Group #18075810 — subgroups

Subgroups — #18075810

Order 4864.

414 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14572348	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926297	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562313	C₂	1	2	yes	maximal
4	#14561509	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	—	2	1	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	C₄	1	2	yes	—
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	C₄	1	2	yes	—
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
14	#11926510	—	2	1	no	—
15	#11926297	—	2	1	no	—
16	#11926297	—	2	1	no	—
17	#11926291	—	2	2	no	—
18	#11926287	—	2	2	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#341	—	2	1	no	—
22	C₁₉×#341	—	2	1	no	—
23	C₂×#64541	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597376	—	2	1	no	—
29	#10597376	Q₈	1	2	yes	—
30	C₂×#64520	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	#10597347	—	4	4	no	—
33	C₂×#64515	—	2	2	no	—
34	C₂×C₈×D₁₉	—	2	2	no	—
35	#10597321	—	2	1	no	—
36	#10597320	D₄	1	1	yes	characteristic
37	C₄×D₇₆	—	2	1	no	—
38	C₄×D₇₆	C₂×C₄	1	2	yes	—
39	#10597315	D₄	1	1	yes	characteristic
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	(C₂×D₁₉)⋊C₈	—	2	2	no	—
47	(C₂×D₁₉)⋊C₈	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉	—	2	2	no	—
56	#64541	—	4	2	no	—
57	#64541	—	4	2	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	—	2	1	no	—
60	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
61	C₂×C₄×D₁₉	—	2	2	no	—
62	C₂×Dic₃₈	—	2	1	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	M₁₆×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	(C₂×D₁₉)⋊C₄	—	2	2	no	—
77	(C₂×D₁₉)⋊C₄	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	1	no	—
79	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
80	#64520	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	8	2	no	—
84	#64515	—	4	4	no	—
85	C₈×D₁₉	—	4	4	no	—
86	#8688	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂²×D₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#135	1	2	yes	—
99	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
100	C₂²⋊D₁₉	—	4	4	no	—
101	C₂×Dic₁₉	—	2	2	no	—
102	D₇₆	—	4	2	no	—
103	D₇₆	—	4	2	no	—
104	D₇₆	—	4	1	no	—
105	D₇₆	—	4	1	no	—
106	C₄×D₁₉	—	4	2	no	—
107	C₄×D₁₉	—	4	2	no	—
108	Dic₃₈	—	4	2	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	1	no	—
113	C₈×C₁₉	—	8	2	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	C₁₉⋊C₈	—	8	2	no	—
116	#2931	—	19	1	no	—
117	#1837	D₁₉	1	1	yes	characteristic, complemented
118	C₂×#335	—	19	1	no	—
119	#1547	—	19	2	no	—
120	#1292	—	19	2	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	#380	1	1	yes	characteristic
124	C₂²×C₁₉	#478	1	2	yes	—
125	C₂×D₁₉	—	4	2	no	—
126	C₂×D₁₉	—	4	2	no	—
127	C₂×D₁₉	—	4	2	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	#416	1	1	yes	characteristic
132	C₄×C₁₉	#418	1	1	yes	characteristic
133	C₄×C₁₉	#463	1	2	yes	—
134	C₄×C₁₉	#472	1	1	yes	characteristic
135	C₄×C₁₉	#473	1	1	yes	characteristic
136	Dic₁₉	—	4	2	no	—
137	C₂×#131	—	38	1	no	—
138	#532	—	19	1	no	—
139	#436	—	19	2	no	—
140	#436	—	38	1	no	—
141	C₈×D₄	—	19	2	no	—
142	C₈×D₄	—	38	1	no	—
143	#423	—	19	1	no	—
144	#423	C₂×D₁₉	1	2	yes	—
145	C₂×C₄⋊C₈	—	19	2	no	—
146	#408	—	38	1	no	—
147	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
148	#341	—	2	1	no	—
149	#341	—	2	1	no	—
