Group #18083515 — subgroups

Subgroups — #18083515

Order 4864.

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

normal subgroups only

This group has 584 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	#14573662	C₂	1	2	yes	maximal, complemented
2	#14564575	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562034	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926860	—	2	2	no	—
8	#11926826	—	2	2	no	—
9	#11926741	—	2	2	no	—
10	#11926682	—	2	2	no	—
11	C₄×#64526	—	2	4	no	—
12	#11926597	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	#11926298	—	2	2	no	—
15	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
16	C₂×C₁₉×#135	—	2	2	no	—
17	C₁₉×#532	C₂²	1	2	yes	—
18	C₁₉×#497	—	2	2	no	—
19	C₁₉×#496	—	2	2	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂×#41×C₁₉	—	2	2	no	—
22	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
23	C₁₉×#135	—	4	4	no	—
24	C₁₉×#135	—	4	4	no	—
25	C₂×Q₁₆×C₁₉	—	2	2	no	—
26	C₂×SD₁₆×C₁₉	—	2	4	no	—
27	C₂×D₈×C₁₉	—	2	2	no	—
28	C₂²×C₈×C₁₉	D₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#127	D₄	1	2	yes	—
31	C₁₉×#124	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64526	—	2	4	no	—
38	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
39	C₂×Dic₁₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂²×C₁₉⋊C₈	—	2	1	no	—
42	C₄×Dic₃₈	—	2	2	no	—
43	C₄×Dic₃₈	—	2	2	no	—
44	C₁₉×#97	—	2	2	no	—
45	#10597289	—	2	4	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	#10597267	—	2	4	no	—
48	#10597265	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
52	#41×C₁₉	—	4	4	no	—
53	#41×C₁₉	—	4	4	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂²×Dic₁₉	—	2	1	no	—
64	C₂²×Dic₁₉	—	2	1	no	—
65	C₂×Dic₃₈	—	2	2	no	—
66	C₂×Dic₃₈	—	4	2	no	—
67	Q₁₆×C₁₉	—	4	4	no	—
68	SD₁₆×C₁₉	—	4	8	no	—
69	D₈×C₁₉	—	4	4	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂²⋊C₄×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	C₄²×C₁₉	C₂×D₄	1	2	yes	—
79	#64526	—	4	8	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	Dic₁₉⋊C₄	—	4	2	no	—
82	C₄×Dic₁₉	—	4	1	no	—
83	C₄×Dic₁₉	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	2	4	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	#10034	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	#121	1	1	yes	characteristic
90	Q₈×C₁₉	—	4	4	no	—
91	D₄×C₁₉	—	4	4	no	—
92	D₄×C₁₉	—	4	4	no	—
93	D₄×C₁₉	—	4	4	no	—
94	D₄×C₁₉	—	8	4	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	8	2	no	—
99	C₂×C₄×C₁₉	—	8	2	no	—
100	C₂×C₄×C₁₉	#120	1	2	yes	—
101	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#121	1	2	yes	—
103	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
105	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
106	C₂×Dic₁₉	—	2	2	no	—
107	C₂×Dic₁₉	—	4	1	no	—
108	C₂×Dic₁₉	—	4	1	no	—
109	C₂×Dic₁₉	—	4	2	no	—
110	C₂×Dic₁₉	—	4	1	no	—
111	Dic₃₈	—	2	4	no	—
112	Dic₃₈	—	4	2	no	—
113	C₈×C₁₉	—	2	4	no	—
114	C₁₉⋊C₈	—	4	4	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	#3150	D₁₉	1	1	yes	characteristic
117	#3103	—	19	2	no	—
118	#1985	—	19	1	no	—
119	#1480	—	19	2	no	—
120	#1275	—	19	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	#392	1	1	yes	characteristic
127	C₂²×C₁₉	#460	1	2	yes	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	2	2	no	—
130	C₄×C₁₉	—	8	2	no	—
131	C₄×C₁₉	#450	1	2	yes	—
132	C₄×C₁₉	#492	1	1	yes	characteristic
133	C₄×C₁₉	#496	1	1	yes	characteristic
134	Dic₁₉	—	4	2	no	—
135	Dic₁₉	—	8	1	no	—
136	C₂×#135	—	2	2	no	—
137	#532	C₂×D₁₉	1	2	yes	—
