Group #18083527 — subgroups

Subgroups — #18083527

Order 4864.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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	#14573639	C₂	1	2	yes	maximal
2	#14564433	C₂	1	1	yes	maximal, characteristic
3	#14562038	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
7	#11926872	—	2	2	no	—
8	#11926831	—	2	2	no	—
9	#11926746	—	2	2	no	—
10	#11926694	—	2	2	no	—
11	C₄×#64527	—	2	4	no	—
12	#11926597	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
15	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₁₉×#501	—	2	2	no	—
18	C₁₉×#501	—	2	2	no	—
19	C₁₉×#427	—	2	2	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂²×D₇₆	D₄	1	1	yes	characteristic
22	C₂²×C₄×D₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	D₄	1	2	yes	—
24	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₁₉×#125	—	2	2	no	—
27	C₁₉×C₂²⋊Q₈	—	2	2	no	—
28	C₁₉×C₂²⋊Q₈	—	2	2	no	—
29	C₄×Q₈×C₁₉	—	2	2	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₁₉×#117	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×#64527	—	2	4	no	—
34	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
36	C₂²×C₁₉⋊C₈	—	2	1	no	—
37	C₄×D₇₆	—	2	2	no	—
38	C₄×D₇₆	—	2	2	no	—
39	C₁₉×#107	—	2	2	no	—
40	C₁₉×#107	—	2	2	no	—
41	C₁₉×#106	—	2	4	no	—
42	C₁₉×#97	—	2	2	no	—
43	#10597292	—	2	4	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	(C₂×D₁₉)⋊C₈	—	4	4	no	—
46	#10597266	—	2	4	no	—
47	#10597265	—	2	4	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
51	C₂³×D₁₉	—	2	1	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂²×Dic₁₉	—	2	1	no	—
58	C₂×D₇₆	—	2	2	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×C₄×D₁₉	—	4	1	no	—
61	C₂×C₄×D₁₉	—	4	1	no	—
62	C₂×C₄×D₁₉	—	4	2	no	—
63	C₂×C₄×D₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	—	4	2	no	—
73	C₂²⋊C₄×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	2	no	—
75	C₄²×C₁₉	C₂×D₄	1	2	yes	—
76	C₄²×C₁₉	C₂×D₄	1	2	yes	—
77	#64527	—	4	8	no	—
78	(C₂×D₁₉)⋊C₄	—	4	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₂×C₁₉⋊C₈	—	2	4	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#10036	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	#121	1	1	yes	characteristic
85	C₂²×D₁₉	—	2	2	no	—
86	C₂²×D₁₉	—	4	1	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	C₂²×D₁₉	—	4	1	no	—
89	C₂²×D₁₉	—	4	2	no	—
90	Q₈×C₁₉	—	4	4	no	—
91	Q₈×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	#120	1	2	yes	—
97	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#121	1	2	yes	—
99	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
101	C₂×C₄×C₁₉	#137	1	2	yes	—
102	C₂×Dic₁₉	—	4	1	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	D₇₆	—	2	4	no	—
105	D₇₆	—	4	2	no	—
106	C₄×D₁₉	—	8	2	no	—
107	C₄×D₁₉	—	8	1	no	—
108	C₄×D₁₉	—	8	1	no	—
109	C₈×C₁₉	—	2	4	no	—
110	C₁₉⋊C₈	—	4	4	no	—
111	C₁₉⋊C₈	—	8	1	no	—
112	#3162	D₁₉	1	1	yes	characteristic, complemented
113	#3101	—	19	2	no	—
114	#1955	—	19	1	no	—
115	#1481	—	19	2	no	—
116	#1275	—	19	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	#392	1	1	yes	characteristic
120	C₂²×C₁₉	#461	1	2	yes	—
121	C₂×D₁₉	—	4	4	no	—
122	C₂×D₁₉	—	4	2	no	—
123	C₂×D₁₉	—	8	2	no	—
124	C₂×D₁₉	—	8	1	no	—
125	C₂×D₁₉	—	8	1	no	—
126	C₄×C₁₉	—	2	2	no	—
127	C₄×C₁₉	—	2	2	no	—
128	C₄×C₁₉	—	8	2	no	—
129	C₄×C₁₉	—	8	2	no	—
130	C₄×C₁₉	#448	1	2	yes	—
131	C₄×C₁₉	#492	1	1	yes	characteristic
132	C₄×C₁₉	#497	1	1	yes	characteristic
133	Dic₁₉	—	8	1	no	—
134	#533	C₂×D₁₉	1	2	yes	—
