄×C₁₃₇	—	2	2	no	—
198	C₂×C₄×C₁₃₇	—	2	2	no	—
199	C₂×C₄×C₁₃₇	—	4	32	no	—
200	C₂×C₄×C₁₃₇	—	4	2	no	—
201	C₂×C₄×C₁₃₇	—	4	2	no	—
202	C₂×C₄×C₁₃₇	—	4	2	no	—
203	C₂×C₄×C₁₃₇	—	4	2	no	—
204	C₂×C₄×C₁₃₇	—	4	8	no	—
205	C₂×C₄×C₁₃₇	—	4	4	no	—
206	C₂×C₄×C₁₃₇	—	4	8	no	—
207	C₂×C₄×C₁₃₇	—	4	2	no	—
208	C₂×C₄×C₁₃₇	—	4	2	no	—
209	C₂×C₄×C₁₃₇	—	4	2	no	—
210	C₂×C₄×C₁₃₇	—	8	4	no	—
211	C₂×C₄×C₁₃₇	C₂×C₄⋊C₄	1	4	yes	—
212	C₂×C₄×C₁₃₇	C₄×D₄	1	4	yes	—
213	C₂×C₄×C₁₃₇	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₁₃₇	#120	1	2	yes	—
215	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	4	yes	—
216	C₂×C₄×C₁₃₇	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₄×C₁₃₇	#123	1	4	yes	—
218	C₂×C₄×C₁₃₇	C₂×SD₁₆	1	4	yes	—
219	C₂×C₄×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃₇	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃₇	C₂×#41	1	1	yes	characteristic
225	C₈×C₁₃₇	—	2	4	no	—
226	C₈×C₁₃₇	—	4	2	no	—
227	C₂²×C₁₃₇	—	2	8	no	—
228	C₂²×C₁₃₇	—	4	4	no	—
229	C₂²×C₁₃₇	—	4	32	no	—
230	C₂²×C₁₃₇	—	4	4	no	—
231	C₂²×C₁₃₇	—	4	4	no	—
232	C₂²×C₁₃₇	—	4	4	no	—
233	C₂²×C₁₃₇	—	4	4	no	—
234	C₂²×C₁₃₇	—	4	4	no	—
235	C₂²×C₁₃₇	#385	1	4	yes	—
236	C₂²×C₁₃₇	C₄×SD₁₆	1	4	yes	—
237	C₂²×C₁₃₇	#442	1	4	yes	—
238	C₂²×C₁₃₇	#449	1	4	yes	—
239	C₂²×C₁₃₇	#450	1	4	yes	—
240	C₂²×C₁₃₇	#476	1	4	yes	—
241	C₂²×C₁₃₇	#478	1	4	yes	—
242	C₂²×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₁₃₇	C₂×#120	1	1	yes	characteristic
244	C₂²×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
245	C₂²×C₁₃₇	C₂²×SD₁₆	1	1	yes	characteristic
246	C₂²×C₁₃₇	C₂×#135	1	1	yes	characteristic
247	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂²×C₁₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₄×C₁₃₇	—	2	4	no	—
250	C₄×C₁₃₇	—	4	4	no	—
251	C₄×C₁₃₇	—	4	4	no	—
252	C₄×C₁₃₇	—	4	2	no	—
253	C₄×C₁₃₇	—	8	2	no	—
254	C₄×C₁₃₇	#385	1	4	yes	—
255	C₄×C₁₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
256	C₄×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₃₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
258	C₄×C₁₃₇	C₂×#123	1	1	yes	characteristic
259	C₂×C₁₃₇	—	4	8	no	—
260	C₂×C₁₃₇	#1864	1	8	yes	direct product factor
261	C₂×C₁₃₇	C₂×#385	1	1	yes	characteristic
262	C₂×C₁₃₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
263	C₂×C₁₃₇	C₂×#442	1	1	yes	characteristic
264	C₂×C₁₃₇	C₂×#450	1	1	yes	characteristic
265	C₂×C₁₃₇	C₂×#449	1	1	yes	characteristic
266	C₂×C₁₃₇	C₂×#476	1	1	yes	characteristic
267	C₂×C₁₃₇	C₂×#478	1	1	yes	characteristic
268	C₂×#1864	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₁₃₇	C₂×#1864	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×C₄×D₄	C₂×C₁₃₇	1	1	yes	characteristic
271	C₂²×#106	C₂×C₁₃₇	1	1	yes	characteristic, complemented
272	C₂²×#102	C₂×C₁₃₇	1	1	yes	characteristic
273	C₂²×#102	C₂×C₁₃₇	1	1	yes	characteristic
274	C₂×#389	C₂×C₁₃₇	1	1	yes	characteristic, complemented
275	#1864	C₂×C₁₃₇	1	8	yes	direct product factor
276	C₂×#340	C₂×C₁₃₇	1	1	yes	characteristic, complemented
277	C₂×#336	C₂×C₁₃₇	1	1	yes	characteristic, complemented
278	C₂³×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
279	C₂⁴×C₄	—	2	1	no	—
280	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
281	C₂³×C₈	C₂²×C₁₃₇	1	1	yes	characteristic
282	C₂×C₄×D₄	—	2	4	no	—
283	C₂×C₄×D₄	—	2	4	no	—
284	C₂×C₄×D₄	—	2	2	no	—
285	C₂×C₄×D₄	C₂²×C₁₃₇	1	4	yes	—
286	C₂²×C₄⋊C₄	—	2	1	no	—
287	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₁₃₇	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	—	2	1	no	—
