Group #18076137 — subgroups

Subgroups — #18076137

Order 4864.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566608	C₂	1	1	yes	maximal, characteristic
2	#14561956	C₂	1	1	yes	maximal, characteristic
3	#14561536	C₂	1	2	yes	maximal, complemented
4	#14561495	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926447	—	2	1	no	—
8	#11926437	—	2	2	no	—
9	#11926410	C₂²	1	1	yes	characteristic
10	#11926407	C₄	1	2	yes	—
11	C₄⋊C₄×Dic₁₉	—	2	1	no	—
12	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₄×C₂²⋊Dic₁₉	C₄	1	2	yes	—
14	#11926268	—	2	2	no	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#423	C₂²	1	2	yes	—
17	C₂×C₁₉×#100	—	2	1	no	—
18	C₁₉×#343	—	2	1	no	—
19	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₄×D₄×C₁₉	—	2	2	no	—
23	C₄×D₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
28	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄×Dic₁₉	—	2	1	no	—
32	C₂×C₄×Dic₁₉	—	2	2	no	—
33	C₁₉×C₄⋊C₈	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×#100	—	4	2	no	—
36	C₁₉⋊#95	—	2	2	no	—
37	C₁₉⋊#95	—	2	1	no	—
38	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
39	C₁₉⋊#95	C₂×C₄	1	2	yes	—
40	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	1	no	—
48	C₂×D₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	8	2	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	2	1	no	—
57	C₂²×Dic₁₉	—	2	2	no	—
58	C₂²×Dic₁₉	—	2	1	no	—
59	M₁₆×C₁₉	—	4	2	no	—
60	M₁₆×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₄²×C₁₉	#41	1	2	yes	—
65	C₄²×C₁₉	#41	1	2	yes	—
66	C₂²⋊Dic₁₉	—	4	4	no	—
67	C₂²⋊Dic₁₉	—	8	2	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₄⋊Dic₁₉	—	4	1	no	—
70	C₄⋊Dic₁₉	—	4	1	no	—
71	C₄×Dic₁₉	—	4	2	no	—
72	C₄×Dic₁₉	—	8	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	#8771	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	—	2	2	no	—
76	C₂³×C₁₉	—	2	2	no	—
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	—	4	2	no	—
80	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	D₄×C₁₉	—	4	2	no	—
82	D₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	8	2	no	—
88	C₂×C₄×C₁₉	—	8	2	no	—
89	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#123	1	2	yes	—
92	C₂×C₄×C₁₉	#123	1	2	yes	—
93	C₂×C₄×C₁₉	#135	1	2	yes	—
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	—	4	1	no	—
98	C₂×Dic₁₉	—	4	1	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	C₂×Dic₁₉	—	4	1	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	1	no	—
103	C₂×Dic₁₉	—	4	1	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₈×C₁₉	—	8	2	no	—
106	C₁₉⋊C₈	—	8	2	no	—
107	#2357	—	19	1	no	—
108	#1800	D₁₉	1	1	yes	characteristic
109	#1460	—	19	1	no	—
110	#1303	—	19	2	no	—
111	#1286	—	19	2	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	4	2	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	4	2	no	—
117	C₂²×C₁₉	—	8	2	no	—
118	C₂²×C₁₉	—	8	2	no	—
119	C₂²×C₁₉	#381	1	1	yes	characteristic
120	C₂²×C₁₉	#416	1	1	yes	characteristic
121	C₂²×C₁₉	#417	1	1	yes	characteristic
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	4	2	no	—
126	C₄×C₁₉	#482	1	2	yes	—
127	C₄×C₁₉	#485	1	2	yes	—
128	Dic₁₉	—	4	2	no	—
129	Dic₁₉	—	8	1	no	—
130	Dic₁₉	—	8	2	no	—
131	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
