Group #18087273 — subgroups

Subgroups — #18087273

Order 4864.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563763	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563635	C₂	1	2	yes	maximal
3	#14561519	C₂	1	2	yes	maximal, complemented
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×#10597289	—	2	2	no	—
8	#11926414	C₂²	1	2	yes	—
9	#11926307	—	2	2	no	—
10	#11926306	—	2	2	no	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₈×C₁₉	D₄	1	2	yes	—
19	C₄×D₄×C₁₉	—	2	2	no	—
20	C₄×D₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₂²⋊C₈	—	4	4	no	—
30	C₄×C₈×C₁₉	—	2	2	no	—
31	#10597289	—	4	4	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₂⁴×C₁₉	—	2	1	no	—
35	C₂×D₄×C₁₉	—	2	2	no	—
36	C₂×D₄×C₁₉	—	2	1	no	—
37	C₂×D₄×C₁₉	—	2	2	no	—
38	C₂×D₄×C₁₉	D₈	1	2	yes	—
39	C₂²×C₄×C₁₉	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	4	1	no	—
41	C₂²×C₄×C₁₉	—	4	1	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	—	4	2	no	—
44	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂²×Dic₁₉	—	4	2	no	—
48	C₂×C₈×C₁₉	—	2	2	no	—
49	C₂×C₈×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	4	1	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂²⋊C₄×C₁₉	—	4	2	no	—
55	C₄²×C₁₉	#41	1	2	yes	—
56	C₄²×C₁₉	#41	1	2	yes	—
57	C₄⋊Dic₁₉	—	4	2	no	—
58	C₄⋊Dic₁₉	—	4	2	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	8	2	no	—
62	C₂×C₁₉⋊C₈	—	4	2	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	#10621	—	19	1	no	maximal, Sylow
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	—	4	1	no	—
68	C₂³×C₁₉	—	4	2	no	—
69	C₂³×C₁₉	—	4	1	no	—
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	#121	1	1	yes	characteristic
72	D₄×C₁₉	—	2	4	no	—
73	D₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	—	8	1	no	—
79	C₂×C₄×C₁₉	—	8	1	no	—
80	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#123	1	2	yes	—
82	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#126	1	2	yes	—
84	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#135	1	2	yes	—
86	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
87	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×C₄×C₁₉	#137	1	2	yes	—
89	C₂×Dic₁₉	—	8	2	no	—
90	C₂×Dic₁₉	—	8	2	no	—
91	C₂×Dic₁₉	—	8	2	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₈×C₁₉	—	8	1	no	—
94	C₁₉⋊C₈	—	8	2	no	—
95	#1954	D₁₉	1	1	yes	characteristic
96	#1834	—	19	1	no	—
97	#1802	—	19	2	no	—
98	#1296	—	19	2	no	—
99	#1277	—	19	1	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	—	8	1	no	—
103	C₂²×C₁₉	—	8	1	no	—
104	C₂²×C₁₉	—	8	2	no	—
105	C₂²×C₁₉	#397	1	1	yes	characteristic
106	C₂²×C₁₉	#463	1	2	yes	—
107	C₂²×C₁₉	#466	1	1	yes	characteristic
108	C₂²×C₁₉	#470	1	1	yes	characteristic
109	C₂²×C₁₉	#471	1	2	yes	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	8	1	no	—
112	C₄×C₁₉	#480	1	2	yes	—
113	C₄×C₁₉	#482	1	2	yes	—
114	C₄×C₁₉	#485	1	2	yes	—
115	C₄×C₁₉	#488	1	1	yes	characteristic
116	C₄×C₁₉	#490	1	1	yes	characteristic
117	Dic₁₉	—	16	2	no	—
118	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄⋊C₈	—	19	2	no	—
120	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
121	C₂×#102	—	38	2	no	—
122	C₂×C₂²⋊C₈	—	2	2	no	—
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#384	—	19	2	no	—
125	#340	—	38	2	no	—
126	#340	—	38	2	no	—
127	C₂×C₁₉	—	8	2	no	—
128	C₂×C₁₉	#1681	1	2	yes	—
129	C₂×C₁₉	#1703	1	2	yes	—
130	C₂×C₁₉	#2073	1	1	yes	characteristic
131	C₂×C₁₉	#2075	1	1	yes	characteristic
132	C₂×C₁₉	#2079	1	1	yes	characteristic
133	C₂²×D₄	D₇₆	1	1	yes	characteristic
134	C₂³×C₄	—	2	1	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	—	38	2	no	—
137	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
138	C₄×D₄	—	2	2	no	—
139	C₄×D₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	38	2	no	—
141	C₂×C₄⋊C₄	—	38	2	no	—
142	C₂×C₄⋊C₄	—	38	2	no	—
143	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	38	2	no	—
149	#102	—	76	4	no	—
150	C₂²⋊C₈	—	4	4	no	—
151	C₄×C₈	—	2	2	no	—
152	C₁₉	#10621	1	1	yes	characteristic, complemented, Sylow
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	D₁₅₂	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	76	2	no	—
164	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂²×C₄	#64541	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	—	76	2	no	—
174	C₂×C₈	—	76	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	76	2	no	—
177	C₄⋊C₄	—	76	2	no	—
178	C₄⋊C₄	—	76	2	no	—
179	C₄⋊C₄	—	76	2	no	—
180	C₄⋊C₄	—	152	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#64543	1	2	yes	—
183	C₄²	#64543	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#10597376	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	152	2	no	—
199	C₂×C₄	—	152	2	no	—
200	C₂×C₄	—	152	2	no	—
201	C₂×C₄	#10597325	1	2	yes	—
202	C₂×C₄	#10597332	1	2	yes	—
203	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
204	C₂×C₄	#10597350	1	1	yes	characteristic
205	C₂×C₄	#10597355	1	2	yes	—
206	C₂×C₄	#10597378	1	2	yes	—
207	C₂×C₄	#10597381	1	1	yes	characteristic
208	C₂×C₄	#10597382	1	1	yes	characteristic
209	C₂×C₄	#10597396	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	152	2	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	8	2	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	1	no	—
218	C₂²	#11926469	1	1	yes	characteristic
219	C₂²	#11926759	1	2	yes	—
220	C₂²	#11926780	1	1	yes	characteristic
221	C₂²	#11926802	1	1	yes	characteristic
222	C₂²	#11926807	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	304	2	no	—
226	C₄	#11926858	1	2	yes	—
227	C₄	#11926865	1	2	yes	—
228	C₄	#11926886	1	2	yes	—
229	C₄	#11926898	1	1	yes	characteristic
230	C₄	#11926908	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#14563072	1	2	yes	—
233	C₂	#14563210	1	2	yes	—
234	C₂	#14565048	1	1	yes	characteristic
235	C₂	#14565058	1	1	yes	characteristic
236	C₂	#14565080	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563763