291	C₂²×C₄²	C₂²×C₁₃₇	1	1	yes	characteristic
292	C₂×#106	—	2	4	no	—
293	C₂×#106	C₂²×C₁₃₇	1	4	yes	complemented
294	C₂×#102	—	2	4	no	—
295	C₂×#102	C₄×C₁₃₇	1	8	yes	complemented
296	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
297	C₂×#102	C₂²×C₁₃₇	1	4	yes	—
298	#389	—	2	2	no	—
299	#389	C₂²×C₁₃₇	1	4	yes	complemented
300	C₂×#95	—	2	1	no	—
301	#340	C₂²×C₁₃₇	1	4	yes	complemented
302	#336	C₂²×C₁₃₇	1	4	yes	complemented
303	C₂⁵	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	C₂×C₄×C₁₃₇	1	4	yes	—
309	C₂²×D₄	D₄×C₁₃₇	1	4	yes	—
310	C₂²×D₄	Q₈×C₁₃₇	1	4	yes	—
311	C₂²×D₄	C₂³×C₁₃₇	1	2	yes	—
312	C₂³×C₄	—	2	8	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	4	4	no	—
318	C₂³×C₄	—	4	4	no	—
319	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₁₃₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₃₇	1	1	yes	characteristic
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	complemented
328	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
330	C₄×D₄	—	2	16	no	—
331	C₄×D₄	—	2	8	no	—
332	C₄×D₄	—	2	8	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	4	4	no	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	1	4	yes	complemented
343	C₂×C₄⋊C₄	D₄×C₁₃₇	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃₇	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	8	no	—
348	C₂×C₂²⋊C₄	—	2	4	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	D₄×C₁₃₇	1	2	yes	—
352	C₂×C₄²	C₂³×C₁₃₇	1	2	yes	—
353	#106	—	2	8	no	—
354	#102	—	2	8	no	—
355	#102	C₂×C₄×C₁₃₇	1	16	yes	complemented
356	#95	—	2	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	2	no	—
363	C₂⁴	—	4	2	no	—
364	C₂⁴	—	4	2	no	—
365	C₂⁴	C₂×D₄×C₁₃₇	1	1	yes	characteristic
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₄⋊C₄×C₁₃₇	1	16	yes	complemented
376	C₂×D₄	C₂²×C₄×C₁₃₇	1	4	yes	—
377	C₂×D₄	C₂×D₄×C₁₃₇	1	4	yes	—
378	C₂×D₄	C₂×Q₈×C₁₃₇	1	4	yes	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	16	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	32	no	—
391	C₂²×C₄	—	4	8	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	SD₁₆×C₁₃₇	1	4	yes	—
401	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
407	C₂²×C₄	C₂×Q₈×C₁₃₇	1	2	yes	—
408	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
409	C₂²×C₄	#41×C₁₃₇	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₃₇	1	1	yes	characteristic
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	4	4	no	—
418	C₂×C₈	C₂²×C₄×C₁₃₇	1	4	yes	complemented
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	8	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	C₂²×C₄×C₁₃₇	1	4	yes	complemented
428	C₄⋊C₄	C₂×D₄×C₁₃₇	1	4	yes	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₄²	—	2	4	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₂³	—	2	16	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₄×D₄×C₁₃₇	1	2	yes	—
448	C₂³	#120×C₁₃₇	1	2	yes	—
449	C₂³	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
450	C₂³	C₂×SD₁₆×C₁₃₇	1	2	yes	—
451	C₂³	#135×C₁₃₇	1	2	yes	—
452	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
453	C₂³	AGL(1,ℤ/8)×C₁₃₇	1	2	yes	—
454	C₂³	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
455	D₄	—	2	16	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	C₂×C₄⋊C₄×C₁₃₇	1	8	yes	complemented
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	32	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₂×C₄⋊C₄×C₁₃₇	1	4	yes	—
481	C₂×C₄	C₄×D₄×C₁₃₇	1	2	yes	—
482	C₂×C₄	C₄×D₄×C₁₃₇	1	4	yes	—