132	#431	—	19	2	no	—
133	#423	C₂×D₁₉	1	2	yes	—
134	C₂×#100	—	2	1	no	—
135	#390	—	38	1	no	—
136	#388	—	38	2	no	—
137	#382	—	19	1	no	—
138	#381	—	19	2	no	—
139	C₄×C₄⋊C₄	—	19	1	no	—
140	C₄×C₄⋊C₄	—	38	1	no	—
141	C₄×C₂²⋊C₄	—	19	2	no	—
142	#343	—	2	1	no	—
143	#323	—	38	2	no	—
144	C₂×C₁₉	—	2	1	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	8	2	no	—
147	C₂×C₁₉	#1825	1	1	yes	characteristic
148	C₂×C₁₉	#1827	1	1	yes	characteristic
149	C₂×C₁₉	#1829	1	1	yes	characteristic
150	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
151	C₂³×C₄	C₄×D₁₉	1	2	yes	—
152	C₂×M₁₆	—	2	2	no	—
153	C₄×D₄	—	2	2	no	—
154	C₄×D₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	38	1	no	—
156	C₂×C₄⋊C₄	—	38	1	no	—
157	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
158	C₂×C₂²⋊C₄	—	38	2	no	—
159	C₂×C₂²⋊C₄	—	38	2	no	—
160	C₂×C₂²⋊C₄	D₇₆	1	2	yes	—
161	C₂×C₄²	—	38	1	no	—
162	C₂×C₄²	—	38	2	no	—
163	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	38	2	no	—
167	#100	—	4	2	no	—
168	C₂²⋊C₈	—	38	2	no	—
169	C₄×C₈	—	38	2	no	—
170	#95	—	19	1	no	—
171	#95	—	19	2	no	—
172	#95	—	19	1	no	—
173	#95	—	38	2	no	—
174	#95	—	38	1	no	—
175	C₁₉	#8771	1	1	yes	characteristic, complemented, Sylow
176	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
177	C₂×D₄	—	2	1	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	2	1	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	8	2	no	—
184	C₂²×C₄	—	38	1	no	—
185	C₂²×C₄	—	38	2	no	—
186	C₂²×C₄	—	38	1	no	—
187	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
188	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
191	M₁₆	—	4	2	no	—
192	M₁₆	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	76	2	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	76	2	no	—
197	C₄⋊C₄	—	76	1	no	—
198	C₄⋊C₄	—	76	1	no	—
199	C₂²⋊C₄	—	2	4	no	—
200	C₂²⋊C₄	—	76	4	no	—
201	C₂²⋊C₄	—	152	2	no	—
202	C₄²	—	76	2	no	—
203	C₄²	—	152	2	no	—
204	C₄²	#64543	1	2	yes	—
205	C₄²	#64543	1	2	yes	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	2	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	D₄	—	4	2	no	—
213	D₄	—	4	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	—	38	2	no	—
221	C₂×C₄	—	76	1	no	—
222	C₂×C₄	—	76	1	no	—
223	C₂×C₄	—	76	2	no	—
224	C₂×C₄	—	76	2	no	—
225	C₂×C₄	—	76	1	no	—
226	C₂×C₄	—	76	1	no	—
227	C₂×C₄	—	76	1	no	—
228	C₂×C₄	—	76	2	no	—
229	C₂×C₄	#10597323	1	1	yes	characteristic
230	C₂×C₄	#10597323	1	1	yes	characteristic
231	C₂×C₄	#10597332	1	2	yes	—
232	C₂×C₄	#10597378	1	1	yes	characteristic
233	C₂×C₄	#10597381	1	2	yes	—
234	C₂×C₄	#10597388	1	1	yes	characteristic
235	C₂×C₄	#10597396	1	2	yes	—
236	C₈	—	8	2	no	—
237	C₈	—	152	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	2	no	—
244	C₂²	—	8	2	no	—
245	C₂²	#11926405	1	1	yes	characteristic
246	C₂²	#11926538	1	1	yes	characteristic
247	C₂²	#11926543	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	4	2	no	—
252	C₄	—	76	2	no	—
253	C₄	—	152	1	no	—
254	C₄	—	152	2	no	—
255	C₄	#11926865	1	2	yes	—
256	C₄	#11926882	1	2	yes	—
257	C₂	—	2	1	no	—
258	C₂	—	2	1	no	—
259	C₂	—	8	2	no	—
260	C₂	#14563727	1	1	yes	characteristic
261	C₂	#14563740	1	1	yes	characteristic
262	C₂	#14563744	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566608