135	C₂×C₄×D₄	—	19	1	no	—
136	#501	—	2	2	no	—
137	#501	—	2	2	no	—
138	#483	—	38	2	no	—
139	#476	—	38	2	no	—
140	#461	—	38	2	no	—
141	#450	—	38	2	no	—
142	C₄×SD₁₆	—	38	4	no	—
143	#431	—	19	2	no	—
144	#427	—	2	2	no	—
145	C₂×C₄⋊C₈	—	19	1	no	—
146	C₂×C₂²⋊C₈	—	38	2	no	—
147	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
148	Q₈⋊C₈	—	38	4	no	—
149	C₂×C₁₉	—	2	2	no	—
150	C₂×C₁₉	#2010	1	1	yes	characteristic
151	C₂×C₁₉	#2013	1	1	yes	characteristic
152	C₂×C₁₉	#2017	1	1	yes	characteristic
153	D₁₉	—	8	2	no	—
154	C₂²×D₄	—	19	1	no	—
155	C₂³×C₄	—	38	1	no	—
156	C₂×SD₁₆	—	38	4	no	—
157	C₂²×C₈	—	38	1	no	—
158	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
159	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
160	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
161	#125	—	2	2	no	—
162	C₂²⋊Q₈	—	2	2	no	—
163	C₂²⋊Q₈	—	2	2	no	—
164	C₄×Q₈	—	2	2	no	—
165	C₄×Q₈	—	2	2	no	—
166	C₄×D₄	—	38	2	no	—
167	C₄×D₄	—	38	2	no	—
168	#117	—	2	2	no	—
169	C₂×C₄⋊C₄	—	19	1	no	—
170	C₂×C₂²⋊C₄	—	38	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	#107	—	2	2	no	—
173	#107	—	2	2	no	—
174	#106	—	2	4	no	—
175	#106	—	38	4	no	—
176	C₄⋊C₈	—	38	2	no	—
177	C₄⋊C₈	—	38	2	no	—
178	#103	—	38	4	no	—
179	#102	—	38	4	no	—
180	C₂²⋊C₈	—	38	2	no	—
181	C₂²⋊C₈	—	76	4	no	—
182	#97	—	2	2	no	—
183	C₄×C₈	—	19	4	no	—
184	C₁₉	#10036	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	38	1	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×D₄	—	38	2	no	—
189	C₂×D₄	—	76	2	no	—
190	C₂²×C₄	—	38	1	no	—
191	C₂²×C₄	—	76	1	no	—
192	C₂²×C₄	—	76	2	no	—
193	C₂²×C₄	—	76	2	no	—
194	C₂²×C₄	—	76	1	no	—
195	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
196	C₂²×C₄	#64543	1	1	yes	characteristic
197	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
198	SD₁₆	—	76	8	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	38	4	no	—
202	C₂×C₈	—	76	1	no	—
203	C₂×C₈	—	76	2	no	—
204	C₂×C₈	#64527	1	4	yes	complemented
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	2	no	—
211	C₄⋊C₄	—	38	2	no	—
212	C₂²⋊C₄	—	4	2	no	—
213	C₂²⋊C₄	—	76	2	no	—
214	C₄²	—	4	2	no	—
215	C₄²	D₄×D₁₉	1	2	yes	—
216	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
217	C₂³	—	38	2	no	—
218	C₂³	—	76	1	no	—
219	C₂³	—	76	2	no	—
220	C₂³	—	76	1	no	—
221	C₂³	—	76	2	no	—
222	C₂³	#10597384	1	1	yes	characteristic
223	Q₈	—	4	4	no	—
224	Q₈	—	4	4	no	—
225	D₄	—	38	4	no	—
226	D₄	—	76	2	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	76	1	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	152	1	no	—
234	C₂×C₄	—	152	1	no	—
235	C₂×C₄	—	152	2	no	—
236	C₂×C₄	#10597383	1	2	yes	—
237	C₂×C₄	#10597385	1	2	yes	—
238	C₂×C₄	#10597386	1	1	yes	characteristic
239	C₂×C₄	C₂×#64527	1	2	yes	—
240	C₂×C₄	#10597388	1	2	yes	—
241	C₂×C₄	#10597399	1	1	yes	characteristic
242	C₈	—	2	4	no	—
243	C₈	—	76	4	no	—
244	C₈	—	152	1	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	76	4	no	—
248	C₂²	—	76	2	no	—
249	C₂²	—	152	2	no	—
250	C₂²	—	152	1	no	—
251	C₂²	—	152	1	no	—
252	C₂²	#11926452	1	1	yes	characteristic
253	C₂²	#11926746	1	2	yes	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	8	2	no	—
257	C₄	—	8	2	no	—
258	C₄	—	152	1	no	—
259	C₄	#11926683	1	2	yes	—
260	C₄	#11926918	1	1	yes	characteristic
261	C₄	#11926936	1	1	yes	characteristic
262	C₂	—	2	2	no	—
263	C₂	—	152	2	no	—
264	C₂	#14564699	1	1	yes	characteristic
265	C₂	#14564718	1	1	yes	characteristic
266	C₂	#14564738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573639