483	C₂×C₄	#120×C₁₃₇	1	2	yes	—
484	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	2	yes	—
485	C₂×C₄	C₂²⋊Q₈×C₁₃₇	1	4	yes	—
486	C₂×C₄	#123×C₁₃₇	1	4	yes	—
487	C₂×C₄	C₂×SD₁₆×C₁₃₇	1	4	yes	—
488	C₂×C₄	C₂³×C₄×C₁₃₇	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
491	C₂×C₄	C₂²×Q₈×C₁₃₇	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₁₃₇	1	1	yes	characteristic
494	C₈	—	2	4	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	32	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	#385×C₁₃₇	1	4	yes	—
505	C₂²	C₄×SD₁₆×C₁₃₇	1	4	yes	—
506	C₂²	#442×C₁₃₇	1	4	yes	—
507	C₂²	#449×C₁₃₇	1	4	yes	—
508	C₂²	#450×C₁₃₇	1	4	yes	—
509	C₂²	#476×C₁₃₇	1	4	yes	—
510	C₂²	#478×C₁₃₇	1	4	yes	—
511	C₂²	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
512	C₂²	C₂×#120×C₁₃₇	1	1	yes	characteristic
513	C₂²	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
514	C₂²	C₂²×SD₁₆×C₁₃₇	1	1	yes	characteristic
515	C₂²	C₂×#135×C₁₃₇	1	1	yes	characteristic
516	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
517	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₇	1	1	yes	characteristic
518	C₄	—	2	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	#385×C₁₃₇	1	4	yes	—
524	C₄	C₂²×C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
525	C₄	C₂×C₄×D₄×C₁₃₇	1	1	yes	characteristic
526	C₄	C₂×C₂²⋊Q₈×C₁₃₇	1	1	yes	characteristic
527	C₄	C₂×#123×C₁₃₇	1	1	yes	characteristic
528	C₂	—	4	8	no	—
529	C₂	#1864×C₁₃₇	1	8	yes	direct product factor
530	C₂	C₂×#385×C₁₃₇	1	1	yes	characteristic
531	C₂	C₂×C₄×SD₁₆×C₁₃₇	1	1	yes	characteristic
532	C₂	C₂×#442×C₁₃₇	1	1	yes	characteristic
533	C₂	C₂×#450×C₁₃₇	1	1	yes	characteristic
534	C₂	C₂×#449×C₁₃₇	1	1	yes	characteristic
535	C₂	C₂×#476×C₁₃₇	1	1	yes	characteristic
536	C₂	C₂×#478×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₇
prime radical	C₂³×D₄×C₁₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₇ ◁ C₂²×C₄²×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#106×C₁₃₇	C₂	semidirect
5. C₂×#389×C₁₃₇	C₂	semidirect
6. #1864×C₁₃₇	C₂	direct (N × H)
7. C₂×#340×C₁₃₇	C₂	semidirect
8. C₂×#336×C₁₃₇	C₂	semidirect
24. C₂×#106×C₁₃₇	C₂²	semidirect
26. C₂×#102×C₁₃₇	C₄	semidirect
30. #389×C₁₃₇	C₂²	semidirect
32. #340×C₁₃₇	C₂²	semidirect
33. #336×C₁₃₇	C₂²	semidirect
58. C₂²×C₈×C₁₃₇	C₂×C₄	semidirect
73. C₂×C₄⋊C₄×C₁₃₇	C₂×C₄	semidirect
86. #102×C₁₃₇	C₂×C₄	semidirect
106. C₂×D₄×C₁₃₇	C₄⋊C₄	semidirect
149. C₂×C₈×C₁₃₇	C₂²×C₄	semidirect
158. C₄⋊C₄×C₁₃₇	C₂²×C₄	semidirect
190. D₄×C₁₃₇	C₂×C₄⋊C₄	semidirect
260. C₂×C₁₃₇	#1864	direct (N × H)
268. C₂×#1864	C₁₃₇	direct (N × H)
269. C₁₃₇	C₂×#1864	direct (N × H)
271. C₂²×#106	C₂×C₁₃₇	semidirect
274. C₂×#389	C₂×C₁₃₇	semidirect
275. #1864	C₂×C₁₃₇	direct (N × H)
276. C₂×#340	C₂×C₁₃₇	semidirect
277. C₂×#336	C₂×C₁₃₇	semidirect
293. C₂×#106	C₂²×C₁₃₇	semidirect
295. C₂×#102	C₄×C₁₃₇	semidirect
299. #389	C₂²×C₁₃₇	semidirect
301. #340	C₂²×C₁₃₇	semidirect
302. #336	C₂²×C₁₃₇	semidirect
327. C₂²×C₈	C₂×C₄×C₁₃₇	semidirect
342. C₂×C₄⋊C₄	C₂×C₄×C₁₃₇	semidirect
355. #102	C₂×C₄×C₁₃₇	semidirect
375. C₂×D₄	C₄⋊C₄×C₁₃₇	semidirect
418. C₂×C₈	C₂²×C₄×C₁₃₇	semidirect
427. C₄⋊C₄	C₂²×C₄×C₁₃₇	semidirect
459. D₄	C₂×C₄⋊C₄×C₁₃₇	semidirect
529. C₂	#1864×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃₇	2
C₂²×#106×C₁₃₇	2
C₂²×#102×C₁₃₇	2
C₂×#389×C₁₃₇	2
#1864×C₁₃₇	2
C₂×#340×C₁₃₇	2
C₂×#336×C₁₃₇	2
C₂×#1864	137

Subgroups — C2×#1864×C137 #46870255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1864×C₁₃₇ #46870255