Group #18075041 — subgroups

Subgroups — #18075041

Order 4864.

818 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14563718	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563712	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562164	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#540	C₂	1	1	yes	maximal, characteristic
5	#11926508	C₂²	1	2	yes	—
6	#11926407	C₂²	1	2	yes	—
7	#11926313	—	2	2	no	—
8	#11926311	—	2	2	no	—
9	#11926278	—	2	8	no	—
10	C₁₉×#540	—	2	8	no	—
11	C₂×C₁₉×#127	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₉×#123	—	2	2	no	—
14	C₂×C₁₉×#121	—	2	2	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	complemented
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₉	—	2	2	no	—
19	C₂²×D₄×C₁₉	—	2	2	no	—
20	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₁₉×#127	—	2	4	no	—
24	C₁₉×#125	—	2	4	no	—
25	C₁₉×#123	—	2	16	no	—
26	C₁₉×#121	—	2	16	no	—
27	C₁₉×#121	—	2	4	no	—
28	C₁₉×#121	D₄	1	8	yes	—
29	C₄×D₄×C₁₉	—	2	4	no	—
30	C₄×D₄×C₁₉	—	2	4	no	—
31	C₁₉×#117	—	2	4	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
41	C₂×#64520	—	2	2	no	—
42	C₁₉⋊#95	—	2	4	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₂⁴×C₁₉	—	2	2	no	—
45	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×D₄×C₁₉	—	2	8	no	—
47	C₂×D₄×C₁₉	—	2	8	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	—	4	4	no	—
50	C₂×D₄×C₁₉	—	8	4	no	—
51	C₂×D₄×C₁₉	—	8	4	no	—
52	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	8	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	8	4	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
62	C₂²×Dic₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	2	8	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
67	C₂²⋊C₄×C₁₉	—	2	8	no	—
68	C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂²⋊C₄×C₁₉	—	2	8	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₂²⋊Dic₁₉	—	4	4	no	—
73	#64520	—	4	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	#8518	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	—	2	2	no	—
77	C₂³×C₁₉	—	2	4	no	—
78	C₂³×C₁₉	—	4	2	no	—
79	C₂³×C₁₉	—	4	4	no	—
80	C₂³×C₁₉	—	4	4	no	—
81	C₂³×C₁₉	—	4	4	no	—
82	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂³×C₁₉	#120	1	2	yes	—
84	D₄×C₁₉	—	4	4	no	—
85	D₄×C₁₉	—	4	4	no	—
86	D₄×C₁₉	—	8	8	no	—
87	D₄×C₁₉	—	8	8	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	4	4	no	—
94	C₂×C₄×C₁₉	—	4	4	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	8	8	no	—
98	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
99	C₂×C₄×C₁₉	#120	1	2	yes	—
100	C₂×Dic₁₉	—	8	2	no	—
101	C₂×Dic₁₉	—	8	4	no	—
102	C₁₉⋊C₈	—	8	2	no	—
103	C₂×#540	D₁₉	1	1	yes	characteristic
104	#1822	—	19	1	no	—
105	#1820	—	19	1	no	—
106	#1510	—	19	4	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	4	no	—
109	C₂²×C₁₉	—	2	2	no	—
110	C₂²×C₁₉	—	4	4	no	—
111	C₂²×C₁₉	—	4	4	no	—
112	C₂²×C₁₉	—	4	4	no	—
113	C₂²×C₁₉	—	8	2	no	—
114	C₂²×C₁₉	—	8	8	no	—
115	C₂²×C₁₉	#379	1	1	yes	characteristic
116	C₂²×C₁₉	#410	1	2	yes	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	4	4	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	4	2	no	—
122	Dic₁₉	—	16	2	no	—
123	#540	—	2	8	no	—
124	C₂×#127	Dic₁₉	1	1	yes	characteristic, complemented
