Group #18079910 — subgroups

Subgroups — #18079910

Order 4864.

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

normal subgroups only

This group has 506 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	#14572716	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	#14562307	C₂	1	2	yes	maximal
4	#14561538	C₂	1	2	yes	maximal
5	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926568	C₂²	1	2	yes	—
10	C₂×#10597293	—	2	1	no	—
11	#11926313	—	2	1	no	—
12	#11926290	—	2	4	no	—
13	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#398	C₄	1	4	yes	—
17	C₁₉×#391	—	2	1	no	—
18	C₁₉×#389	—	2	2	no	—
19	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	4	2	no	—
25	C₁₉×C₄⋊Q₈	—	4	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64520	—	2	2	no	—
38	C₁₉×#95	—	2	4	no	—
39	C₁₉×#95	C₂×C₄	1	2	yes	—
40	#10597293	—	4	2	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
46	C₄×C₁₉⋊C₈	—	2	4	no	—
47	C₄×C₁₉⋊C₈	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	1	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	D₈	1	2	yes	—
55	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	8	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₄²×C₁₉	C₂×D₄	1	2	yes	—
75	C₄²×C₁₉	#41	1	2	yes	—
76	#64520	—	4	2	no	—
77	#64520	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	2	4	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#9394	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₁₉	—	2	4	no	—
83	Q₈×C₁₉	—	2	4	no	—
84	Q₈×C₁₉	—	8	2	no	—
85	Q₈×C₁₉	—	8	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	1	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	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	#102	1	4	yes	—
99	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
100	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	2	yes	—
102	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#135	1	2	yes	—
106	C₁₉⋊C₈	—	4	4	no	—
107	C₁₉⋊C₈	—	8	2	no	—
108	#2982	—	19	1	no	—
109	#2546	D₁₉	1	1	yes	characteristic
110	#1801	—	19	1	no	—
111	#1546	—	19	2	no	—
112	#1303	—	19	2	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	#386	1	1	yes	characteristic
116	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
117	C₂²×C₁₉	#416	1	1	yes	characteristic
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	4	no	—
120	C₄×C₁₉	—	2	2	no	—
121	C₄×C₁₉	—	4	4	no	—
122	C₄×C₁₉	—	4	2	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₄×C₁₉	#456	1	2	yes	—
125	C₄×C₁₉	#465	1	2	yes	—
126	C₄×C₁₉	#466	1	2	yes	—
127	C₂×C₄⋊Q₈	—	2	1	no	—
128	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
129	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
130	C₈×Q₈	—	38	4	no	—
131	#431	—	19	2	no	—
132	#431	—	38	2	no	—
133	#423	—	19	2	no	—
134	C₂×#101	—	38	1	no	—
135	#398	Dic₁₉	1	4	yes	—
136	#391	—	2	1	no	—
137	#389	—	2	2	no	—
138	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
139	#343	—	38	1	no	—
140	#332	—	38	4	no	—
141	C₂×C₁₉	—	2	1	no	—
142	C₂×C₁₉	—	2	1	no	—
143	C₂×C₁₉	#1886	1	1	yes	characteristic
144	C₂×C₁₉	#1893	1	1	yes	characteristic
145	C₂×C₁₉	#1915	1	1	yes	characteristic
146	C₂²×Q₈	—	2	1	no	—
147	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
148	C₂×M₁₆	—	38	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	4	2	no	—
152	C₄⋊Q₈	—	4	2	no	—
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	4	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
159	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
160	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
161	C₂×C₄²	—	2	1	no	—
162	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
163	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
164	C₄⋊C₈	—	19	4	no	—
165	C₄⋊C₈	—	38	4	no	—
166	C₄⋊C₈	—	38	2	no	—
167	C₄⋊C₈	—	38	2	no	—
168	#101	—	76	2	no	—
169	C₂²⋊C₈	—	38	2	no	—
170	C₄×C₈	—	38	4	no	—
171	C₄×C₈	—	38	2	no	—
172	#95	—	2	4	no	—
173	#95	C₂×Dic₁₉	1	2	yes	—
174	C₁₉	#9394	1	1	yes	characteristic, complemented, Sylow
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×Q₈	—	4	2	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	#64525	1	2	yes	—
182	C₂×Q₈	#64526	1	2	yes	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
186	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
190	M₁₆	—	76	2	no	—
191	M₁₆	—	76	2	no	—
192	C₂×C₈	—	38	4	no	—
193	C₂×C₈	—	76	2	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	4	no	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	4	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	8	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	4	1	no	—
204	C₄²	—	4	1	no	—
205	C₄²	D₄×D₁₉	1	2	yes	—
206	C₄²	#64543	1	2	yes	—
207	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
208	Q₈	—	2	4	no	—
209	Q₈	—	2	4	no	—
210	Q₈	—	8	2	no	—
211	Q₈	—	8	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	#10597289	1	4	yes	—
225	C₂×C₄	C₂×#64525	1	1	yes	characteristic
226	C₂×C₄	C₂×#64526	1	1	yes	characteristic
227	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
228	C₂×C₄	#10597381	1	1	yes	characteristic
229	C₂×C₄	#10597383	1	1	yes	characteristic
230	C₂×C₄	#10597385	1	2	yes	—
231	C₂×C₄	#10597396	1	2	yes	—
232	C₈	—	76	4	no	—
233	C₈	—	152	2	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	#11926424	1	1	yes	characteristic
237	C₂²	C₂×#10597289	1	1	yes	characteristic
238	C₂²	#11926540	1	1	yes	characteristic
239	C₄	—	2	2	no	—
240	C₄	—	2	1	no	—
241	C₄	—	2	4	no	—
242	C₄	—	4	4	no	—
243	C₄	—	4	2	no	—
244	C₄	—	8	2	no	—
245	C₄	#11926726	1	2	yes	—
246	C₄	#11926771	1	2	yes	—
247	C₄	#11926778	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	#14564029	1	1	yes	characteristic
251	C₂	#14564064	1	1	yes	characteristic
252	C₂	#14564188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14562307

