Group #18075361 — subgroups

Subgroups — #18075361

Order 4864.

644 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14563752	C₂	1	2	yes	maximal, complemented
2	C₂×#11926288	C₂	1	2	yes	maximal
3	#14561518	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
6	#11926299	—	2	2	no	—
7	#11926299	—	2	2	no	—
8	#11926288	—	2	4	no	—
9	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₉	—	2	2	no	—
11	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
12	C₁₉×#390	—	2	2	no	—
13	C₁₉×#390	C₄	1	2	yes	—
14	C₁₉×#384	C₂²	1	1	yes	characteristic
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₁₉	—	2	2	no	—
17	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₉	—	2	2	no	—
19	C₁₉×#127	—	2	2	no	—
20	C₁₉×#127	D₄	1	2	yes	—
21	C₁₉×#127	Q₈	1	2	yes	—
22	C₄×D₄×C₁₉	—	4	8	no	—
23	C₄×D₄×C₁₉	—	4	4	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	2	yes	—
31	C₂×C₄²×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	—	2	4	no	—
34	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
35	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₂⁴×C₁₉	—	2	2	no	—
37	C₂×D₄×C₁₉	—	2	2	no	—
38	C₂×D₄×C₁₉	—	2	4	no	—
39	C₂×D₄×C₁₉	—	2	4	no	—
40	C₂×D₄×C₁₉	—	4	2	no	—
41	C₂×D₄×C₁₉	—	4	2	no	—
42	C₂×D₄×C₁₉	—	4	4	no	—
43	C₂×D₄×C₁₉	—	4	4	no	—
44	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	4	8	no	—
47	C₂²×C₄×C₁₉	—	4	4	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₄⋊C₄×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	4	4	no	—
55	C₂²⋊C₄×C₁₉	—	4	4	no	—
56	C₂²⋊C₄×C₁₉	—	4	8	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	—	2	4	no	—
59	C₄²×C₁₉	—	2	4	no	—
60	C₄²×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₂×C₁₉⋊C₈	—	4	4	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	#8592	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	—	2	4	no	—
69	C₂³×C₁₉	—	4	2	no	—
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	—	4	4	no	—
72	C₂³×C₁₉	—	4	4	no	—
73	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	D₄×C₁₉	—	4	4	no	—
75	D₄×C₁₉	—	4	4	no	—
76	D₄×C₁₉	—	4	8	no	—
77	D₄×C₁₉	—	4	8	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	8	8	no	—
89	C₂×C₄×C₁₉	#100	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	2	yes	—
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
94	C₂×C₄×C₁₉	#135	1	4	yes	—
95	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
96	C₁₉⋊C₈	—	8	4	no	—
97	C₄×#127	D₁₉	1	1	yes	characteristic
98	#1831	—	19	2	no	—
99	C₂×#331	—	19	2	no	—
100	#1296	—	19	2	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	—	4	8	no	—
103	C₂²×C₁₉	—	8	2	no	—
104	C₂²×C₁₉	—	8	4	no	—
105	C₂²×C₁₉	—	8	2	no	—
106	C₂²×C₁₉	#380	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
108	C₂²×C₁₉	#413	1	1	yes	characteristic
109	C₂²×C₁₉	#416	1	2	yes	—
110	C₂²×C₁₉	#418	1	2	yes	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	4	1	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	—	8	2	no	—
117	C₄×C₁₉	#463	1	4	yes	—
118	C₄×C₁₉	#478	1	4	yes	—
119	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
120	C₂×C₄×D₄	—	2	2	no	—
121	C₂×C₄×D₄	Dic₁₉	1	2	yes	—
122	C₂×C₄⋊C₈	—	19	4	no	—
123	#390	—	2	2	no	—
