Group #18080384 — subgroups

Subgroups — #18080384

Order 4864.

474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14562064	C₂	1	2	yes	maximal
4	#14561493	C₂	1	2	yes	maximal
5	C₁₉×#2581	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	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#400	C₄	1	2	yes	—
16	C₁₉×#395	C₄	1	2	yes	—
17	C₁₉×#391	—	2	1	no	—
18	C₁₉×#389	—	2	1	no	—
19	C₁₉×#387	—	2	2	no	—
20	C₁₉×#382	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×#64520	—	2	2	no	—
37	C₁₉×#95	—	2	2	no	—
38	C₁₉×#95	—	2	2	no	—
39	C₁₉×#95	—	2	2	no	—
40	C₁₉×#95	—	2	1	no	—
41	C₁₉×#95	C₂×C₄	1	2	yes	—
42	#10597293	—	4	2	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄×C₁₉⋊C₈	—	2	4	no	—
49	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
55	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₄⋊C₄×C₁₉	—	2	4	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	4	4	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	4	2	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	#9484	—	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	—	2	4	no	—
85	Q₈×C₁₉	—	4	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	2	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	#103	1	4	yes	—
101	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
102	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#121	1	2	yes	—
104	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#135	1	2	yes	—
108	C₁₉⋊C₈	—	4	4	no	—
109	C₁₉⋊C₈	—	8	2	no	—
110	#2982	—	19	1	no	—
111	#2581	D₁₉	1	1	yes	characteristic
112	#1801	—	19	1	no	—
113	#1487	—	19	2	no	—
114	#1286	—	19	2	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	#386	1	1	yes	characteristic
118	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
119	C₂²×C₁₉	#416	1	1	yes	characteristic
120	C₄×C₁₉	—	2	2	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	4	2	no	—
125	C₄×C₁₉	—	4	2	no	—
126	C₄×C₁₉	—	8	2	no	—
127	C₄×C₁₉	—	8	1	no	—
128	C₄×C₁₉	#465	1	2	yes	—
129	C₄×C₁₉	#467	1	2	yes	—
130	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
132	C₈×Q₈	—	38	4	no	—
133	#431	—	19	2	no	—
134	#431	—	38	2	no	—
135	#423	—	19	2	no	—
136	C₂×#101	—	38	1	no	—
137	#400	Dic₁₉	1	2	yes	—
138	#395	Dic₁₉	1	2	yes	—
139	#391	—	2	1	no	—
140	#389	—	2	1	no	—
141	#387	—	2	2	no	—
142	#382	C₂×D₁₉	1	1	yes	characteristic
143	#343	—	38	1	no	—
144	Q₈⋊C₈	—	38	4	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	#1891	1	1	yes	characteristic
148	C₂×C₁₉	#1892	1	1	yes	characteristic
149	C₂×C₁₉	#1912	1	1	yes	characteristic
150	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
151	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₂×M₁₆	—	38	2	no	—
153	C₄×Q₈	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×Q₈	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	—	2	1	no	—
160	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
161	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
162	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
163	C₂×C₄²	—	2	1	no	—
164	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
165	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₈	—	38	4	no	—
167	C₄⋊C₈	—	38	2	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	2	no	—
170	#101	—	76	2	no	—
171	C₂²⋊C₈	—	38	2	no	—
172	C₄×C₈	—	19	4	no	—
173	C₄×C₈	—	38	4	no	—
174	#95	—	2	2	no	—
175	#95	—	2	2	no	—
176	#95	—	2	2	no	—
177	#95	—	2	1	no	—
178	#95	C₂×Dic₁₉	1	2	yes	—
179	C₁₉	#9484	1	1	yes	characteristic, complemented, Sylow
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	#64527	1	2	yes	—
185	C₂×Q₈	#64528	1	2	yes	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
190	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
191	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
194	M₁₆	—	76	2	no	—
195	M₁₆	—	76	2	no	—
196	C₂×C₈	—	38	4	no	—
197	C₂×C₈	—	76	2	no	—
198	C₄⋊C₄	—	2	4	no	—
199	C₄⋊C₄	—	2	2	no	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	4	4	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	2	no	—
208	C₄²	D₄×D₁₉	1	2	yes	—
209	C₄²	#64543	1	2	yes	—
210	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
211	Q₈	—	2	4	no	—
212	Q₈	—	2	4	no	—
213	Q₈	—	2	4	no	—
214	Q₈	—	4	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	#10597292	1	4	yes	—
230	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
231	C₂×C₄	#10597381	1	1	yes	characteristic
232	C₂×C₄	#10597383	1	1	yes	characteristic
233	C₂×C₄	#10597385	1	2	yes	—
234	C₂×C₄	C₂×#64527	1	1	yes	characteristic
235	C₂×C₄	C₂×#64528	1	1	yes	characteristic
236	C₂×C₄	#10597396	1	2	yes	—
237	C₈	—	76	4	no	—
238	C₈	—	152	2	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	#11926424	1	1	yes	characteristic
242	C₂²	C₂×#10597292	1	1	yes	characteristic
243	C₂²	#11926540	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	4	no	—
248	C₄	—	4	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	1	no	—
252	C₄	#11926775	1	2	yes	—
253	C₄	#11926783	1	2	yes	—
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	#14564054	1	1	yes	characteristic
257	C₂	#14564059	1	1	yes	characteristic
258	C₂	#14564173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14562064