150	#335	—	38	1	no	—
151	#335	—	38	1	no	—
152	#332	—	38	2	no	—
153	#331	—	38	2	no	—
154	C₂×C₁₉	—	2	2	no	—
155	C₂×C₁₉	#1804	1	1	yes	characteristic
156	C₂×C₁₉	#1813	1	1	yes	characteristic
157	C₂×C₁₉	#1816	1	1	yes	characteristic
158	D₁₉	—	8	2	no	—
159	C₂×#41	—	38	1	no	—
160	#131	—	76	4	no	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	—	38	1	no	—
163	C₂×M₁₆	—	38	2	no	—
164	C₂²×C₈	—	38	2	no	—
165	C₂²×C₈	—	38	2	no	—
166	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
168	C₄⋊Q₈	—	19	1	no	—
169	#127	—	19	1	no	—
170	#124	—	38	1	no	—
171	#121	—	19	2	no	—
172	#121	—	38	1	no	—
173	C₄×D₄	—	19	2	no	—
174	C₄×D₄	—	38	1	no	—
175	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	19	2	no	—
179	C₄⋊C₈	—	38	1	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₄⋊C₈	—	38	2	no	—
182	C₂²⋊C₈	—	38	2	no	—
183	C₂²⋊C₈	—	38	2	no	—
184	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
186	C₄×C₈	D₇₆	1	1	yes	characteristic
187	C₄×C₈	D₇₆	1	1	yes	characteristic
188	C₁₉	#8688	1	1	yes	characteristic, complemented, Sylow
189	#41	—	76	2	no	—
190	#41	—	76	2	no	—
191	C₂×Q₈	—	38	1	no	—
192	C₂×D₄	—	19	2	no	—
193	C₂×D₄	—	38	2	no	—
194	C₂×D₄	—	38	1	no	—
195	C₂×D₄	—	38	1	no	—
196	C₂²×C₄	—	38	2	no	—
197	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
198	C₂²×C₄	#64545	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	M₁₆	—	76	4	no	—
203	M₁₆	—	76	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	38	2	no	—
208	C₂×C₈	—	76	4	no	—
209	C₂×C₈	—	76	2	no	—
210	C₂×C₈	—	152	2	no	—
211	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
213	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
214	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
215	C₄⋊C₄	—	19	2	no	—
216	C₄⋊C₄	—	38	1	no	—
217	C₂²⋊C₄	—	38	2	no	—
218	C₂²⋊C₄	—	38	2	no	—
219	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
220	C₄²	C₂×D₇₆	1	1	yes	characteristic
221	C₄²	D₄×D₁₉	1	1	yes	characteristic
222	C₄²	#64543	1	1	yes	characteristic
223	C₂³	—	38	2	no	—
224	C₂³	#10597392	1	1	yes	characteristic
225	Q₈	—	76	2	no	—
226	D₄	—	76	2	no	—
227	D₄	—	76	4	no	—
228	D₄	—	76	1	no	—
229	D₄	—	76	1	no	—
230	D₄	—	76	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	38	2	no	—
235	C₂×C₄	—	76	2	no	—
236	C₂×C₄	—	76	2	no	—
237	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
238	C₂×C₄	#10597338	1	1	yes	characteristic
239	C₂×C₄	#10597341	1	1	yes	characteristic
240	C₂×C₄	#10597343	1	1	yes	characteristic
241	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
242	C₂×C₄	#10597384	1	1	yes	characteristic
243	C₂×C₄	#10597395	1	2	yes	—
244	C₂×C₄	#10597396	1	2	yes	—
245	C₈	—	2	1	no	—
246	C₈	—	2	1	no	—
247	C₈	—	2	1	no	—
248	C₈	—	2	1	no	—
249	C₈	—	8	2	no	—
250	C₈	—	76	2	no	—
251	C₈	—	152	2	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	76	2	no	—
255	C₂²	—	76	2	no	—
256	C₂²	—	76	2	no	—
257	C₂²	#11926401	1	1	yes	characteristic
258	C₂²	#11926841	1	2	yes	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	76	2	no	—
263	C₄	#11926538	1	1	yes	characteristic
264	C₄	#11926548	1	1	yes	characteristic
265	C₄	#11926756	1	2	yes	—
266	C₄	#11926815	1	1	yes	characteristic
267	C₄	#11926820	1	1	yes	characteristic
268	C₂	—	2	2	no	—
269	C₂	—	152	2	no	—
270	C₂	#14563642	1	1	yes	characteristic
271	C₂	#14563682	1	1	yes	characteristic
272	C₂	#14563696	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572348

