Group #14564954 — subgroups

Subgroups — #14564954

Order 2432.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#64516	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597267	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597266	C₂	1	1	yes	maximal, characteristic
5	#11926449	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926445	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
14	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×#64516	—	2	2	no	—
18	C₂×#64516	—	2	2	no	—
19	C₂×#64516	—	2	2	no	—
20	C₁₉⋊#95	—	2	1	no	—
21	C₁₉⋊#95	—	2	1	no	—
22	Dic₁₉⋊C₈	—	2	2	no	—
23	#10597267	—	2	2	no	—
24	#10597266	—	2	2	no	—
25	C₂³×D₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	—	2	1	no	—
27	C₂²×C₄×C₁₉	—	2	1	no	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
31	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
32	C₂×D₇₆	—	2	1	no	—
33	C₂×D₇₆	—	2	1	no	—
34	C₂×D₇₆	—	2	1	no	—
35	C₂×D₇₆	—	2	1	no	—
36	C₂×D₇₆	—	2	1	no	—
37	C₂×D₇₆	D₄	1	2	yes	—
38	C₂×Dic₃₈	—	2	1	no	—
39	C₂×Dic₃₈	—	2	1	no	—
40	C₂×Dic₃₈	—	2	1	no	—
41	C₂×Dic₃₈	—	2	1	no	—
42	C₂×Dic₃₈	—	2	1	no	—
43	C₂×Dic₃₈	D₄	1	2	yes	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	D₄	1	2	yes	—
47	C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₄⋊C₄×C₁₉	—	2	1	no	—
51	(C₂×D₁₉)⋊C₄	—	4	2	no	—
52	(C₂×D₁₉)⋊C₄	—	4	2	no	—
53	C₄×Dic₁₉	—	2	1	no	—
54	C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₁₉⋊C₈	—	2	1	no	—
56	C₂×C₁₉⋊C₈	—	2	1	no	—
57	C₂×C₁₉⋊C₈	—	2	1	no	—
58	#64516	—	2	8	no	—
59	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×D₁₉	—	2	2	no	—
61	C₂²×D₁₉	—	4	1	no	—
62	C₂²×D₁₉	—	4	1	no	—
63	C₂²×D₁₉	—	4	1	no	—
64	C₂²×D₁₉	—	4	1	no	—
65	C₂²×D₁₉	—	4	1	no	—
66	C₂²×D₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	—	4	1	no	—
69	C₂×C₄×C₁₉	—	4	1	no	—
70	C₂×C₄×C₁₉	—	4	1	no	—
71	C₂×C₄×C₁₉	—	4	1	no	—
72	C₂×C₄×C₁₉	—	4	1	no	—
73	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂×Dic₁₉	—	2	1	no	—
80	C₂×Dic₁₉	—	2	1	no	—
81	C₂×Dic₁₉	—	2	1	no	—
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	2	1	no	—
84	C₂×Dic₁₉	—	2	1	no	—
85	C₂×Dic₁₉	—	4	1	no	—
86	C₂×Dic₁₉	—	4	1	no	—
87	C₂×Dic₁₉	SD₁₆	1	2	yes	complemented
88	D₇₆	—	2	2	no	—
89	D₇₆	—	2	2	no	—
90	D₇₆	—	4	1	no	—
91	D₇₆	—	4	1	no	—
92	Dic₃₈	—	2	2	no	—