138	C₂×C₄×Q₈	—	19	1	no	—
139	#497	—	2	2	no	—
140	#496	—	2	2	no	—
141	#481	—	38	2	no	—
142	#475	—	38	2	no	—
143	#460	—	38	2	no	—
144	#448	—	38	2	no	—
145	C₄×SD₁₆	—	38	4	no	—
146	#431	—	19	2	no	—
147	C₂×C₄⋊C₈	—	19	1	no	—
148	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
149	#336	—	38	2	no	—
150	D₄⋊C₈	—	38	4	no	—
151	C₂×C₁₉	—	2	2	no	—
152	C₂×C₁₉	—	16	2	no	—
153	C₂×C₁₉	#2010	1	1	yes	characteristic
154	C₂×C₁₉	#2014	1	1	yes	characteristic
155	C₂×C₁₉	#2017	1	1	yes	characteristic
156	C₂×#41	—	2	2	no	—
157	C₂²×Q₈	—	19	1	no	—
158	#135	—	4	4	no	—
159	#135	—	4	4	no	—
160	C₂×Q₁₆	—	2	2	no	—
161	C₂×SD₁₆	—	2	4	no	—
162	C₂×SD₁₆	—	38	4	no	—
163	C₂×D₈	—	2	2	no	—
164	C₂²×C₈	—	38	1	no	—
165	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
166	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
167	#127	C₂²⋊D₁₉	1	2	yes	—
168	#124	—	2	2	no	—
169	#121	—	2	2	no	—
170	#121	—	2	2	no	—
171	C₄×Q₈	—	38	2	no	—
172	C₄×Q₈	—	38	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₂×C₄⋊C₄	—	19	1	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄²	—	38	1	no	—
178	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
179	#106	—	38	4	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₄⋊C₈	—	38	2	no	—
182	#103	—	38	4	no	—
183	#102	—	38	4	no	—
184	C₂²⋊C₈	—	38	2	no	—
185	#97	—	2	2	no	—
186	C₄×C₈	—	19	4	no	—
187	C₁₉	#10034	1	1	yes	characteristic, complemented, Sylow
188	#41	—	4	4	no	—
189	#41	—	4	4	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	—	38	2	no	—
192	C₂×Q₈	—	76	2	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	2	2	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	—	38	1	no	—
199	C₂²×C₄	—	38	1	no	—
200	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
201	C₂²×C₄	#64543	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
203	Q₁₆	—	4	4	no	—
204	SD₁₆	—	4	8	no	—
205	SD₁₆	—	76	8	no	—
206	D₈	—	4	4	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	38	4	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	1	no	—
212	C₂×C₈	#64526	1	4	yes	complemented
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	38	2	no	—
216	C₄⋊C₄	—	76	2	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₂²⋊C₄	—	4	2	no	—
219	C₄²	—	76	1	no	—
220	C₄²	—	76	1	no	—
221	C₄²	D₄×D₁₉	1	2	yes	—
222	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
223	C₂³	—	4	2	no	—
224	C₂³	#10597384	1	1	yes	characteristic
225	Q₈	—	4	4	no	—
226	Q₈	—	38	4	no	—
227	Q₈	—	76	2	no	—
228	D₄	—	4	4	no	—
229	D₄	—	4	4	no	—
230	D₄	—	4	4	no	—
231	D₄	—	8	4	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	8	2	no	—
237	C₂×C₄	—	38	2	no	—
238	C₂×C₄	—	76	1	no	—
239	C₂×C₄	—	76	1	no	—
240	C₂×C₄	—	76	2	no	—
241	C₂×C₄	—	76	1	no	—
242	C₂×C₄	#10597378	1	2	yes	—
243	C₂×C₄	C₂×#64526	1	2	yes	—
244	C₂×C₄	#10597383	1	2	yes	—
245	C₂×C₄	#10597385	1	2	yes	—
246	C₂×C₄	#10597386	1	1	yes	characteristic
247	C₂×C₄	#10597399	1	1	yes	characteristic
248	C₈	—	2	4	no	—
249	C₈	—	76	4	no	—
250	C₈	—	152	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	8	2	no	—
255	C₂²	—	8	2	no	—
256	C₂²	#11926452	1	1	yes	characteristic
257	C₂²	#11926741	1	2	yes	—
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	76	2	no	—
262	C₄	—	152	1	no	—
263	C₄	#11926695	1	2	yes	—
264	C₄	#11926916	1	1	yes	characteristic
265	C₄	#11926931	1	1	yes	characteristic
266	C₂	—	2	2	no	—
267	C₂	—	16	2	no	—
268	C₂	#14564699	1	1	yes	characteristic
269	C₂	#14564723	1	1	yes	characteristic
270	C₂	#14564738	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573662

