Group #18087511 — subgroups

Subgroups — #18087511

Order 4864.

356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14564432	C₂	1	1	yes	maximal, characteristic
2	#14563775	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562409	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562061	C₂	1	1	yes	maximal, characteristic
5	#14562059	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
12	C₂×#10597260	C₂²	1	1	yes	characteristic
13	#11926308	—	2	2	no	—
14	#11926296	—	2	2	no	—
15	#11926273	—	2	2	no	—
16	#11926271	—	2	2	no	—
17	C₁₉×#431	C₂²	1	1	yes	characteristic
18	C₁₉×#423	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₉×#334	—	2	2	no	—
21	C₂²×D₇₆	Q₈	1	1	yes	characteristic
22	C₂²×C₄×D₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
27	C₂×C₄⋊Dic₁₉	Q₈	1	1	yes	characteristic
28	C₂×#64520	—	2	1	no	—
29	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
30	C₄×D₇₆	—	2	1	no	—
31	C₄×D₇₆	—	2	1	no	—
32	C₄×D₇₆	—	2	1	no	—
33	C₄×D₇₆	—	2	1	no	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₂²⋊C₈	—	2	1	no	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
42	(C₂×D₁₉)⋊C₈	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
46	#10597260	—	2	1	no	—
47	#10597260	—	2	1	no	—
48	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
49	C₂³×D₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂×D₇₆	—	2	1	no	—
55	C₂×D₇₆	—	2	1	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×C₄×D₁₉	—	4	1	no	—
58	C₂×C₄×D₁₉	—	4	1	no	—
59	C₂×C₄×D₁₉	—	4	2	no	—
60	C₂×C₄×D₁₉	—	4	2	no	—
61	M₁₆×C₁₉	—	4	2	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄²×C₁₉	#41	1	1	yes	characteristic
70	(C₂×D₁₉)⋊C₄	—	4	1	no	—
71	(C₂×D₁₉)⋊C₄	—	4	1	no	—
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	—	2	1	no	—
74	#64520	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	2	2	no	—
77	C₂×C₁₉⋊C₈	—	2	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	1	no	—
80	#10659	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂²×D₁₉	—	2	2	no	—
83	C₂²×D₁₉	—	4	1	no	—
84	C₂²×D₁₉	—	4	2	no	—
85	C₂²×D₁₉	—	4	1	no	—
86	C₂²×D₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	2	yes	—
96	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
97	C₂×Dic₁₉	—	4	1	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	D₇₆	—	2	2	no	—
100	D₇₆	—	2	2	no	—
101	D₇₆	—	4	1	no	—
102	D₇₆	—	4	1	no	—
103	C₄×D₁₉	—	8	2	no	—
104	C₄×D₁₉	—	8	1	no	—
105	C₄×D₁₉	—	8	1	no	—
106	C₈×C₁₉	—	4	2	no	—
107	C₈×C₁₉	—	8	1	no	—
108	C₈×C₁₉	—	8	1	no	—
109	C₁₉⋊C₈	—	4	2	no	—
110	C₁₉⋊C₈	—	4	2	no	—
111	C₁₉⋊C₈	—	8	1	no	—
112	#1955	—	19	1	no	—
113	#1838	—	19	1	no	—
114	#1571	—	19	1	no	—
115	#1570	D₁₉	1	1	yes	characteristic, complemented
116	#1486	—	19	1	no	—
117	#1486	—	19	1	no	—
118	#1275	—	19	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#399	1	1	yes	characteristic
122	C₂²×C₁₉	#478	1	2	yes	—
123	C₂×D₁₉	—	4	4	no	—
124	C₂×D₁₉	—	4	2	no	—
125	C₂×D₁₉	—	8	2	no	—
126	C₂×D₁₉	—	8	1	no	—
127	C₂×D₁₉	—	8	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	#482	1	2	yes	—
133	C₄×C₁₉	#495	1	1	yes	characteristic
134	C₄×C₁₉	#496	1	1	yes	characteristic
135	Dic₁₉	—	8	1	no	—
136	C₂×C₄×D₄	—	19	1	no	—
137	#431	—	19	1	no	—
138	#431	C₂×D₁₉	1	1	yes	characteristic
139	#423	—	19	1	no	—
140	#423	C₂×D₁₉	1	1	yes	characteristic