124	#390	Dic₁₉	1	2	yes	—
125	#384	C₂×D₁₉	1	1	yes	characteristic
126	C₄³	C₂×D₁₉	1	1	yes	characteristic
127	#336	—	38	2	no	—
128	#336	—	38	2	no	—
129	#331	—	38	4	no	—
130	C₂×C₁₉	—	8	4	no	—
131	C₂×C₁₉	#1543	1	1	yes	characteristic
132	C₂×C₁₉	#1553	1	2	yes	—
133	C₂×C₁₉	#1555	1	1	yes	characteristic
134	C₂×C₁₉	#1800	1	1	yes	characteristic
135	C₂×C₁₉	#1804	1	2	yes	—
136	C₂²×D₄	—	2	2	no	—
137	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
138	C₂³×C₄	—	2	2	no	—
139	C₂²×C₈	—	38	4	no	—
140	#127	—	2	2	no	—
141	#127	Dic₃₈	1	2	yes	—
142	#127	D₇₆	1	2	yes	—
143	C₄×D₄	—	4	8	no	—
144	C₄×D₄	—	4	4	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
147	C₂×C₂²⋊C₄	—	2	4	no	—
148	C₂×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
150	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	C₄⋊C₈	—	38	4	no	—
155	C₄⋊C₈	—	38	4	no	—
156	C₁₉	#8592	1	1	yes	characteristic, complemented, Sylow
157	C₂⁴	—	2	2	no	—
158	C₂×D₄	—	2	4	no	—
159	C₂×D₄	—	2	4	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	—	4	2	no	—
162	C₂×D₄	—	4	2	no	—
163	C₂×D₄	—	4	4	no	—
164	C₂×D₄	—	4	4	no	—
165	C₂×D₄	C₄⋊Dic₁₉	1	4	yes	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	4	8	no	—
168	C₂²×C₄	—	4	4	no	—
169	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
170	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
171	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
172	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
174	C₂×C₈	—	76	4	no	—
175	C₂×C₈	—	76	4	no	—
176	C₂×C₈	—	76	4	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	4	no	—
179	C₂²⋊C₄	—	4	8	no	—
180	C₂²⋊C₄	—	4	4	no	—
181	C₄²	—	2	4	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	4	1	no	—
185	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
186	C₄²	C₂×D₇₆	1	1	yes	characteristic
187	C₄²	#64541	1	2	yes	—
188	C₂³	—	2	4	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	4	4	no	—
191	C₂³	—	4	4	no	—
192	C₂³	—	4	2	no	—
193	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
194	D₄	—	4	4	no	—
195	D₄	—	4	4	no	—
196	D₄	—	4	8	no	—
197	D₄	—	4	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	8	8	no	—
209	C₂×C₄	#10597290	1	2	yes	—
210	C₂×C₄	#10597370	1	2	yes	—
211	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
212	C₂×C₄	#10597372	1	1	yes	characteristic
213	C₂×C₄	#10597376	1	2	yes	—
214	C₂×C₄	#10597378	1	4	yes	—
215	C₂×C₄	#10597396	1	4	yes	—
216	C₈	—	152	4	no	—
217	C₂²	—	4	4	no	—
218	C₂²	—	4	8	no	—
219	C₂²	—	8	4	no	—
220	C₂²	—	8	2	no	—
221	C₂²	—	8	2	no	—
222	C₂²	#11926404	1	1	yes	characteristic
223	C₂²	C₂×#10597290	1	1	yes	characteristic
224	C₂²	#11926528	1	1	yes	characteristic
225	C₂²	#11926540	1	2	yes	—
226	C₂²	#11926549	1	2	yes	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	2	no	—
230	C₄	—	4	2	no	—
231	C₄	—	4	1	no	—
232	C₄	—	8	2	no	—
233	C₄	#11926759	1	4	yes	—
234	C₄	#11926844	1	4	yes	—
235	C₂	—	8	4	no	—
236	C₂	#14562297	1	1	yes	characteristic
237	C₂	#14562340	1	2	yes	—
238	C₂	#14562349	1	1	yes	characteristic
239	C₂	#14563627	1	1	yes	characteristic
240	C₂	#14563645	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal, complemented