C₂

yes

maximal

#14561493

C₂

yes

maximal

C₁₉×#2581

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#400

C₄

yes

—

C₁₉×#395

C₄

yes

—

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#387

—

C₁₉×#382

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

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

characteristic

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

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

—

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

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9484

—

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

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

#103

yes

—

101

C₂×C₄×C₁₉

C₄×D₄

yes

—

102

C₂×C₄×C₁₉

#120

yes

characteristic

103

C₂×C₄×C₁₉

#121

yes

—

104

C₂×C₄×C₁₉

#123

yes

characteristic

105

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

106

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

107

C₂×C₄×C₁₉

#135

yes

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

#2982

—

111

#2581

D₁₉

yes

characteristic

112

#1801

—

113

#1487

—

114

#1286

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

#386

yes

characteristic

118

C₂²×C₁₉

C₂×#103

yes

characteristic

119

C₂²×C₁₉

#416

yes

characteristic

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

#465

yes

—

129

C₄×C₁₉

#467

yes

—

130

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

131

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

132

C₈×Q₈

—

133

#431

—

134

#431

—

135

#423

—

136

C₂×#101

—

137

#400

Dic₁₉

yes

—

138

#395

Dic₁₉

yes

—

139

#391

—

140

#389

—

141

#387

—

142

#382

C₂×D₁₉

yes

characteristic

143

#343

—

144

Q₈⋊C₈

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1891

yes

characteristic

148

C₂×C₁₉

#1892

yes

characteristic

149

C₂×C₁₉

#1912

yes

characteristic

150

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

151

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

152

C₂×M₁₆

—

153

C₄×Q₈

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

161

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

162

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

163

C₂×C₄²

—

164

C₂×C₄²

C₂²⋊D₁₉

yes

—

165

C₂×C₄²

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#101

—

171

C₂²⋊C₈

—

172

C₄×C₈

—

173

C₄×C₈

—

174

#95

—

175

#95

—

176

#95

—

177

#95

—

178

#95

C₂×Dic₁₉

yes

—

179

C₁₉

#9484

yes

characteristic, complemented, Sylow

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

#64527

yes

—

185

C₂×Q₈

#64528

yes

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

190

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

191

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

D₄×D₁₉

yes

—

209

C₄²

#64543

yes

—

210

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

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

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

#10597292

yes

—

230

C₂×C₄

D₄×Dic₁₉

yes

—

231

C₂×C₄

#10597381

yes

characteristic

232

C₂×C₄

#10597383

yes

characteristic

233

C₂×C₄

#10597385

yes

—

234

C₂×C₄

C₂×#64527

yes

characteristic

235

C₂×C₄

C₂×#64528

yes

characteristic

236

C₂×C₄

#10597396

yes

—

237

C₈

—

238

C₈

—

152

—

239

C₂²

—

240

C₂²

—

241

C₂²

#11926424

yes

characteristic

242

C₂²

C₂×#10597292

yes

characteristic

243

C₂²

#11926540

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#11926775

yes

—

253

C₄

#11926783

yes

—

254

C₂

—

255

C₂

—

256

C₂

#14564054

yes

characteristic

257

C₂

#14564059

yes

characteristic

258

C₂

#14564173

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2581	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2581	D₁₉
hypocenter	C₁₉	#9484
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2581

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2581

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 ◁ #2581

N	H ≅ G/N	type
179. C₁₉	#9484	semidirect

H ≅ G/N

type

179. C₁₉

#9484

semidirect

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

subgroup	index
#14572716	2
#14563631	2
#14562064	2
#14561493	2
C₁₉×#2581	2
#9484	19

subgroup

index

C₁₉×#2581

Subgroups — #18080384

Conjugacy classes of subgroups

Complements

Maximal subgroups