141	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₂²⋊C₈	—	38	2	no	—
143	C₂×#97	—	19	1	no	—
144	#341	—	38	2	no	—
145	#335	—	38	2	no	—
146	#334	—	2	2	no	—
147	D₄⋊C₈	—	38	2	no	—
148	D₄⋊C₈	—	38	2	no	—
149	C₂×C₁₉	—	2	2	no	—
150	C₂×C₁₉	#2091	1	1	yes	characteristic
151	C₂×C₁₉	#2092	1	1	yes	characteristic
152	C₂×C₁₉	#2098	1	1	yes	characteristic
153	D₁₉	—	8	2	no	—
154	C₂²×D₄	—	19	1	no	—
155	C₂³×C₄	—	38	1	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	38	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	19	2	no	—
160	C₄×D₄	—	38	1	no	—
161	C₄×D₄	—	38	1	no	—
162	C₄×D₄	—	38	1	no	—
163	C₄×D₄	—	38	1	no	—
164	C₂×C₄⋊C₄	—	19	1	no	—
165	C₂×C₂²⋊C₄	—	38	1	no	—
166	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
167	C₄⋊C₈	—	2	1	no	—
168	C₄⋊C₈	—	2	1	no	—
169	C₄⋊C₈	—	2	1	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	38	1	no	—
173	C₄⋊C₈	—	38	1	no	—
174	C₄⋊C₈	—	38	1	no	—
175	C₂²⋊C₈	—	2	1	no	—
176	C₂²⋊C₈	—	38	1	no	—
177	C₂²⋊C₈	—	76	4	no	—
178	#97	—	38	1	no	—
179	#97	—	38	1	no	—
180	C₄×C₈	—	19	2	no	—
181	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
182	C₁₉	#10659	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	—	38	1	no	—
184	C₂×D₄	—	38	1	no	—
185	C₂×D₄	—	38	1	no	—
186	C₂×D₄	—	76	2	no	—
187	C₂²×C₄	—	38	1	no	—
188	C₂²×C₄	—	76	1	no	—
189	C₂²×C₄	—	76	1	no	—
190	C₂²×C₄	—	76	2	no	—
191	C₂²×C₄	—	76	2	no	—
192	C₂²×C₄	#64541	1	1	yes	characteristic
193	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
194	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
195	M₁₆	—	4	2	no	—
196	M₁₆	—	76	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	38	2	no	—
202	C₂×C₈	—	38	2	no	—
203	C₂×C₈	—	38	2	no	—
204	C₂×C₈	—	38	2	no	—
205	C₂×C₈	—	76	1	no	—
206	C₄⋊C₄	—	38	1	no	—
207	C₄⋊C₄	—	38	1	no	—
208	C₂²⋊C₄	—	76	1	no	—
209	C₂²⋊C₄	—	76	1	no	—
210	C₄²	#64541	1	1	yes	characteristic
211	C₄²	D₄×D₁₉	1	1	yes	characteristic
212	C₄²	#64545	1	1	yes	characteristic
213	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
214	C₂³	—	38	2	no	—
215	C₂³	—	76	1	no	—
216	C₂³	—	76	2	no	—
217	C₂³	—	76	2	no	—
218	C₂³	—	76	1	no	—
219	C₂³	#10597342	1	1	yes	characteristic
220	D₄	—	38	2	no	—
221	D₄	—	38	2	no	—
222	D₄	—	76	1	no	—
223	D₄	—	76	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	1	no	—
228	C₂×C₄	—	152	2	no	—
229	C₂×C₄	—	152	1	no	—
230	C₂×C₄	—	152	1	no	—
231	C₂×C₄	#10597340	1	1	yes	characteristic
232	C₂×C₄	#10597340	1	1	yes	characteristic
233	C₂×C₄	#10597342	1	1	yes	characteristic
234	C₂×C₄	#10597360	1	2	yes	—
235	C₂×C₄	#10597362	1	2	yes	—
236	C₂×C₄	#10597375	1	1	yes	characteristic
237	C₂×C₄	#10597386	1	1	yes	characteristic
238	C₂×C₄	#10597392	1	1	yes	characteristic
239	C₈	—	4	2	no	—
240	C₈	—	8	1	no	—
241	C₈	—	8	1	no	—
242	C₈	—	76	2	no	—
243	C₈	—	76	2	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	#11926479	1	1	yes	characteristic
253	C₂²	#11926843	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	152	1	no	—
259	C₄	#11926870	1	2	yes	—
260	C₄	#11926925	1	1	yes	characteristic
261	C₄	#11926930	1	1	yes	characteristic
262	C₂	—	2	2	no	—
263	C₂	—	152	2	no	—
264	C₂	#14565150	1	1	yes	characteristic
265	C₂	#14565157	1	1	yes	characteristic
266	C₂	#14565191	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564432

