Group #18075554 — subgroups

Subgroups — #18075554

Order 4864.

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

normal subgroups only

This group has 404 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	#14572348	C₂	1	1	yes	maximal, characteristic
2	#14562391	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562368	C₂	1	2	yes	maximal
4	C₁₉⋊#1309	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	C₄	1	2	yes	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	—	2	1	no	—
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	—	2	1	no	—
12	#11926568	C₂²	1	2	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926510	C₄	1	2	yes	—
15	#11926295	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926292	—	2	2	no	—
18	#11926287	—	2	2	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#334	—	2	1	no	—
22	C₁₉×#334	—	2	1	no	—
23	C₂×#64541	C₂×C₄	1	2	yes	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597376	—	2	1	no	—
29	#10597376	—	2	1	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂×#64520	C₂×C₄	1	2	yes	—
32	#10597347	—	4	4	no	—
33	C₂×#64515	—	2	2	no	—
34	C₂×C₈×D₁₉	—	2	2	no	—
35	#10597321	Q₈	1	2	yes	—
36	#10597320	D₄	1	1	yes	characteristic
37	C₄×D₇₆	—	2	1	no	—
38	C₄×D₇₆	—	2	1	no	—
39	#10597315	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	(C₂×D₁₉)⋊C₈	—	2	2	no	—
47	(C₂×D₁₉)⋊C₈	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉	—	2	2	no	—
56	#64541	—	4	2	no	—
57	#64541	—	4	2	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	—	2	1	no	—
60	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
61	C₂×C₄×D₁₉	—	2	2	no	—
62	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
63	M₁₆×C₁₉	—	8	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
75	(C₂×D₁₉)⋊C₄	—	2	2	no	—
76	(C₂×D₁₉)⋊C₄	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	1	no	—
78	C₄⋊Dic₁₉	—	2	1	no	—
79	#64520	—	4	2	no	—
80	#64520	—	8	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#64515	—	4	4	no	—
84	C₈×D₁₉	—	4	4	no	—
85	#8636	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	#117	1	1	yes	characteristic
87	C₂²×D₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂²⋊D₁₉	—	4	4	no	—
99	C₂×Dic₁₉	—	2	2	no	—
100	D₇₆	—	4	2	no	—
101	D₇₆	—	4	2	no	—
102	D₇₆	—	4	2	no	—
103	C₄×D₁₉	—	4	2	no	—
104	C₄×D₁₉	—	4	2	no	—
105	Dic₃₈	—	4	2	no	—
106	C₈×C₁₉	—	2	1	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	8	2	no	—
110	C₈×C₁₉	#100	1	2	yes	—
111	C₁₉⋊C₈	—	4	2	no	—
112	C₁₉⋊C₈	—	8	2	no	—
113	#2931	—	19	1	no	—
114	#1566	—	19	1	no	—
115	#1566	D₁₉	1	1	yes	characteristic, complemented
116	#1560	—	19	2	no	—
117	#1309	—	19	2	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#380	1	1	yes	characteristic
122	C₂×D₁₉	—	4	2	no	—
123	C₂×D₁₉	—	4	2	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
129	C₄×C₁₉	#413	1	1	yes	characteristic
130	C₄×C₁₉	#471	1	2	yes	—
131	C₄×C₁₉	#471	1	2	yes	—
132	Dic₁₉	—	4	2	no	—
133	C₂×#131	—	19	2	no	—
134	#532	—	19	1	no	—
135	#436	—	38	1	no	—
136	#436	—	38	1	no	—
137	C₈×D₄	—	38	1	no	—
138	C₈×D₄	—	38	1	no	—
139	#423	—	19	1	no	—
140	#423	—	19	2	no	—
141	#423	C₂×D₁₉	1	2	yes	—
142	#408	—	19	2	no	—
143	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
