Group #18070774 — subgroups

Subgroups — #18070774

Order 4864.

658 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563397	C₂	1	2	yes	maximal
2	#14561461	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×#10597260	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#391	—	2	2	no	—
11	C₁₉×#391	C₄	1	2	yes	—
12	C₁₉×#391	C₂²	1	2	yes	—
13	C₂×C₁₉×#95	—	2	2	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	1	no	—
16	C₂²×Q₈×C₁₉	—	4	2	no	—
17	C₂²×Q₈×C₁₉	—	4	2	no	—
18	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	—	4	2	no	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₁₉⋊C₈	—	2	4	no	—
31	C₁₉×#95	—	2	4	no	—
32	C₁₉×#95	—	2	4	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
34	#10597260	—	4	4	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	4	16	no	—
39	C₂×Q₈×C₁₉	—	4	2	no	—
40	C₂×Q₈×C₁₉	—	4	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	—	2	4	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	4	4	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	—	2	4	no	—
64	C₄²×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	—	4	1	no	—
66	C₂×C₁₉⋊C₈	—	2	8	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	#7629	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	—	2	1	no	—
71	C₂³×C₁₉	—	2	1	no	—
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	#100	1	2	yes	—
74	C₂³×C₁₉	#104	1	4	yes	—
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	4	4	no	—
77	Q₈×C₁₉	—	4	8	no	—
78	Q₈×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	—	2	8	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	4	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	4	8	no	—
91	C₂×C₄×C₁₉	—	4	8	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	8	4	no	—
97	C₂×C₄×C₁₉	#99	1	2	yes	—
98	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
99	C₂×C₄×C₁₉	#137	1	4	yes	—
100	C₁₉⋊C₈	—	4	8	no	—
101	C₂×#391	D₁₉	1	1	yes	characteristic
102	#1749	—	19	2	no	—
103	#1272	—	19	4	no	—
104	C₂²×C₁₉	—	2	2	no	—
105	C₂²×C₁₉	—	2	2	no	—
106	C₂²×C₁₉	—	2	4	no	—
107	C₂²×C₁₉	—	2	4	no	—
108	C₂²×C₁₉	#329	1	4	yes	—
109	C₂²×C₁₉	#407	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
112	C₂²×C₁₉	#419	1	2	yes	—
113	C₂²×C₁₉	C₂×#104	1	2	yes	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	2	2	no	—
116	C₄×C₁₉	—	2	4	no	—
117	C₄×C₁₉	—	4	4	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	8	2	no	—
120	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
122	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
123	C₂×C₂²⋊C₈	—	38	2	no	—
124	C₂×#97	—	38	2	no	—
125	#391	—	2	2	no	—
126	#391	Dic₁₉	1	2	yes	—
127	#391	C₂×D₁₉	1	2	yes	—
128	C₂×#95	—	2	2	no	—
129	#336	—	19	4	no	—
130	C₂×C₁₉	—	2	4	no	—
131	C₂×C₁₉	#1462	1	1	yes	characteristic
132	C₂×C₁₉	#1491	1	2	yes	—
133	C₂×C₁₉	#1508	1	2	yes	—
134	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
135	C₂×C₁₉	#1558	1	1	yes	characteristic
136	C₂²×Q₈	—	2	4	no	—
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×Q₈	—	4	2	no	—
139	C₂²×Q₈	—	4	2	no	—
140	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
141	C₂³×C₄	—	2	1	no	—
142	C₂³×C₄	—	2	1	no	—
143	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
144	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
145	C₂²×C₈	—	38	4	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	4	2	no	—
148	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
149	C₂×C₄²	—	4	2	no	—
150	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
152	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
153	C₂²⋊C₈	—	38	8	no	—
154	#97	—	76	4	no	—
155	#95	—	2	4	no	—
156	#95	—	2	4	no	—
157	C₁₉	#7629	1	1	yes	characteristic, complemented, Sylow
158	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
159	C₂×Q₈	—	2	4	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	4	16	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	#64520	1	4	yes	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	4	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	4	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	4	2	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	—	4	2	no	—
179	C₂²×C₄	—	4	4	no	—
180	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
181	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
182	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
184	C₂×C₈	—	38	8	no	—
185	C₂×C₈	—	76	4	no	—
186	C₂×C₈	—	76	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄²	—	2	4	no	—
190	C₄²	—	4	1	no	—
191	C₄²	—	4	1	no	—
192	C₂³	—	2	2	no	—
193	C₂³	—	2	1	no	—
194	C₂³	—	2	1	no	—
195	C₂³	#10597290	1	2	yes	—
196	C₂³	#10597294	1	4	yes	—
197	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
198	Q₈	—	4	4	no	—
199	Q₈	—	4	8	no	—
200	Q₈	—	4	4	no	—
201	C₂×C₄	—	2	8	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	8	no	—
213	C₂×C₄	—	4	8	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	8	4	no	—
219	C₂×C₄	#10597291	1	2	yes	—
220	C₂×C₄	C₂×#64520	1	2	yes	—
221	C₂×C₄	#10597388	1	4	yes	—
222	C₈	—	76	8	no	—
223	C₂²	—	2	4	no	—
224	C₂²	—	2	2	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	2	2	no	—
227	C₂²	#11926284	1	4	yes	—
228	C₂²	#11926508	1	1	yes	characteristic
229	C₂²	C₂×#10597291	1	1	yes	characteristic
230	C₂²	C₂×#10597290	1	1	yes	characteristic
231	C₂²	#11926553	1	2	yes	—
232	C₂²	C₂×#10597294	1	2	yes	—
233	C₄	—	2	4	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	4	2	no	—
237	C₄	—	4	4	no	—
238	C₄	—	8	2	no	—
239	C₂	—	2	4	no	—
240	C₂	#14561962	1	1	yes	characteristic
241	C₂	#14562082	1	2	yes	—
242	C₂	#14562155	1	2	yes	—
243	C₂	C₂×#11926284	1	1	yes	characteristic
244	C₂	#14562361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563397

