Group #18080139 — subgroups

Subgroups — #18080139

Order 4864.

504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572702	C₂	1	1	yes	maximal, characteristic
2	#14562370	C₂	1	1	yes	maximal, characteristic
3	#14562320	C₂	1	2	yes	maximal, complemented
4	#14561525	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic
6	#11926622	—	2	2	no	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926568	C₂²	1	2	yes	—
10	#11926511	—	2	2	no	—
11	#11926293	—	2	1	no	—
12	#11926290	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	#11926288	—	2	1	no	—
15	C₂×C₁₉×#137	—	2	2	no	—
16	C₁₉×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₉×#497	C₄	1	4	yes	—
19	C₁₉×#494	—	2	1	no	—
20	C₁₉×#492	—	2	1	no	—
21	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×#41×C₁₉	D₄	1	2	yes	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₁₉×#137	—	4	4	no	—
25	C₁₉×#137	—	4	4	no	—
26	C₂×Q₁₆×C₁₉	—	2	4	no	—
27	C₂×SD₁₆×C₁₉	—	2	4	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	2	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
32	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
33	C₁₉×#127	D₄	1	1	yes	characteristic
34	C₁₉×#124	C₂×C₄	1	2	yes	—
35	C₁₉×#121	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×#64520	—	2	2	no	—
40	C₂×#64520	—	2	2	no	—
41	C₂²×C₁₉⋊C₈	—	2	2	no	—
42	C₁₉×#97	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
49	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
50	C₄×C₁₉⋊C₈	—	2	2	no	—
51	#41×C₁₉	—	4	2	no	—
52	#41×C₁₉	—	4	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	4	2	no	—
55	C₂×Q₈×C₁₉	—	4	2	no	—
56	C₂×Q₈×C₁₉	—	4	1	no	—
57	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	2	yes	—
65	Q₁₆×C₁₉	—	4	8	no	—
66	SD₁₆×C₁₉	—	4	8	no	—
67	M₁₆×C₁₉	—	2	2	no	—
68	M₁₆×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	2	4	no	—
72	C₄⋊C₄×C₁₉	—	4	2	no	—
73	C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂×D₄	1	2	yes	—
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	#64520	—	8	2	no	—
78	#64520	—	8	2	no	—
79	C₂×C₁₉⋊C₈	—	2	2	no	—
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	8	2	no	—
83	#9435	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	2	no	—
85	C₂³×C₁₉	#123	1	1	yes	characteristic
86	Q₈×C₁₉	—	4	2	no	—
87	Q₈×C₁₉	—	4	4	no	—
88	Q₈×C₁₉	—	8	1	no	—
89	Q₈×C₁₉	—	8	1	no	—
90	D₄×C₁₉	—	4	2	no	—
91	D₄×C₁₉	—	4	2	no	—
92	D₄×C₁₉	—	4	2	no	—
93	D₄×C₁₉	—	8	2	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	8	2	no	—
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	2	yes	—
107	C₈×C₁₉	—	2	4	no	—
108	C₁₉⋊C₈	—	4	2	no	—
109	C₁₉⋊C₈	—	4	2	no	—
110	C₁₉⋊C₈	—	8	2	no	—
111	#3152	D₁₉	1	1	yes	characteristic
112	#2979	—	19	1	no	—
113	#1560	—	19	1	no	—
114	#1549	—	19	2	no	—
115	#1299	—	19	2	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	2	no	—
118	C₂²×C₁₉	—	4	2	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	#386	1	1	yes	characteristic
121	C₄×C₁₉	—	2	1	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	—	8	2	no	—
125	C₄×C₁₉	#453	1	1	yes	characteristic