144	#334	—	2	1	no	—
145	#334	—	2	1	no	—
146	#334	—	38	1	no	—
147	#334	—	38	1	no	—
148	#333	—	38	2	no	—
149	#331	—	38	2	no	—
150	C₂×C₁₉	—	4	1	no	—
151	C₂×C₁₉	#1800	1	1	yes	characteristic
152	C₂×C₁₉	#1815	1	1	yes	characteristic
153	C₂×C₁₉	#1815	1	1	yes	characteristic
154	D₁₉	—	8	2	no	—
155	C₂×#41	—	19	2	no	—
156	#131	—	76	4	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	19	2	no	—
159	C₂×M₁₆	—	38	2	no	—
160	C₂×M₁₆	—	38	2	no	—
161	C₂²×C₈	—	38	2	no	—
162	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
163	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
164	C₄⋊Q₈	—	19	1	no	—
165	#127	—	19	1	no	—
166	#124	—	19	2	no	—
167	#121	—	38	1	no	—
168	#121	—	38	1	no	—
169	C₄×D₄	—	38	1	no	—
170	C₄×D₄	—	38	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	2	2	no	—
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₄⋊C₈	—	38	2	no	—
176	C₄⋊C₈	—	38	2	no	—
177	C₄⋊C₈	—	38	1	no	—
178	C₂²⋊C₈	—	38	2	no	—
179	C₂²⋊C₈	—	38	2	no	—
180	C₄×C₈	D₇₆	1	1	yes	characteristic
181	C₄×C₈	D₇₆	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	C₁₉	#8636	1	1	yes	characteristic, complemented, Sylow
185	#41	—	76	2	no	—
186	#41	—	76	2	no	—
187	C₂×Q₈	—	19	2	no	—
188	C₂×D₄	—	19	2	no	—
189	C₂×D₄	—	38	2	no	—
190	C₂×D₄	—	38	1	no	—
191	C₂×D₄	—	38	1	no	—
192	C₂²×C₄	—	38	2	no	—
193	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
194	C₂²×C₄	#64543	1	1	yes	characteristic
195	C₂²×C₄	#64545	1	1	yes	characteristic
196	M₁₆	—	8	2	no	—
197	M₁₆	—	76	4	no	—
198	M₁₆	—	76	2	no	—
199	M₁₆	—	152	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	76	4	no	—
205	C₂×C₈	—	76	2	no	—
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₄⋊C₄	—	38	1	no	—
211	C₄⋊C₄	—	38	1	no	—
212	C₂²⋊C₄	—	38	2	no	—
213	C₂²⋊C₄	—	38	2	no	—
214	C₄²	C₂×D₇₆	1	1	yes	characteristic
215	C₄²	D₄×D₁₉	1	1	yes	characteristic
216	C₄²	Q₈×D₁₉	1	1	yes	characteristic
217	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂³	—	38	2	no	—
219	C₂³	#10597338	1	1	yes	characteristic
220	Q₈	—	76	2	no	—
221	D₄	—	76	2	no	—
222	D₄	—	76	4	no	—
223	D₄	—	76	2	no	—
224	D₄	—	76	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	76	2	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
233	C₂×C₄	#10597341	1	1	yes	characteristic
234	C₂×C₄	#10597343	1	1	yes	characteristic
235	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
236	C₂×C₄	#10597384	1	1	yes	characteristic
237	C₂×C₄	#10597392	1	1	yes	characteristic
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	2	1	no	—
241	C₈	—	8	2	no	—
242	C₈	—	76	2	no	—
243	C₈	—	152	2	no	—
244	C₈	#10597280	1	2	yes	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	76	2	no	—
249	C₂²	—	76	2	no	—
250	C₂²	—	76	2	no	—
251	C₂²	#11926401	1	1	yes	characteristic
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	2	1	no	—
255	C₄	—	76	2	no	—
256	C₄	C₂×#10597280	1	1	yes	characteristic
257	C₄	#11926526	1	1	yes	characteristic
258	C₄	#11926804	1	2	yes	—
259	C₄	#11926808	1	2	yes	—
260	C₂	—	4	1	no	—
261	C₂	—	152	2	no	—
262	C₂	#14563624	1	1	yes	characteristic
263	C₂	#14563691	1	1	yes	characteristic
264	C₂	#14563695	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572348