C₂

yes

maximal

#14561538

C₂

yes

maximal

C₁₉×#2546

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

#11926290

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#398

C₄

yes

—

C₁₉×#391

—

C₁₉×#389

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9394

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

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

#102

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

100

C₂×C₄×C₁₉

#120

yes

characteristic

101

C₂×C₄×C₁₉

#121

yes

—

102

C₂×C₄×C₁₉

#123

yes

characteristic

103

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

104

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

105

C₂×C₄×C₁₉

#135

yes

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

—

108

#2982

—

109

#2546

D₁₉

yes

characteristic

110

#1801

—

111

#1546

—

112

#1303

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

#386

yes

characteristic

116

C₂²×C₁₉

C₂×#102

yes

characteristic

117

C₂²×C₁₉

#416

yes

characteristic

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

#456

yes

—

125

C₄×C₁₉

#465

yes

—

126

C₄×C₁₉

#466

yes

—

127

C₂×C₄⋊Q₈

—

128

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

129

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

130

C₈×Q₈

—

131

#431

—

132

#431

—

133

#423

—

134

C₂×#101

—

135

#398

Dic₁₉

yes

—

136

#391

—

137

#389

—

138

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

139

#343

—

140

#332

—

141

C₂×C₁₉

—

142

C₂×C₁₉

—

143

C₂×C₁₉

#1886

yes

characteristic

144

C₂×C₁₉

#1893

yes

characteristic

145

C₂×C₁₉

#1915

yes

characteristic

146

C₂²×Q₈

—

147

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

148

C₂×M₁₆

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

159

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

160

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

161

C₂×C₄²

—

162

C₂×C₄²

C₂²⋊D₁₉

yes

—

163

C₂×C₄²

C₂²×D₁₉

yes

characteristic

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

#101

—

169

C₂²⋊C₈

—

170

C₄×C₈

—

171

C₄×C₈

—

172

#95

—

173

#95

C₂×Dic₁₉

yes

—

174

C₁₉

#9394

yes

characteristic, complemented, Sylow

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

#64525

yes

—

182

C₂×Q₈

#64526

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

186

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

187

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

D₄×D₁₉

yes

—

206

C₄²

#64543

yes

—

207

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

208

Q₈

—

209

Q₈

—

210

Q₈

—

211

Q₈

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#10597289

yes

—

225

C₂×C₄

C₂×#64525

yes

characteristic

226

C₂×C₄

C₂×#64526

yes

characteristic

227

C₂×C₄

D₄×Dic₁₉

yes

—

228

C₂×C₄

#10597381

yes

characteristic

229

C₂×C₄

#10597383

yes

characteristic

230

C₂×C₄

#10597385

yes

—

231

C₂×C₄

#10597396

yes

—

232

C₈

—

233

C₈

—

152

—

234

C₂²

—

235

C₂²

—

236

C₂²

#11926424

yes

characteristic

237

C₂²

C₂×#10597289

yes

characteristic

238

C₂²

#11926540

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#11926726

yes

—

246

C₄

#11926771

yes

—

247

C₄

#11926778

yes

—

248

C₂

—

249

C₂

—

250

C₂

#14564029

yes

characteristic

251

C₂

#14564064

yes

characteristic

252

C₂

#14564188

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2546	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2546	D₁₉
hypocenter	C₁₉	#9394
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2546

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2546

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2546

N	H ≅ G/N	type
174. C₁₉	#9394	semidirect

H ≅ G/N

type

174. C₁₉

#9394

semidirect

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

subgroup	index
#14572716	2
#14563631	2
#14562307	2
#14561538	2
C₁₉×#2546	2
#9394	19

subgroup

index

C₁₉×#2546

Subgroups — #18079910

Conjugacy classes of subgroups

Complements

Maximal subgroups