126	C₄×C₁₉	#453	1	1	yes	characteristic
127	C₄×C₁₉	#471	1	2	yes	—
128	C₄×C₁₉	#473	1	2	yes	—
129	C₂×#137	—	2	2	no	—
130	#532	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
132	#497	Dic₁₉	1	4	yes	—
133	#494	—	2	1	no	—
134	#492	—	2	1	no	—
135	#436	—	38	2	no	—
136	C₈×D₄	—	38	2	no	—
137	#431	—	19	2	no	—
138	#423	—	19	2	no	—
139	#408	—	38	2	no	—
140	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
141	#333	—	38	1	no	—
142	#332	—	38	2	no	—
143	#332	—	38	2	no	—
144	#331	—	38	1	no	—
145	C₂×C₁₉	—	4	1	no	—
146	C₂×C₁₉	—	8	2	no	—
147	C₂×C₁₉	#1887	1	1	yes	characteristic
148	C₂×C₁₉	#1908	1	2	yes	—
149	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
150	C₂²×Q₈	—	2	1	no	—
151	#137	—	4	4	no	—
152	#137	—	4	4	no	—
153	C₂×Q₁₆	—	2	4	no	—
154	C₂×SD₁₆	—	2	4	no	—
155	C₂×M₁₆	—	2	1	no	—
156	C₂×M₁₆	—	38	2	no	—
157	C₂×M₁₆	—	38	2	no	—
158	C₂²×C₈	—	38	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
162	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
163	#127	C₂²⋊D₁₉	1	1	yes	characteristic
164	#124	C₂×Dic₁₉	1	2	yes	—
165	#121	—	2	2	no	—
166	C₄×D₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
169	C₄⋊C₈	—	19	2	no	—
170	C₄⋊C₈	—	19	2	no	—
171	C₄⋊C₈	—	38	2	no	—
172	C₄⋊C₈	—	38	2	no	—
173	C₂²⋊C₈	—	38	4	no	—
174	C₂²⋊C₈	—	38	2	no	—
175	#97	C₂×Dic₁₉	1	2	yes	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	—	38	2	no	—
178	C₁₉	#9435	1	1	yes	characteristic, complemented, Sylow
179	#41	—	4	2	no	—
180	#41	—	4	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	#64543	1	2	yes	—
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	Q₁₆	—	4	8	no	—
194	SD₁₆	—	4	8	no	—
195	M₁₆	—	2	2	no	—
196	M₁₆	—	2	2	no	—
197	M₁₆	—	152	2	no	—
198	M₁₆	—	152	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	38	2	no	—
201	C₂×C₈	—	38	2	no	—
202	C₂×C₈	—	76	2	no	—
203	C₂×C₈	—	152	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	4	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	2	4	no	—
208	C₄²	D₄×D₁₉	1	2	yes	—
209	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
210	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
211	C₂³	—	2	2	no	—
212	C₂³	#10597381	1	1	yes	characteristic
213	Q₈	—	4	2	no	—
214	Q₈	—	4	4	no	—
215	Q₈	—	8	1	no	—
216	Q₈	—	8	1	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	D₄	—	8	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
231	C₂×C₄	#10597383	1	1	yes	characteristic
232	C₂×C₄	#10597385	1	2	yes	—
233	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
234	C₈	—	2	4	no	—
235	C₈	—	76	2	no	—
236	C₈	—	76	2	no	—
237	C₈	—	152	2	no	—
238	C₂²	—	2	2	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	#11926424	1	1	yes	characteristic
243	C₄	—	2	2	no	—
244	C₄	—	2	1	no	—
245	C₄	—	4	2	no	—
246	C₄	—	8	2	no	—
247	C₄	#11926711	1	1	yes	characteristic
248	C₄	#11926711	1	1	yes	characteristic
249	C₄	#11926809	1	2	yes	—
250	C₄	#11926817	1	2	yes	—
251	C₂	—	4	1	no	—
252	C₂	—	8	2	no	—
253	C₂	#14564034	1	1	yes	characteristic
254	C₂	#14564152	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572702