C₂

yes

maximal, characteristic

C₂×#11926297

C₂

yes

maximal, characteristic, complemented

#14562313

C₂

yes

maximal

#14561509

C₂

yes

maximal, complemented

C₁₉×#1837

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

—

#11927094

C₂²

yes

characteristic

#11926623

—

#11926623

C₄

yes

—

C₈×D₇₆

—

C₈×D₇₆

C₄

yes

—

#11926568

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#341

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

Q₈

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

#10597347

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

—

#10597320

D₄

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

C₂×C₄

yes

—

#10597315

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

#8688

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

100

C₂²⋊D₁₉

—

101

C₂×Dic₁₉

—

102

D₇₆

—

103

D₇₆

—

104

D₇₆

—

105

D₇₆

—

106

C₄×D₁₉

—

107

C₄×D₁₉

—

108

Dic₃₈

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

#2931

—

117

#1837

D₁₉

yes

characteristic, complemented

118

C₂×#335

—

119

#1547

—

120

#1292

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#380

yes

characteristic

124

C₂²×C₁₉

#478

yes

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

#416

yes

characteristic

132

C₄×C₁₉

#418

yes

characteristic

133

C₄×C₁₉

#463

yes

—

134

C₄×C₁₉

#472

yes

characteristic

135

C₄×C₁₉

#473

yes

characteristic

136

Dic₁₉

—

137

C₂×#131

—

138

#532

—

139

#436

—

140

#436

—

141

C₈×D₄

—

142

C₈×D₄

—

143

#423

—

144

#423

C₂×D₁₉

yes

—

145

C₂×C₄⋊C₈

—

146

#408

—

147

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

148

#341

—

149

#341

—

150

#335

—

151

#335

—

152

#332

—

153

#331

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#1804

yes

characteristic

156

C₂×C₁₉

#1813

yes

characteristic

157

C₂×C₁₉

#1816

yes

characteristic

158

D₁₉

—

159

C₂×#41

—

160

#131

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂²×C₈

—

165

C₂²×C₈

—

166

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

167

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

168

C₄⋊Q₈

—

169

#127

—

170

#124

—

171

#121

—

172

#121

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄²

C₂²×D₁₉

yes

characteristic

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₂²⋊C₈

—

183

C₂²⋊C₈

—

184

C₄×C₈

C₄×D₁₉

yes

characteristic

185

C₄×C₈

C₄×D₁₉

yes

characteristic

186

C₄×C₈

D₇₆

yes

characteristic

187

C₄×C₈

D₇₆

yes

characteristic

188

C₁₉

#8688

yes

characteristic, complemented, Sylow

189

#41

—

190

#41

—

191

C₂×Q₈

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

Q₈×D₁₉

yes

characteristic

198

C₂²×C₄

#64545

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

152

—

211

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

212

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

213

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

214

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

C₂×C₄×D₁₉

yes

characteristic

220

C₄²

C₂×D₇₆

yes

characteristic

221

C₄²

D₄×D₁₉

yes

characteristic

222

C₄²

#64543

yes

characteristic

223

C₂³

—

224

C₂³

#10597392

yes

characteristic

225

Q₈

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

D₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

238

C₂×C₄

#10597338

yes

characteristic

239

C₂×C₄

#10597341

yes

characteristic

240

C₂×C₄

#10597343

yes

characteristic

241

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

242

C₂×C₄

#10597384

yes

characteristic

243

C₂×C₄

#10597395

yes

—

244

C₂×C₄

#10597396

yes

—

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

152

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

#11926401

yes

characteristic

258

C₂²

#11926841

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#11926538

yes

characteristic

264

C₄

#11926548

yes

characteristic

265

C₄

#11926756

yes

—

266

C₄

#11926815

yes

characteristic

267

C₄

#11926820

yes

characteristic

268

C₂

—

269

C₂

—

152

—

270

C₂

#14563642

yes

characteristic

271

C₂

#14563682

yes

characteristic

272

C₂

#14563696

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#8688
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#11926401

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1837

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. C₂×#11926297	C₂	semidirect
4. #14561509	C₂	semidirect
5. C₁₉×#1837	C₂	semidirect
117. #1837	D₁₉	semidirect
188. C₁₉	#8688	semidirect

H ≅ G/N

type

2. C₂×#11926297

C₂

semidirect

4. #14561509

C₂

semidirect

5. C₁₉×#1837

C₂

semidirect

117. #1837

D₁₉

semidirect

188. C₁₉

#8688

semidirect

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

subgroup	index
#14572348	2
C₂×#11926297	2
#14562313	2
#14561509	2
C₁₉×#1837	2
#8688	19

subgroup

index

C₁₉×#1837

Subgroups — #18075810

Conjugacy classes of subgroups

Complements

Maximal subgroups