93	Dic₃₈	—	2	2	no	—
94	Dic₃₈	—	4	1	no	—
95	Dic₃₈	—	4	1	no	—
96	C₈×C₁₉	—	2	2	no	—
97	C₁₉⋊C₈	—	4	1	no	—
98	#2055	—	19	1	no	maximal, Sylow
99	C₂²×C₁₉	#121	1	1	yes	characteristic
100	C₂²×C₁₉	#121	1	1	yes	characteristic
101	C₂²×C₁₉	#121	1	1	yes	characteristic
102	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
103	C₂²×C₁₉	#135	1	1	yes	characteristic
104	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₂²×C₁₉	#137	1	1	yes	characteristic
106	C₂×D₁₉	—	4	2	no	—
107	C₂×D₁₉	—	4	2	no	—
108	C₂×D₁₉	—	4	2	no	—
109	C₂×D₁₉	—	8	1	no	—
110	C₂×D₁₉	—	8	1	no	—
111	C₂×D₁₉	—	8	1	no	—
112	C₂×D₁₉	—	8	1	no	—
113	C₄×C₁₉	—	8	1	no	—
114	C₄×C₁₉	—	8	1	no	—
115	C₄×C₁₉	#120	1	1	yes	characteristic
116	C₄×C₁₉	#123	1	1	yes	characteristic
117	C₄×C₁₉	#123	1	1	yes	characteristic
118	C₄×C₁₉	#124	1	1	yes	characteristic
119	Dic₁₉	—	2	2	no	—
120	Dic₁₉	—	4	2	no	—
121	Dic₁₉	—	4	1	no	—
122	C₂²×SD₁₆	—	19	1	no	—
123	C₂×C₄⋊C₈	—	19	1	no	—
124	C₂×#103	—	19	1	no	—
125	C₂×#102	—	19	1	no	—
126	#391	—	19	1	no	—
127	#390	—	19	1	no	—
128	#340	D₁₉	1	1	yes	characteristic, complemented
129	C₂×C₁₉	#394	1	1	yes	characteristic
130	C₂×C₁₉	#460	1	1	yes	characteristic
131	C₂×C₁₉	#461	1	1	yes	characteristic
132	C₂×C₁₉	#463	1	1	yes	characteristic
133	C₂×C₁₉	#464	1	1	yes	characteristic
134	C₂×C₁₉	#465	1	1	yes	characteristic
135	C₂×C₁₉	#468	1	1	yes	characteristic
136	D₁₉	—	8	2	no	—
137	C₂²×Q₈	—	19	1	no	—
138	C₂²×D₄	—	19	1	no	—
139	C₂×SD₁₆	—	38	2	no	—
140	C₂×SD₁₆	—	38	2	no	—
141	C₂×SD₁₆	—	38	2	no	—
142	C₂²×C₈	—	19	1	no	—
143	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
146	C₂×C₂²⋊C₄	—	38	1	no	—
147	C₂×C₂²⋊C₄	—	38	1	no	—
148	C₂×C₄²	—	19	1	no	—
149	C₄⋊C₈	—	38	2	no	—
150	#103	—	38	2	no	—
151	#102	—	38	2	no	—
152	#95	—	38	1	no	—
153	#95	—	38	1	no	—
154	C₁₉	#2055	1	1	yes	characteristic, complemented, Sylow
155	C₂⁴	—	38	1	no	—
156	C₂×Q₈	—	19	2	no	—
157	C₂×Q₈	—	38	1	no	—
158	C₂×Q₈	—	38	1	no	—
159	C₂×Q₈	—	38	1	no	—
160	C₂×Q₈	—	38	1	no	—
161	C₂×Q₈	—	38	1	no	—
162	C₂×D₄	—	19	2	no	—
163	C₂×D₄	—	38	1	no	—
164	C₂×D₄	—	38	1	no	—
165	C₂×D₄	—	38	1	no	—
166	C₂×D₄	—	38	1	no	—
167	C₂×D₄	—	38	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	19	1	no	—
171	C₂²×C₄	—	19	1	no	—
172	C₂²×C₄	—	38	1	no	—
173	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