C₂

yes

maximal, characteristic

#14562370

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, complemented

#14561525

C₂

yes

maximal, complemented

C₁₉×#3152

C₂

yes

maximal, characteristic

#11926622

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

—

—

—

—

—

C₂×C₁₉×#137

—

C₁₉×#532

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#497

C₄

yes

—

C₁₉×#494

—

C₁₉×#492

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#97

C₂×C₄

yes

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9435

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₁₉

C₄×D₄

yes

—

105

C₂×C₄×C₁₉

#120

yes

characteristic

106

C₂×C₄×C₁₉

#121

yes

—

107

C₈×C₁₉

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

C₁₉⋊C₈

—

111

#3152

D₁₉

yes

characteristic

112

#2979

—

113

#1560

—

114

#1549

—

115

#1299

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

#386

yes

characteristic

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

#453

yes

characteristic

126

C₄×C₁₉

#453

yes

characteristic

127

C₄×C₁₉

#471

yes

—

128

C₄×C₁₉

#473

yes

—

129

C₂×#137

—

130

#532

C₂×D₁₉

yes

characteristic

131

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

132

#497

Dic₁₉

yes

—

133

#494

—

134

#492

—

135

#436

—

136

C₈×D₄

—

137

#431

—

138

#423

—

139

#408

—

140

C₄×M₁₆

C₂×D₁₉

yes

characteristic

141

#333

—

142

#332

—

143

#332

—

144

#331

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1887

yes

characteristic

148

C₂×C₁₉

#1908

yes

—

149

C₂×#41

C₂²⋊D₁₉

yes

—

150

C₂²×Q₈

—

151

#137

—

152

#137

—

153

C₂×Q₁₆

—

154

C₂×SD₁₆

—

155

C₂×M₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

C₂×Dic₁₉

yes

—

162

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

163

#127

C₂²⋊D₁₉

yes

characteristic

164

#124

C₂×Dic₁₉

yes

—

165

#121

—

166

C₄×D₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄²

C₂²×D₁₉

yes

characteristic

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₂²⋊C₈

—

174

C₂²⋊C₈

—

175

#97

C₂×Dic₁₉

yes

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₁₉

#9435

yes

characteristic, complemented, Sylow

179

#41

—

180

#41

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

C₂²⋊Dic₁₉

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

#64543

yes

—

192

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

Q₁₆

—

194

SD₁₆

—

195

M₁₆

—

196

M₁₆

—

197

M₁₆

—

152

—

198

M₁₆

—

152

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

152

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

D₄×D₁₉

yes

—

209

C₄²

C₂²×Dic₁₉

yes

characteristic

210

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

211

C₂³

—

212

C₂³

#10597381

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

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

—

230

C₂×C₄

D₄×Dic₁₉

yes

—

231

C₂×C₄

#10597383

yes

characteristic

232

C₂×C₄

#10597385

yes

—

233

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

—

152

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

#11926424

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#11926711

yes

characteristic

248

C₄

#11926711

yes

characteristic

249

C₄

#11926809

yes

—

250

C₄

#11926817

yes

—

251

C₂

—

252

C₂

—

253

C₂

#14564034

yes

characteristic

254

C₂

#14564152

yes

—

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3152	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3152	D₁₉
hypocenter	C₁₉	#9435
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

subgroup

G/H

center

C₂²

#11926424

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3152

C₂

socle

C₂²×C₁₉

#386

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

N	H ≅ G/N	type
3. #14562320	C₂	semidirect
4. #14561525	C₂	semidirect
178. C₁₉	#9435	semidirect

H ≅ G/N

type

3. #14562320

C₂

semidirect

4. #14561525

C₂

semidirect

178. C₁₉

#9435

semidirect

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

subgroup	index
#14572702	2
#14562370	2
#14562320	2
#14561525	2
C₁₉×#3152	2
#9435	19

subgroup

index

C₁₉×#3152

Subgroups — #18080139

Conjugacy classes of subgroups

Complements

Maximal subgroups