C₂

yes

maximal, characteristic

#14563775

C₂

yes

maximal, characteristic, complemented

#14562409

C₂

yes

maximal, characteristic, complemented

#14562061

C₂

yes

maximal, characteristic

#14562059

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic, complemented

C₁₉×#1570

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₇₆

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₈

—

C₂×#10597260

C₂²

yes

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#334

—

C₂²×D₇₆

Q₈

yes

characteristic

C₂²×C₄×D₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

Q₈

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10659

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

100

D₇₆

—

101

D₇₆

—

102

D₇₆

—

103

C₄×D₁₉

—

104

C₄×D₁₉

—

105

C₄×D₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₁₉⋊C₈

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

#1955

—

113

#1838

—

114

#1571

—

115

#1570

D₁₉

yes

characteristic, complemented

116

#1486

—

117

#1486

—

118

#1275

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#399

yes

characteristic

122

C₂²×C₁₉

#478

yes

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#482

yes

—

133

C₄×C₁₉

#495

yes

characteristic

134

C₄×C₁₉

#496

yes

characteristic

135

Dic₁₉

—

136

C₂×C₄×D₄

—

137

#431

—

138

#431

C₂×D₁₉

yes

characteristic

139

#423

—

140

#423

C₂×D₁₉

yes

characteristic

141

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

142

C₂×C₂²⋊C₈

—

143

C₂×#97

—

144

#341

—

145

#335

—

146

#334

—

147

D₄⋊C₈

—

148

D₄⋊C₈

—

149

C₂×C₁₉

—

150

C₂×C₁₉

#2091

yes

characteristic

151

C₂×C₁₉

#2092

yes

characteristic

152

C₂×C₁₉

#2098

yes

characteristic

153

D₁₉

—

154

C₂²×D₄

—

155

C₂³×C₄

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄×D₄

—

161

C₄×D₄

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₄²

C₂²×D₁₉

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₂²⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

C₄×C₈

—

181

C₄×C₈

C₂²⋊D₁₉

yes

—

182

C₁₉

#10659

yes

characteristic, complemented, Sylow

183

C₂⁴

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

#64541

yes

characteristic

193

C₂²×C₄

D₄×D₁₉

yes

characteristic

194

C₂²×C₄

Q₈×D₁₉

yes

characteristic

195

M₁₆

—

196

M₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₂²⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

#64541

yes

characteristic

211

C₄²

D₄×D₁₉

yes

characteristic

212

C₄²

#64545

yes

characteristic

213

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

#10597342

yes

characteristic

220

D₄

—

221

D₄

—

222

D₄

—

223

D₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

152

—

229

C₂×C₄

—

152

—

230

C₂×C₄

—

152

—

231

C₂×C₄

#10597340

yes

characteristic

232

C₂×C₄

#10597340

yes

characteristic

233

C₂×C₄

#10597342

yes

characteristic

234

C₂×C₄

#10597360

yes

—

235

C₂×C₄

#10597362

yes

—

236

C₂×C₄

#10597375

yes

characteristic

237

C₂×C₄

#10597386

yes

characteristic

238

C₂×C₄

#10597392

yes

characteristic

239

C₈

—

240

C₈

—

241

C₈

—

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

#11926479

yes

characteristic

253

C₂²

#11926843

yes

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

152

—

259

C₄

#11926870

yes

—

260

C₄

#11926925

yes

characteristic

261

C₄

#11926930

yes

characteristic

262

C₂

—

263

C₂

—

152

—

264

C₂

#14565150

yes

characteristic

265

C₂

#14565157

yes

characteristic

266

C₂

#14565191

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1570	C₂
socle	C₂²×C₁₉	#399
prime radical	C₂²×D₇₆	Q₈
hypercenter	#1570	D₁₉
hypocenter	C₁₉	#10659
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1570

C₂

socle

C₂²×C₁₉

#399

prime radical

C₂²×D₇₆

Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

N	H ≅ G/N	type
2. #14563775	C₂	semidirect
3. #14562409	C₂	semidirect
6. #14561465	C₂	semidirect
7. C₁₉×#1570	C₂	semidirect
115. #1570	D₁₉	semidirect
182. C₁₉	#10659	semidirect

H ≅ G/N

type

2. #14563775

C₂

semidirect

3. #14562409

C₂

semidirect

6. #14561465

C₂

semidirect

7. C₁₉×#1570

C₂

semidirect

115. #1570

D₁₉

semidirect

182. C₁₉

#10659

semidirect

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

subgroup	index
#14564432	2
#14563775	2
#14562409	2
#14562061	2
#14562059	2
#14561465	2
C₁₉×#1570	2
#10659	19

subgroup

index

C₁₉×#1570

Subgroups — #18087511

Conjugacy classes of subgroups

Complements

Maximal subgroups