C₂

yes

maximal, complemented

#14564575

C₂

yes

maximal, characteristic, complemented

#14562034

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#3150

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926298

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₁₉×#135

—

C₁₉×#532

C₂²

yes

—

C₁₉×#497

—

C₁₉×#496

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×Dic₃₈

D₄

yes

characteristic

C₁₉×#135

—

C₁₉×#135

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

D₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64526

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#97

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

#10597267

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64526

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10034

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

#120

yes

—

101

C₂×C₄×C₁₉

#120

yes

characteristic

102

C₂×C₄×C₁₉

#121

yes

—

103

C₂×C₄×C₁₉

#127

yes

characteristic

104

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

105

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

Dic₃₈

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

#3150

D₁₉

yes

characteristic

117

#3103

—

118

#1985

—

119

#1480

—

120

#1275

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#392

yes

characteristic

127

C₂²×C₁₉

#460

yes

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#450

yes

—

132

C₄×C₁₉

#492

yes

characteristic

133

C₄×C₁₉

#496

yes

characteristic

134

Dic₁₉

—

135

Dic₁₉

—

136

C₂×#135

—

137

#532

C₂×D₁₉

yes

—

138

C₂×C₄×Q₈

—

139

#497

—

140

#496

—

141

#481

—

142

#475

—

143

#460

—

144

#448

—

145

C₄×SD₁₆

—

146

#431

—

147

C₂×C₄⋊C₈

—

148

C₂×#97

C₂×D₁₉

yes

characteristic

149

#336

—

150

D₄⋊C₈

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#2010

yes

characteristic

154

C₂×C₁₉

#2014

yes

characteristic

155

C₂×C₁₉

#2017

yes

characteristic

156

C₂×#41

—

157

C₂²×Q₈

—

158

#135

—

159

#135

—

160

C₂×Q₁₆

—

161

C₂×SD₁₆

—

162

C₂×SD₁₆

—

163

C₂×D₈

—

164

C₂²×C₈

—

165

C₂²×C₈

C₂²⋊D₁₉

yes

—

166

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

167

#127

C₂²⋊D₁₉

yes

—

168

#124

—

169

#121

—

170

#121

—

171

C₄×Q₈

—

172

C₄×Q₈

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄²

—

178

C₂×C₄²

C₂²×D₁₉

yes

characteristic

179

#106

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

#103

—

183

#102

—

184

C₂²⋊C₈

—

185

#97

—

186

C₄×C₈

—

187

C₁₉

#10034

yes

characteristic, complemented, Sylow

188

#41

—

189

#41

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

D₄×D₁₉

yes

characteristic

201

C₂²×C₄

#64543

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

203

Q₁₆

—

204

SD₁₆

—

205

SD₁₆

—

206

D₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

#64526

yes

complemented

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

—

220

C₄²

—

221

C₄²

D₄×D₁₉

yes

—

222

C₄²

C₂×C₂²⋊D₁₉

yes

—

223

C₂³

—

224

C₂³

#10597384

yes

characteristic

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

#10597378

yes

—

243

C₂×C₄

C₂×#64526

yes

—

244

C₂×C₄

#10597383

yes

—

245

C₂×C₄

#10597385

yes

—

246

C₂×C₄

#10597386

yes

characteristic

247

C₂×C₄

#10597399

yes

characteristic

248

C₈

—

249

C₈

—

250

C₈

—

152

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926452

yes

characteristic

257

C₂²

#11926741

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

152

—

263

C₄

#11926695

yes

—

264

C₄

#11926916

yes

characteristic

265

C₄

#11926931

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

#14564699

yes

characteristic

269

C₂

#14564723

yes

characteristic

270

C₂

#14564738

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3150	C₂
socle	C₂²×C₁₉	#392
hypercenter	#3150	D₁₉
hypocenter	C₁₉	#10034
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#3150

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3150

N	H ≅ G/N	type
1. #14573662	C₂	semidirect
2. #14564575	C₂	semidirect
3. #14562034	C₂	semidirect
4. #14561466	C₂	semidirect
72. C₂×C₈×C₁₉	SD₁₆	semidirect
187. C₁₉	#10034	semidirect
212. C₂×C₈	#64526	semidirect

H ≅ G/N

type

1. #14573662

C₂

semidirect

2. #14564575

C₂

semidirect

3. #14562034

C₂

semidirect

4. #14561466

C₂

semidirect

72. C₂×C₈×C₁₉

SD₁₆

semidirect

187. C₁₉

#10034

semidirect

212. C₂×C₈

#64526

semidirect

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

subgroup	index
#14573662	2
#14564575	2
#14562034	2
#14561466	2
C₁₉×#3150	2
#10034	19

subgroup

index

C₁₉×#3150

Subgroups — #18083515

Conjugacy classes of subgroups

Complements

Maximal subgroups