C₂

yes

maximal, characteristic, complemented

#14563635

C₂

yes

maximal

#14561519

C₂

yes

maximal, complemented

#14561470

C₂

yes

maximal, characteristic, complemented

C₁₉×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597289

—

#11926414

C₂²

yes

—

#11926307

—

#11926306

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597289

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10621

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

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

#123

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#126

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#135

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1954

D₁₉

yes

—

—

—

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#397

yes

characteristic

106

C₂²×C₁₉

#463

yes

—

107

C₂²×C₁₉

#466

yes

characteristic

108

C₂²×C₁₉

#470

yes

characteristic

109

C₂²×C₁₉

#471

yes

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#480

yes

—

113

C₄×C₁₉

#482

yes

—

114

C₄×C₁₉

#485

yes

—

115

C₄×C₁₉

#488

yes

characteristic

116

C₄×C₁₉

#490

yes

characteristic

117

Dic₁₉

—

118

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

119

C₂×C₄⋊C₈

—

120

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

121

C₂×#102

—

122

C₂×C₂²⋊C₈

—

123

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

124

#384

—

125

#340

—

126

#340

—

127

C₂×C₁₉

—

128

C₂×C₁₉

#1681

yes

—

129

C₂×C₁₉

#1703

yes

—

130

C₂×C₁₉

#2073

yes

characteristic

131

C₂×C₁₉

#2075

yes

characteristic

132

C₂×C₁₉

#2079

yes

characteristic

133

C₂²×D₄

D₇₆

yes

characteristic

134

C₂³×C₄

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

C₂²⋊D₁₉

yes

—

138

C₄×D₄

—

139

C₄×D₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

D₇₆

yes

characteristic

144

C₂×C₂²⋊C₄

—

145

C₂×C₄²

C₂²×D₁₉

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

#102

—

150

C₂²⋊C₈

—

151

C₄×C₈

—

152

C₁₉

#10621

yes

characteristic, complemented, Sylow

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

D₁₅₂

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₇₆

yes

characteristic

165

C₂²×C₄

#64541

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

152

—

181

C₂²⋊C₄

—

182

C₄²

#64543

yes

—

183

C₄²

#64543

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#10597376

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

152

—

199

C₂×C₄

—

152

—

200

C₂×C₄

—

152

—

201

C₂×C₄

#10597325

yes

—

202

C₂×C₄

#10597332

yes

—

203

C₂×C₄

C₂×D₁₅₂

yes

characteristic

204

C₂×C₄

#10597350

yes

characteristic

205

C₂×C₄

#10597355

yes

—

206

C₂×C₄

#10597378

yes

—

207

C₂×C₄

#10597381

yes

characteristic

208

C₂×C₄

#10597382

yes

characteristic

209

C₂×C₄

#10597396

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

152

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#11926469

yes

characteristic

219

C₂²

#11926759

yes

—

220

C₂²

#11926780

yes

characteristic

221

C₂²

#11926802

yes

characteristic

222

C₂²

#11926807

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

304

—

226

C₄

#11926858

yes

—

227

C₄

#11926865

yes

—

228

C₄

#11926886

yes

—

229

C₄

#11926898

yes

characteristic

230

C₄

#11926908

yes

characteristic

231

C₂

—

232

C₂

#14563072

yes

—

233

C₂

#14563210

yes

—

234

C₂

#14565048

yes

characteristic

235

C₂

#14565058

yes

characteristic

236

C₂

#14565080

yes

characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1954	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₄×C₁₉	D₄
hypercenter	#1954	D₁₉
hypocenter	C₁₉	#10621
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#10597376

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1954

C₂

socle

C₂³×C₁₉

#121

prime radical

C₂²×D₄×C₁₉

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #14563763	C₂	semidirect
3. #14561519	C₂	semidirect
4. #14561470	C₂	semidirect
152. C₁₉	#10621	semidirect

H ≅ G/N

type

1. #14563763

C₂

semidirect

3. #14561519

C₂

semidirect

4. #14561470

C₂

semidirect

152. C₁₉

#10621

semidirect

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

subgroup	index
#14563763	2
#14563635	2
#14561519	2
#14561470	2
C₁₉×#1954	2
#10621	19

subgroup

index

C₁₉×#1954

Subgroups — #18087273

Conjugacy classes of subgroups

Complements

Maximal subgroups