174	SD₁₆	—	38	8	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	2	1	no	—
177	C₂×C₈	—	38	1	no	—
178	C₂×C₈	—	38	1	no	—
179	C₂×C₈	—	38	1	no	—
180	C₂×C₈	D₇₆	1	2	yes	—
181	C₄⋊C₄	—	2	1	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₂²⋊C₄	—	76	2	no	—
186	C₂²⋊C₄	—	76	2	no	—
187	C₄²	—	38	1	no	—
188	C₄²	—	38	1	no	—
189	C₂³	—	38	2	no	—
190	C₂³	—	76	1	no	—
191	C₂³	—	76	1	no	—
192	C₂³	—	76	1	no	—
193	C₂³	—	76	1	no	—
194	C₂³	—	76	1	no	—
195	C₂³	—	76	1	no	—
196	C₂³	D₄×D₁₉	1	1	yes	characteristic
197	Q₈	—	38	2	no	—
198	Q₈	—	38	2	no	—
199	Q₈	—	76	1	no	—
200	Q₈	—	76	1	no	—
201	D₄	—	38	2	no	—
202	D₄	—	38	2	no	—
203	D₄	—	76	1	no	—
204	D₄	—	76	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	19	2	no	—
212	C₂×C₄	—	38	1	no	—
213	C₂×C₄	—	38	1	no	—
214	C₂×C₄	—	38	2	no	—
215	C₂×C₄	—	38	1	no	—
216	C₂×C₄	—	38	1	no	—
217	C₂×C₄	—	38	1	no	—
218	C₂×C₄	—	76	1	no	—
219	C₂×C₄	—	76	1	no	—
220	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
221	C₂×C₄	#64541	1	1	yes	characteristic
222	C₂×C₄	#64541	1	1	yes	characteristic
223	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂×C₄	#64545	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	76	1	no	—
228	C₂²	—	76	2	no	—
229	C₂²	—	76	2	no	—
230	C₂²	—	76	2	no	—
231	C₂²	—	152	1	no	—
232	C₂²	—	152	1	no	—
233	C₂²	—	152	1	no	—
234	C₂²	—	152	1	no	—
235	C₂²	#10597330	1	1	yes	characteristic
236	C₂²	#10597330	1	1	yes	characteristic
237	C₂²	#10597341	1	1	yes	characteristic
238	C₂²	#10597357	1	1	yes	characteristic
239	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
240	C₂²	#10597362	1	1	yes	characteristic
241	C₂²	#10597364	1	1	yes	characteristic
242	C₄	—	8	1	no	—
243	C₄	—	8	1	no	—
244	C₄	—	38	2	no	—
245	C₄	—	76	1	no	—
246	C₄	—	76	2	no	—
247	C₄	#10597321	1	1	yes	characteristic
248	C₄	#10597328	1	1	yes	characteristic
249	C₄	#10597340	1	1	yes	characteristic
250	C₄	#10597340	1	1	yes	characteristic
251	C₂	—	152	2	no	—
252	C₂	#11926462	1	1	yes	characteristic
253	C₂	#11926743	1	1	yes	characteristic
254	C₂	#11926748	1	1	yes	characteristic
255	C₂	#11926758	1	1	yes	characteristic
256	C₂	#11926769	1	1	yes	characteristic
257	C₂	#11926774	1	1	yes	characteristic
258	C₂	#11926791	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64516