125	C₂×#125	Dic₁₉	1	1	yes	characteristic, complemented
126	C₂×#123	—	2	2	no	—
127	C₂×#121	—	2	2	no	—
128	C₂×#121	C₂×D₁₉	1	2	yes	—
129	C₂×C₄×D₄	Dic₁₉	1	2	yes	complemented
130	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
131	#407	—	19	2	no	—
132	#381	—	19	2	no	—
133	#343	—	38	2	no	—
134	#342	—	38	2	no	—
135	#327	—	38	8	no	—
136	C₂×C₁₉	—	2	2	no	—
137	C₂×C₁₉	—	4	2	no	—
138	C₂×C₁₉	—	8	4	no	—
139	C₂×C₁₉	#1782	1	1	yes	characteristic
140	C₂×C₁₉	#1795	1	2	yes	—
141	C₂²×D₄	—	2	2	no	—
142	C₂²×D₄	—	2	2	no	—
143	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
144	C₂³×C₄	—	2	2	no	—
145	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
146	C₂×M₁₆	—	38	2	no	—
147	#127	—	2	4	no	—
148	#125	—	2	4	no	—
149	#123	—	2	16	no	—
150	#121	—	2	16	no	—
151	#121	—	2	4	no	—
152	#121	C₂²⋊D₁₉	1	8	yes	—
153	C₄×D₄	—	2	4	no	—
154	C₄×D₄	—	2	4	no	—
155	#117	—	2	4	no	—
156	C₂×C₄⋊C₄	—	2	2	no	—
157	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
158	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
159	C₂×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₂²⋊C₄	—	38	2	no	—
162	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
163	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
164	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂²⋊C₈	—	38	4	no	—
166	#95	—	38	4	no	—
167	C₁₉	#8518	1	1	yes	characteristic, complemented, Sylow
168	C₂⁴	—	2	2	no	—
169	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂×D₄	—	2	8	no	—
171	C₂×D₄	—	2	8	no	—
172	C₂×D₄	—	2	2	no	—
173	C₂×D₄	—	4	4	no	—
174	C₂×D₄	—	8	4	no	—
175	C₂×D₄	—	8	4	no	—
176	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	8	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	8	4	no	—
181	C₂²×C₄	—	76	2	no	—
182	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
183	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
184	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
187	M₁₆	—	76	4	no	—
188	C₂×C₈	—	76	2	no	—
189	C₄⋊C₄	—	2	8	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
193	C₂²⋊C₄	—	2	8	no	—
194	C₂²⋊C₄	—	2	4	no	—
195	C₂²⋊C₄	—	2	8	no	—
196	C₂²⋊C₄	—	76	4	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	2	2	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	4	no	—
201	C₂³	—	4	2	no	—
202	C₂³	—	4	4	no	—
203	C₂³	—	4	4	no	—
204	C₂³	—	4	4	no	—
205	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
206	C₂³	#10597399	1	2	yes	—
207	D₄	—	4	4	no	—
208	D₄	—	4	4	no	—
209	D₄	—	8	8	no	—
210	D₄	—	8	8	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	8	no	—
221	C₂×C₄	—	152	2	no	—
222	C₂×C₄	—	152	4	no	—
223	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
224	C₂×C₄	#10597399	1	2	yes	—
225	C₈	—	152	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	2	4	no	—
228	C₂²	—	2	2	no	—
229	C₂²	—	4	4	no	—
230	C₂²	—	4	4	no	—
231	C₂²	—	4	4	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	8	no	—
234	C₂²	#11926400	1	1	yes	characteristic
235	C₂²	#11926518	1	2	yes	—
236	C₄	—	2	2	no	—
237	C₄	—	2	2	no	—
238	C₄	—	4	4	no	—
239	C₄	—	4	2	no	—
240	C₄	—	4	2	no	—
241	C₄	—	304	2	no	—
242	C₂	—	2	2	no	—
243	C₂	—	4	2	no	—
244	C₂	—	8	4	no	—
245	C₂	#14563553	1	1	yes	characteristic
246	C₂	#14563605	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563718