C₂×#11926288

C₂

yes

maximal

#14561518

C₂

yes

maximal, complemented

C₄×C₁₉×#127

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926299

—

#11926288

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

—

C₂×C₄×D₄×C₁₉

C₄

yes

—

C₁₉×#390

—

C₁₉×#390

C₄

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₁₉×#127

Q₈

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8592

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₁₉⋊C₈

—

C₄×#127

D₁₉

yes

characteristic

#1831

—

C₂×#331

—

100

#1296

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

#380

yes

characteristic

107

C₂²×C₁₉

C₂×#100

yes

characteristic

108

C₂²×C₁₉

#413

yes

characteristic

109

C₂²×C₁₉

#416

yes

—

110

C₂²×C₁₉

#418

yes

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#463

yes

—

118

C₄×C₁₉

#478

yes

—

119

C₂×#127

C₂×D₁₉

yes

characteristic

120

C₂×C₄×D₄

—

121

C₂×C₄×D₄

Dic₁₉

yes

—

122

C₂×C₄⋊C₈

—

123

#390

—

124

#390

Dic₁₉

yes

—

125

#384

C₂×D₁₉

yes

characteristic

126

C₄³

C₂×D₁₉

yes

characteristic

127

#336

—

128

#336

—

129

#331

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1543

yes

characteristic

132

C₂×C₁₉

#1553

yes

—

133

C₂×C₁₉

#1555

yes

characteristic

134

C₂×C₁₉

#1800

yes

characteristic

135

C₂×C₁₉

#1804

yes

—

136

C₂²×D₄

—

137

C₂²×D₄

C₂×Dic₁₉

yes

—

138

C₂³×C₄

—

139

C₂²×C₈

—

140

#127

—

141

#127

Dic₃₈

yes

—

142

#127

D₇₆

yes

—

143

C₄×D₄

—

144

C₄×D₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

150

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

151

C₂×C₄²

C₂²⋊D₁₉

yes

—

152

C₂×C₄²

C₂²⋊D₁₉

yes

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₁₉

#8592

yes

characteristic, complemented, Sylow

157

C₂⁴

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

C₄⋊Dic₁₉

yes

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

170

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

171

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

172

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₂²⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

C₂×Dic₃₈

yes

characteristic

186

C₄²

C₂×D₇₆

yes

characteristic

187

C₄²

#64541

yes

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

194

D₄

—

195

D₄

—

196

D₄

—

197

D₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

#10597290

yes

—

210

C₂×C₄

#10597370

yes

—

211

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

212

C₂×C₄

#10597372

yes

characteristic

213

C₂×C₄

#10597376

yes

—

214

C₂×C₄

#10597378

yes

—

215

C₂×C₄

#10597396

yes

—

216

C₈

—

152

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

#11926404

yes

characteristic

223

C₂²

C₂×#10597290

yes

characteristic

224

C₂²

#11926528

yes

characteristic

225

C₂²

#11926540

yes

—

226

C₂²

#11926549

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

#11926759

yes

—

234

C₄

#11926844

yes

—

235

C₂

—

236

C₂

#14562297

yes

characteristic

237

C₂

#14562340

yes

—

238

C₂

#14562349

yes

characteristic

239

C₂

#14563627

yes

characteristic

240

C₂

#14563645

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#127	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#127	D₁₉
hypocenter	C₁₉	#8592
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#127

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

N	H ≅ G/N	type
1. #14563752	C₂	semidirect
3. #14561518	C₂	semidirect
156. C₁₉	#8592	semidirect

H ≅ G/N

type

1. #14563752

C₂

semidirect

3. #14561518

C₂

semidirect

156. C₁₉

#8592

semidirect

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

subgroup	index
#14563752	2
C₂×#11926288	2
#14561518	2
C₄×C₁₉×#127	2
#8592	19

subgroup

index

C₄×C₁₉×#127

Subgroups — #18075361

Conjugacy classes of subgroups

Complements

Maximal subgroups