C₂

yes

maximal, characteristic

#14562391

C₂

yes

maximal, characteristic, complemented

#14562368

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal, complemented

C₁₉×#1566

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

C₄

yes

—

#11927094

C₂²

yes

characteristic

#11926623

—

#11926623

—

C₈×D₇₆

—

C₈×D₇₆

—

#11926568

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926510

C₄

yes

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#334

—

C₁₉×#334

—

C₂×#64541

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄

yes

—

#10597347

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

Q₈

yes

—

#10597320

D₄

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

100

D₇₆

—

101

D₇₆

—

102

D₇₆

—

103

C₄×D₁₉

—

104

C₄×D₁₉

—

105

Dic₃₈

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

#100

yes

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

#2931

—

114

#1566

—

115

#1566

D₁₉

yes

characteristic, complemented

116

#1560

—

117

#1309

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#380

yes

characteristic

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

C₂×#100

yes

characteristic

129

C₄×C₁₉

#413

yes

characteristic

130

C₄×C₁₉

#471

yes

—

131

C₄×C₁₉

#471

yes

—

132

Dic₁₉

—

133

C₂×#131

—

134

#532

—

135

#436

—

136

#436

—

137

C₈×D₄

—

138

C₈×D₄

—

139

#423

—

140

#423

—

141

#423

C₂×D₁₉

yes

—

142

#408

—

143

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

144

#334

—

145

#334

—

146

#334

—

147

#334

—

148

#333

—

149

#331

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#1800

yes

characteristic

152

C₂×C₁₉

#1815

yes

characteristic

153

C₂×C₁₉

#1815

yes

characteristic

154

D₁₉

—

155

C₂×#41

—

156

#131

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂²×C₈

—

162

C₂²×C₈

C₄×D₁₉

yes

characteristic

163

C₂²×C₈

C₄×D₁₉

yes

characteristic

164

C₄⋊Q₈

—

165

#127

—

166

#124

—

167

#121

—

168

#121

—

169

C₄×D₄

—

170

C₄×D₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₂²⋊C₈

—

179

C₂²⋊C₈

—

180

C₄×C₈

D₇₆

yes

characteristic

181

C₄×C₈

D₇₆

yes

characteristic

182

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

183

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

184

C₁₉

#8636

yes

characteristic, complemented, Sylow

185

#41

—

186

#41

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

194

C₂²×C₄

#64543

yes

characteristic

195

C₂²×C₄

#64545

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

152

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

C₂×D₇₆

yes

characteristic

215

C₄²

D₄×D₁₉

yes

characteristic

216

C₄²

Q₈×D₁₉

yes

characteristic

217

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

218

C₂³

—

219

C₂³

#10597338

yes

characteristic

220

Q₈

—

221

D₄

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

233

C₂×C₄

#10597341

yes

characteristic

234

C₂×C₄

#10597343

yes

characteristic

235

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

236

C₂×C₄

#10597384

yes

characteristic

237

C₂×C₄

#10597392

yes

characteristic

238

C₈

—

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

152

—

244

C₈

#10597280

yes

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

#11926401

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

C₂×#10597280

yes

characteristic

257

C₄

#11926526

yes

characteristic

258

C₄

#11926804

yes

—

259

C₄

#11926808

yes

—

260

C₂

—

261

C₂

—

152

—

262

C₂

#14563624

yes

characteristic

263

C₂

#14563691

yes

characteristic

264

C₂

#14563695

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1566	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1566	D₁₉
hypocenter	C₁₉	#8636
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1566

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

N	H ≅ G/N	type
2. #14562391	C₂	semidirect
4. C₁₉⋊#1309	C₂	semidirect
5. C₁₉×#1566	C₂	semidirect
115. #1566	D₁₉	semidirect
184. C₁₉	#8636	semidirect

H ≅ G/N

type

2. #14562391

C₂

semidirect

4. C₁₉⋊#1309

C₂

semidirect

5. C₁₉×#1566

C₂

semidirect

115. #1566

D₁₉

semidirect

184. C₁₉

#8636

semidirect

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

subgroup	index
#14572348	2
#14562391	2
#14562368	2
C₁₉⋊#1309	2
C₁₉×#1566	2
#8636	19

subgroup

index

#14572348

#14562391

#14562368

C₁₉⋊#1309

C₁₉×#1566

#8636

Subgroups — #18075554

Conjugacy classes of subgroups

Complements

Maximal subgroups