C₂

yes

maximal

#14561461

C₂

yes

maximal, complemented

C₂×C₁₉×#391

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

C₂²

yes

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#391

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₂×C₁₉×#95

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7629

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#104

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

100

C₁₉⋊C₈

—

101

C₂×#391

D₁₉

yes

characteristic

102

#1749

—

103

#1272

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

#329

yes

—

109

C₂²×C₁₉

#407

yes

characteristic

110

C₂²×C₁₉

C₂×#99

yes

characteristic

111

C₂²×C₁₉

C₂×#100

yes

characteristic

112

C₂²×C₁₉

#419

yes

—

113

C₂²×C₁₉

C₂×#104

yes

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₂³×Q₈

Dic₁₉

yes

characteristic

121

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

122

C₂²×C₄²

C₂×D₁₉

yes

characteristic

123

C₂×C₂²⋊C₈

—

124

C₂×#97

—

125

#391

—

126

#391

Dic₁₉

yes

—

127

#391

C₂×D₁₉

yes

—

128

C₂×#95

—

129

#336

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1462

yes

characteristic

132

C₂×C₁₉

#1491

yes

—

133

C₂×C₁₉

#1508

yes

—

134

C₂×C₁₉

C₂×#329

yes

characteristic

135

C₂×C₁₉

#1558

yes

characteristic

136

C₂²×Q₈

—

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

140

C₂²×Q₈

C₂×Dic₁₉

yes

—

141

C₂³×C₄

—

142

C₂³×C₄

—

143

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

144

C₂³×C₄

C₂²⋊D₁₉

yes

—

145

C₂²×C₈

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

151

C₂×C₄²

C₂²⋊D₁₉

yes

—

152

C₂×C₄²

C₂²×D₁₉

yes

characteristic

153

C₂²⋊C₈

—

154

#97

—

155

#95

—

156

#95

—

157

C₁₉

#7629

yes

characteristic, complemented, Sylow

158

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

#64520

yes

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

181

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

182

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

183

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

#10597290

yes

—

196

C₂³

#10597294

yes

—

197

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

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

—

210

C₂×C₄

—

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

#10597291

yes

—

220

C₂×C₄

C₂×#64520

yes

—

221

C₂×C₄

#10597388

yes

—

222

C₈

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

#11926284

yes

—

228

C₂²

#11926508

yes

characteristic

229

C₂²

C₂×#10597291

yes

characteristic

230

C₂²

C₂×#10597290

yes

characteristic

231

C₂²

#11926553

yes

—

232

C₂²

C₂×#10597294

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₂

—

240

C₂

#14561962

yes

characteristic

241

C₂

#14562082

yes

—

242

C₂

#14562155

yes

—

243

C₂

C₂×#11926284

yes

characteristic

244

C₂

#14562361

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#391	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#391	D₁₉
hypocenter	C₁₉	#7629
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#391

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

N	H ≅ G/N	type
2. #14561461	C₂	semidirect
157. C₁₉	#7629	semidirect

H ≅ G/N

type

2. #14561461

C₂

semidirect

157. C₁₉

#7629

semidirect

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

subgroup	index
#14563397	2
#14561461	2
C₂×C₁₉×#391	2
#7629	19

subgroup

index

#14563397

#14561461

C₂×C₁₉×#391

#7629

Subgroups — #18070774

Conjugacy classes of subgroups

Complements

Maximal subgroups