Group #18079942 — subgroups

Subgroups — #18079942

Order 4864.

534 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14572676	C₂	1	1	yes	maximal, characteristic
2	#14568627	C₂	1	1	yes	maximal, characteristic
3	#14562308	C₂	1	2	yes	maximal, complemented
4	#14561536	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597382	—	2	1	no	—
8	#11926622	—	2	4	no	—
9	#11926597	C₂²	1	2	yes	—
10	#11926508	—	2	2	no	—
11	#11926469	C₄	1	4	yes	—
12	#11926449	—	2	1	no	—
13	#11926404	—	2	2	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926291	—	2	4	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×#100	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×Dic₃₈	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₄×D₄×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
30	#10597382	—	4	4	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄×Dic₁₉	—	2	1	no	—
35	C₂×#64520	—	2	4	no	—
36	#10597315	—	2	2	no	—
37	#10597315	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×#100	—	4	2	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₁₉⋊#95	C₂×C₄	1	2	yes	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	1	no	—
51	C₂×D₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂²×Dic₁₉	—	2	2	no	—
61	C₂×Dic₃₈	—	4	2	no	—
62	C₂×Dic₃₈	—	4	2	no	—
63	C₂×Dic₃₈	—	4	1	no	—
64	C₂×Dic₃₈	—	4	1	no	—
65	M₁₆×C₁₉	—	4	2	no	—
66	M₁₆×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	#41	1	2	yes	—
72	C₂²⋊Dic₁₉	—	4	8	no	—
73	C₄⋊Dic₁₉	—	2	4	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	C₄×Dic₁₉	—	4	2	no	—
78	#64520	—	8	4	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	#9401	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	—	2	2	no	—
82	C₂³×C₁₉	—	2	2	no	—
83	C₂³×C₁₉	—	2	2	no	—
84	C₂³×C₁₉	—	4	2	no	—
85	C₂³×C₁₉	—	4	2	no	—
86	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	D₄×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	4	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	8	2	no	—
95	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	2	yes	—
98	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	4	2	no	—
108	Dic₃₈	—	8	2	no	—
109	Dic₃₈	—	8	2	no	—
110	C₈×C₁₉	—	8	2	no	—
111	C₁₉⋊C₈	—	4	4	no	—
112	#2975	—	19	1	no	—
113	#2547	—	19	1	no	—
114	#1800	D₁₉	1	1	yes	characteristic
115	#1546	—	19	2	no	—
116	#1303	—	19	2	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	2	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	#386	1	1	yes	characteristic
125	C₂²×C₁₉	#417	1	1	yes	characteristic
126	C₂²×C₁₉	#418	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	4	2	no	—
130	C₄×C₁₉	#455	1	2	yes	—
131	C₄×C₁₉	#468	1	2	yes	—
132	C₄×C₁₉	#469	1	2	yes	—
133	Dic₁₉	—	8	2	no	—
134	Dic₁₉	—	8	2	no	—
135	C₂×C₄⋊Q₈	—	19	1	no	—
136	C₂×#124	—	38	1	no	—
137	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
138	#436	—	38	4	no	—
139	#431	—	19	2	no	—
140	#423	C₂×D₁₉	1	2	yes	—
141	C₂×#100	—	2	1	no	—
142	#407	—	38	2	no	—
143	#397	—	19	4	no	—
144	#391	—	38	1	no	—
145	#380	—	38	2	no	—
146	C₄×C₄⋊C₄	—	19	1	no	—
147	#343	—	2	1	no	—
148	#332	—	38	4	no	—
149	C₂×C₁₉	—	2	1	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	—	8	2	no	—
152	C₂×C₁₉	#1885	1	1	yes	characteristic
153	C₂×C₁₉	#1895	1	1	yes	characteristic
154	C₂×C₁₉	#1915	1	1	yes	characteristic
155	C₂²×Q₈	—	38	1	no	—
156	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂³×C₄	D₇₆	1	2	yes	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	—	38	4	no	—
160	C₄⋊Q₈	—	38	2	no	—
161	C₄⋊Q₈	—	38	2	no	—
162	#124	—	76	4	no	—
163	C₄×D₄	—	2	2	no	—
164	C₄×D₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	19	2	no	—
166	C₂×C₄⋊C₄	—	38	1	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	—	38	4	no	—
170	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
171	C₂×C₄²	—	38	1	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	19	4	no	—
176	#100	—	4	2	no	—
177	C₂²⋊C₈	—	38	4	no	—
178	C₂²⋊C₈	—	38	2	no	—
179	C₄×C₈	—	38	2	no	—
180	#95	—	19	2	no	—
181	#95	—	38	4	no	—
182	C₁₉	#9401	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
184	C₂×Q₈	—	76	1	no	—
185	C₂×Q₈	—	76	2	no	—
186	C₂×Q₈	—	76	1	no	—
187	C₂×Q₈	—	76	2	no	—
188	C₂×D₄	—	2	1	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	2	1	no	—
191	C₂×D₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	4	4	no	—
195	C₂²×C₄	—	38	2	no	—
196	C₂²×C₄	—	38	2	no	—
197	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
198	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
201	M₁₆	—	4	2	no	—
202	M₁₆	—	4	2	no	—
203	M₁₆	—	152	4	no	—
204	C₂×C₈	—	4	2	no	—
205	C₂×C₈	—	38	4	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	38	4	no	—
208	C₄⋊C₄	—	76	2	no	—
209	C₄⋊C₄	—	76	1	no	—
210	C₄⋊C₄	—	76	1	no	—
211	C₂²⋊C₄	—	2	4	no	—
212	C₂²⋊C₄	—	76	8	no	—
213	C₄²	—	76	2	no	—
214	C₄²	D₄×D₁₉	1	2	yes	—
215	C₄²	#64543	1	2	yes	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	2	no	—
218	C₂³	—	2	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	2	no	—
221	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
222	Q₈	—	152	2	no	—
223	Q₈	—	152	2	no	—
224	D₄	—	4	2	no	—
225	D₄	—	4	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	4	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	8	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	—	76	2	no	—
235	C₂×C₄	—	76	2	no	—
236	C₂×C₄	—	76	2	no	—
237	C₂×C₄	—	76	2	no	—
238	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
239	C₂×C₄	#10597328	1	1	yes	characteristic
240	C₂×C₄	#10597332	1	1	yes	characteristic
241	C₂×C₄	#10597378	1	1	yes	characteristic
242	C₂×C₄	#10597385	1	2	yes	—
243	C₂×C₄	#10597388	1	1	yes	characteristic
244	C₂×C₄	#10597395	1	2	yes	—
245	C₈	—	8	2	no	—
246	C₈	—	76	4	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	—	4	4	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	8	2	no	—
254	C₂²	#11926421	1	1	yes	characteristic
255	C₂²	#11926543	1	1	yes	characteristic
256	C₂²	#11926548	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	2	1	no	—
259	C₄	—	4	2	no	—
260	C₄	—	152	2	no	—
261	C₄	—	152	2	no	—
262	C₄	#11926724	1	2	yes	—
263	C₄	#11926792	1	2	yes	—
264	C₄	#11926795	1	2	yes	—
265	C₂	—	2	1	no	—
266	C₂	—	2	1	no	—
267	C₂	—	8	2	no	—
268	C₂	#14564021	1	1	yes	characteristic
269	C₂	#14564071	1	1	yes	characteristic
270	C₂	#14564185	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572676