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#10597267

C₂

yes

maximal, characteristic, complemented

C₂×#10597266

C₂

yes

maximal, characteristic

#11926449

C₂

yes

maximal, characteristic, complemented

#11926445

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉⋊#95

—

C₁₉⋊#95

—

Dic₁₉⋊C₈

—

#10597267

—

#10597266

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

complemented

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

100

C₂²×C₁₉

#121

yes

characteristic

101

C₂²×C₁₉

#121

yes

characteristic

102

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

103

C₂²×C₁₉

#135

yes

characteristic

104

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

105

C₂²×C₁₉

#137

yes

characteristic

106

C₂×D₁₉

—

107

C₂×D₁₉

—

108

C₂×D₁₉

—

109

C₂×D₁₉

—

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₂×D₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#120

yes

characteristic

116

C₄×C₁₉

#123

yes

characteristic

117

C₄×C₁₉

#123

yes

characteristic

118

C₄×C₁₉

#124

yes

characteristic

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

C₂²×SD₁₆

—

123

C₂×C₄⋊C₈

—

124

C₂×#103

—

125

C₂×#102

—

126

#391

—

127

#390

—

128

#340

D₁₉

yes

characteristic, complemented

129

C₂×C₁₉

#394

yes

characteristic

130

C₂×C₁₉

#460

yes

characteristic

131

C₂×C₁₉

#461

yes

characteristic

132

C₂×C₁₉

#463

yes

characteristic

133

C₂×C₁₉

#464

yes

characteristic

134

C₂×C₁₉

#465

yes

characteristic

135

C₂×C₁₉

#468

yes

characteristic

136

D₁₉

—

137

C₂²×Q₈

—

138

C₂²×D₄

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

C₂×D₁₉

yes

characteristic

144

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

145

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

146

C₂×C₂²⋊C₄

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₄²

—

149

C₄⋊C₈

—

150

#103

—

151

#102

—

152

#95

—

153

#95

—

154

C₁₉

#2055

yes

characteristic, complemented, Sylow

155

C₂⁴

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂²×D₁₉

yes

characteristic

174

SD₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

D₇₆

yes

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

D₄×D₁₉

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

D₄

—

202

D₄

—

203

D₄

—

204

D₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

C₂×D₇₆

yes

characteristic

221

C₂×C₄

#64541

yes

characteristic

222

C₂×C₄

#64541

yes

characteristic

223

C₂×C₄

D₄×D₁₉

yes

characteristic

224

C₂×C₄

D₄×D₁₉

yes

characteristic

225

C₂×C₄

#64545

yes

characteristic

226

C₈

—

227

C₈

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

152

—

232

C₂²

—

152

—

233

C₂²

—

152

—

234

C₂²

—

152

—

235

C₂²

#10597330

yes

characteristic

236

C₂²

#10597330

yes

characteristic

237

C₂²

#10597341

yes

characteristic

238

C₂²

#10597357

yes

characteristic

239

C₂²

SD₁₆×D₁₉

yes

characteristic

240

C₂²

#10597362

yes

characteristic

241

C₂²

#10597364

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#10597321

yes

characteristic

248

C₄

#10597328

yes

characteristic

249

C₄

#10597340

yes

characteristic

250

C₄

#10597340

yes

characteristic

251

C₂

—

152

—

252

C₂

#11926462

yes

characteristic

253

C₂

#11926743

yes

characteristic

254

C₂

#11926748

yes

characteristic

255

C₂

#11926758

yes

characteristic

256

C₂

#11926769

yes

characteristic

257

C₂

#11926774

yes

characteristic

258

C₂

#11926791

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₇₆	C₂²
hypercenter	#340	D₁₉
hypocenter	C₁₉	#2055
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
2. C₂×Dic₁₉⋊C₈	C₂	semidirect
3. C₂×#10597267	C₂	semidirect
5. #11926449	C₂	semidirect
7. C₁₉×#340	C₂	semidirect
87. C₂×Dic₁₉	SD₁₆	semidirect
128. #340	D₁₉	semidirect
154. C₁₉	#2055	semidirect

H ≅ G/N

type

2. C₂×Dic₁₉⋊C₈

C₂

semidirect

3. C₂×#10597267

C₂

semidirect

5. #11926449

C₂

semidirect

7. C₁₉×#340

C₂

semidirect

87. C₂×Dic₁₉

SD₁₆

semidirect

128. #340

D₁₉

semidirect

154. C₁₉

#2055

semidirect

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

subgroup	index
C₂²×#64516	2
C₂×Dic₁₉⋊C₈	2
C₂×#10597267	2
C₂×#10597266	2
#11926449	2
#11926445	2
C₁₉×#340	2
#2055	19

subgroup

index

C₂²×#64516

C₂×Dic₁₉⋊C₈

C₁₉×#340

Subgroups — #14564954

Conjugacy classes of subgroups

Complements

Maximal subgroups