C₂

yes

maximal, characteristic, complemented

#14563712

C₂

yes

maximal, characteristic, complemented

#14562164

C₂

yes

maximal, complemented

C₂×C₁₉×#540

C₂

yes

maximal, characteristic

#11926508

C₂²

yes

—

#11926407

C₂²

yes

—

#11926313

—

#11926311

—

#11926278

—

C₁₉×#540

—

C₂×C₁₉×#127

C₄

yes

characteristic, complemented

C₂×C₁₉×#125

C₄

yes

characteristic, complemented

C₂×C₁₉×#123

—

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₂²

yes

—

C₂×C₄×D₄×C₁₉

C₄

yes

complemented

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#127

—

C₁₉×#125

—

C₁₉×#123

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×#64520

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂×D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

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

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#8518

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#120

yes

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

#120

yes

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₁₉⋊C₈

—

103

C₂×#540

D₁₉

yes

characteristic

104

#1822

—

105

#1820

—

106

#1510

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

#379

yes

characteristic

116

C₂²×C₁₉

#410

yes

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

Dic₁₉

—

123

#540

—

124

C₂×#127

Dic₁₉

yes

characteristic, complemented

125

C₂×#125

Dic₁₉

yes

characteristic, complemented

126

C₂×#123

—

127

C₂×#121

—

128

C₂×#121

C₂×D₁₉

yes

—

129

C₂×C₄×D₄

Dic₁₉

yes

complemented

130

C₂×#117

C₂×D₁₉

yes

characteristic

131

#407

—

132

#381

—

133

#343

—

134

#342

—

135

#327

—

136

C₂×C₁₉

—

137

C₂×C₁₉

—

138

C₂×C₁₉

—

139

C₂×C₁₉

#1782

yes

characteristic

140

C₂×C₁₉

#1795

yes

—

141

C₂²×D₄

—

142

C₂²×D₄

—

143

C₂²×D₄

C₂×Dic₁₉

yes

—

144

C₂³×C₄

—

145

C₂³×C₄

C₂²×D₁₉

yes

characteristic

146

C₂×M₁₆

—

147

#127

—

148

#125

—

149

#123

—

150

#121

—

151

#121

—

152

#121

C₂²⋊D₁₉

yes

—

153

C₄×D₄

—

154

C₄×D₄

—

155

#117

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

158

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

159

C₂×C₂²⋊C₄

—

160

C₂×C₂²⋊C₄

—

161

C₂×C₂²⋊C₄

—

162

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

163

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

164

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

165

C₂²⋊C₈

—

166

#95

—

167

C₁₉

#8518

yes

characteristic, complemented, Sylow

168

C₂⁴

—

169

C₂⁴

C₂×C₂²⋊D₁₉

yes

characteristic

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

C₂²⋊Dic₁₉

yes

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

183

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

184

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

185

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

187

M₁₆

—

188

C₂×C₈

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

206

C₂³

#10597399

yes

—

207

D₄

—

208

D₄

—

209

D₄

—

210

D₄

—

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

—

221

C₂×C₄

—

152

—

222

C₂×C₄

—

152

—

223

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

224

C₂×C₄

#10597399

yes

—

225

C₈

—

152

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

#11926400

yes

characteristic

235

C₂²

#11926518

yes

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

304

—

242

C₂

—

243

C₂

—

244

C₂

—

245

C₂

#14563553

yes

characteristic

246

C₂

#14563605

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#540	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#540	D₁₉
hypocenter	C₁₉	#8518
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#540

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#540

C₂

socle

C₂²×C₁₉

#379

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#540

N	H ≅ G/N	type
1. #14563718	C₂	semidirect
2. #14563712	C₂	semidirect
3. #14562164	C₂	semidirect
11. C₂×C₁₉×#127	C₄	semidirect
12. C₂×C₁₉×#125	C₄	semidirect
16. C₂×C₄×D₄×C₁₉	C₄	semidirect
124. C₂×#127	Dic₁₉	semidirect
125. C₂×#125	Dic₁₉	semidirect
129. C₂×C₄×D₄	Dic₁₉	semidirect
167. C₁₉	#8518	semidirect

H ≅ G/N

type

1. #14563718

C₂

semidirect

2. #14563712

C₂

semidirect

3. #14562164

C₂

semidirect

11. C₂×C₁₉×#127

C₄

semidirect

12. C₂×C₁₉×#125

C₄

semidirect

16. C₂×C₄×D₄×C₁₉

C₄

semidirect

124. C₂×#127

Dic₁₉

semidirect

125. C₂×#125

Dic₁₉

semidirect

129. C₂×C₄×D₄

Dic₁₉

semidirect

167. C₁₉

#8518

semidirect

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

subgroup	index
#14563718	2
#14563712	2
#14562164	2
C₂×C₁₉×#540	2
#8518	19

subgroup

index

C₂×C₁₉×#540

Subgroups — #18075041

Conjugacy classes of subgroups

Complements

Maximal subgroups