C₂

yes

maximal, characteristic

#14568627

C₂

yes

maximal, characteristic

#14562308

C₂

yes

maximal, complemented

#14561536

C₂

yes

maximal, complemented

C₁₉×#1800

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

C₂²

yes

—

#11926508

—

#11926469

C₄

yes

—

#11926449

—

#11926404

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926291

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#100

—

C₁₉×#343

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×Dic₃₈

—

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

#10597382

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

#10597315

—

#10597315

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×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

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

#9401

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₁₉

#137

yes

characteristic

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

Dic₃₈

—

109

Dic₃₈

—

110

C₈×C₁₉

—

111

C₁₉⋊C₈

—

112

#2975

—

113

#2547

—

114

#1800

D₁₉

yes

characteristic

115

#1546

—

116

#1303

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

#386

yes

characteristic

125

C₂²×C₁₉

#417

yes

characteristic

126

C₂²×C₁₉

#418

yes

characteristic

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#455

yes

—

131

C₄×C₁₉

#468

yes

—

132

C₄×C₁₉

#469

yes

—

133

Dic₁₉

—

134

Dic₁₉

—

135

C₂×C₄⋊Q₈

—

136

C₂×#124

—

137

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

138

#436

—

139

#431

—

140

#423

C₂×D₁₉

yes

—

141

C₂×#100

—

142

#407

—

143

#397

—

144

#391

—

145

#380

—

146

C₄×C₄⋊C₄

—

147

#343

—

148

#332

—

149

C₂×C₁₉

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

#1885

yes

characteristic

153

C₂×C₁₉

#1895

yes

characteristic

154

C₂×C₁₉

#1915

yes

characteristic

155

C₂²×Q₈

—

156

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

157

C₂³×C₄

D₇₆

yes

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

#124

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

169

C₂×C₂²⋊C₄

—

170

C₂×C₂²⋊C₄

C₄×D₁₉

yes

—

171

C₂×C₄²

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

#100

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

#95

—

181

#95

—

182

C₁₉

#9401

yes

characteristic, complemented, Sylow

183

C₂⁴

(C₂×D₁₉)⋊C₄

yes

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

198

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

199

C₂²×C₄

C₂×D₇₆

yes

characteristic

200

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

152

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₂²⋊C₄

—

213

C₄²

—

214

C₄²

D₄×D₁₉

yes

—

215

C₄²

#64543

yes

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

222

Q₈

—

152

—

223

Q₈

—

152

—

224

D₄

—

225

D₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

239

C₂×C₄

#10597328

yes

characteristic

240

C₂×C₄

#10597332

yes

characteristic

241

C₂×C₄

#10597378

yes

characteristic

242

C₂×C₄

#10597385

yes

—

243

C₂×C₄

#10597388

yes

characteristic

244

C₂×C₄

#10597395

yes

—

245

C₈

—

246

C₈

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926421

yes

characteristic

255

C₂²

#11926543

yes

characteristic

256

C₂²

#11926548

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

152

—

261

C₄

—

152

—

262

C₄

#11926724

yes

—

263

C₄

#11926792

yes

—

264

C₄

#11926795

yes

—

265

C₂

—

266

C₂

—

267

C₂

—

268

C₂

#14564021

yes

characteristic

269

C₂

#14564071

yes

characteristic

270

C₂

#14564185

yes

characteristic

	subgroup	G/H
center	C₂²	#11926421
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1800	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1800	D₁₉
hypocenter	C₁₉	#9401
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#11926421

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1800

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

N	H ≅ G/N	type
3. #14562308	C₂	semidirect
4. #14561536	C₂	semidirect
182. C₁₉	#9401	semidirect

H ≅ G/N

type

3. #14562308

C₂

semidirect

4. #14561536

C₂

semidirect

182. C₁₉

#9401

semidirect

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

subgroup	index
#14572676	2
#14568627	2
#14562308	2
#14561536	2
C₁₉×#1800	2
#9401	19

subgroup

index

C₁₉×#1800

Subgroups — #18079942

Conjugacy classes of subgroups

Complements

Maximal subgroups