C₂

yes

maximal

#14564433

C₂

yes

maximal, characteristic

#14562038

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#3162

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₇₆

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

—

Q₈⋊(C₁₉⋊C₈)

—

C₁₉×#533

C₂²

yes

—

C₁₉×#501

—

C₁₉×#501

—

C₁₉×#427

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×D₇₆

D₄

yes

characteristic

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64527

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#97

—

#10597292

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

#10597266

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64527

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

100

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

101

C₂×C₄×C₁₉

#137

yes

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

D₇₆

—

105

D₇₆

—

106

C₄×D₁₉

—

107

C₄×D₁₉

—

108

C₄×D₁₉

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

#3162

D₁₉

yes

characteristic, complemented

113

#3101

—

114

#1955

—

115

#1481

—

116

#1275

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

#392

yes

characteristic

120

C₂²×C₁₉

#461

yes

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#448

yes

—

131

C₄×C₁₉

#492

yes

characteristic

132

C₄×C₁₉

#497

yes

characteristic

133

Dic₁₉

—

134

#533

C₂×D₁₉

yes

—

135

C₂×C₄×D₄

—

136

#501

—

137

#501

—

138

#483

—

139

#476

—

140

#461

—

141

#450

—

142

C₄×SD₁₆

—

143

#431

—

144

#427

—

145

C₂×C₄⋊C₈

—

146

C₂×C₂²⋊C₈

—

147

C₂×#97

C₂×D₁₉

yes

characteristic

148

Q₈⋊C₈

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#2010

yes

characteristic

151

C₂×C₁₉

#2013

yes

characteristic

152

C₂×C₁₉

#2017

yes

characteristic

153

D₁₉

—

154

C₂²×D₄

—

155

C₂³×C₄

—

156

C₂×SD₁₆

—

157

C₂²×C₈

—

158

C₂²×C₈

C₂²⋊D₁₉

yes

—

159

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

160

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

161

#125

—

162

C₂²⋊Q₈

—

163

C₂²⋊Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

C₄×D₄

—

167

C₄×D₄

—

168

#117

—

169

C₂×C₄⋊C₄

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

#107

—

173

#107

—

174

#106

—

175

#106

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#103

—

179

#102

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

#97

—

183

C₄×C₈

—

184

C₁₉

#10036

yes

characteristic, complemented, Sylow

185

C₂⁴

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

D₄×D₁₉

yes

characteristic

196

C₂²×C₄

#64543

yes

characteristic

197

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

198

SD₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

#64527

yes

complemented

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

D₄×D₁₉

yes

—

216

C₄²

C₂×C₂²⋊D₁₉

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

#10597384

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

152

—

234

C₂×C₄

—

152

—

235

C₂×C₄

—

152

—

236

C₂×C₄

#10597383

yes

—

237

C₂×C₄

#10597385

yes

—

238

C₂×C₄

#10597386

yes

characteristic

239

C₂×C₄

C₂×#64527

yes

—

240

C₂×C₄

#10597388

yes

—

241

C₂×C₄

#10597399

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

152

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

152

—

250

C₂²

—

152

—

251

C₂²

—

152

—

252

C₂²

#11926452

yes

characteristic

253

C₂²

#11926746

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

152

—

259

C₄

#11926683

yes

—

260

C₄

#11926918

yes

characteristic

261

C₄

#11926936

yes

characteristic

262

C₂

—

263

C₂

—

152

—

264

C₂

#14564699

yes

characteristic

265

C₂

#14564718

yes

characteristic

266

C₂

#14564738

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3162	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂²×D₇₆	D₄
hypercenter	#3162	D₁₉
hypocenter	C₁₉	#10036
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3162

C₂

socle

C₂²×C₁₉

#392

prime radical

C₂²×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

N	H ≅ G/N	type
3. #14562038	C₂	semidirect
4. #14561466	C₂	semidirect
5. C₁₉×#3162	C₂	semidirect
66. C₂×C₈×C₁₉	SD₁₆	semidirect
112. #3162	D₁₉	semidirect
184. C₁₉	#10036	semidirect
204. C₂×C₈	#64527	semidirect

H ≅ G/N

type

3. #14562038

C₂

semidirect

4. #14561466

C₂

semidirect

5. C₁₉×#3162

C₂

semidirect

66. C₂×C₈×C₁₉

SD₁₆

semidirect

112. #3162

D₁₉

semidirect

184. C₁₉

#10036

semidirect

204. C₂×C₈

#64527

semidirect

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

subgroup	index
#14573639	2
#14564433	2
#14562038	2
#14561466	2
C₁₉×#3162	2
#10036	19

subgroup

index

C₁₉×#3162

Subgroups — #18083527

Conjugacy classes of subgroups

Complements

Maximal subgroups