C₂

yes

maximal, characteristic

#14561956

C₂

yes

maximal, characteristic

#14561536

C₂

yes

maximal, complemented

#14561495

C₂

yes

maximal, complemented

C₁₉×#1800

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926447

—

#11926437

—

#11926410

C₂²

yes

characteristic

#11926407

C₄

yes

—

C₄⋊C₄×Dic₁₉

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₄×C₂²⋊Dic₁₉

C₄

yes

—

#11926268

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#100

—

C₁₉×#343

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₁₉⋊#95

C₂×C₄

yes

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#8771

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₈×C₁₉

—

106

C₁₉⋊C₈

—

107

#2357

—

108

#1800

D₁₉

yes

characteristic

109

#1460

—

110

#1303

—

111

#1286

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#381

yes

characteristic

120

C₂²×C₁₉

#416

yes

characteristic

121

C₂²×C₁₉

#417

yes

characteristic

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

#482

yes

—

127

C₄×C₁₉

#485

yes

—

128

Dic₁₉

—

129

Dic₁₉

—

130

Dic₁₉

—

131

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

132

#431

—

133

#423

C₂×D₁₉

yes

—

134

C₂×#100

—

135

#390

—

136

#388

—

137

#382

—

138

#381

—

139

C₄×C₄⋊C₄

—

140

C₄×C₄⋊C₄

—

141

C₄×C₂²⋊C₄

—

142

#343

—

143

#323

—

144

C₂×C₁₉

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1825

yes

characteristic

148

C₂×C₁₉

#1827

yes

characteristic

149

C₂×C₁₉

#1829

yes

characteristic

150

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

151

C₂³×C₄

C₄×D₁₉

yes

—

152

C₂×M₁₆

—

153

C₄×D₄

—

154

C₄×D₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

158

C₂×C₂²⋊C₄

—

159

C₂×C₂²⋊C₄

—

160

C₂×C₂²⋊C₄

D₇₆

yes

—

161

C₂×C₄²

—

162

C₂×C₄²

—

163

C₂×C₄²

C₂²×D₁₉

yes

characteristic

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#100

—

168

C₂²⋊C₈

—

169

C₄×C₈

—

170

#95

—

171

#95

—

172

#95

—

173

#95

—

174

#95

—

175

C₁₉

#8771

yes

characteristic, complemented, Sylow

176

C₂⁴

(C₂×D₁₉)⋊C₄

yes

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

188

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

189

C₂²×C₄

C₂×D₇₆

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

191

M₁₆

—

192

M₁₆

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

152

—

202

C₄²

—

203

C₄²

—

152

—

204

C₄²

#64543

yes

—

205

C₄²

#64543

yes

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

212

D₄

—

213

D₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

#10597323

yes

characteristic

230

C₂×C₄

#10597323

yes

characteristic

231

C₂×C₄

#10597332

yes

—

232

C₂×C₄

#10597378

yes

characteristic

233

C₂×C₄

#10597381

yes

—

234

C₂×C₄

#10597388

yes

characteristic

235

C₂×C₄

#10597396

yes

—

236

C₈

—

237

C₈

—

152

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926405

yes

characteristic

246

C₂²

#11926538

yes

characteristic

247

C₂²

#11926543

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

152

—

254

C₄

—

152

—

255

C₄

#11926865

yes

—

256

C₄

#11926882

yes

—

257

C₂

—

258

C₂

—

259

C₂

—

260

C₂

#14563727

yes

characteristic

261

C₂

#14563740

yes

characteristic

262

C₂

#14563744

yes

characteristic

	subgroup	G/H
center	C₂²	#11926405
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1800	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1800	D₁₉
hypocenter	C₁₉	#8771
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#11926405

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1800

C₂

socle

C₂²×C₁₉

#381

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

N	H ≅ G/N	type
3. #14561536	C₂	semidirect
4. #14561495	C₂	semidirect
175. C₁₉	#8771	semidirect

H ≅ G/N

type

3. #14561536

C₂

semidirect

4. #14561495

C₂

semidirect

175. C₁₉

#8771

semidirect

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

subgroup	index
#14566608	2
#14561956	2
#14561536	2
#14561495	2
C₁₉×#1800	2
#8771	19

subgroup

index

C₁₉×#1800

Subgroups — #18076137

Conjugacy classes of subgroups

Complements

Maximal subgroups