Group #18081945 — subgroups

Subgroups — #18081945

Order 4864.

462 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14574214	C₂	1	1	yes	maximal, characteristic
2	#14563321	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562247	C₂	1	2	yes	maximal, complemented
4	#14562144	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926921	C₄	1	1	yes	characteristic, complemented
9	#11926891	C₄	1	2	yes	complemented
10	#11926780	—	2	1	no	—
11	#11926780	—	2	1	no	—
12	C₄×D₁₅₂	—	2	1	no	—
13	C₄×D₁₅₂	—	2	1	no	—
14	C₂×#10597260	C₂²	1	1	yes	characteristic
15	C₂×#10597272	—	2	1	no	—
16	C₂×C₈×Dic₁₉	—	2	1	no	—
17	#11926390	C₂²	1	1	yes	characteristic
18	#11926283	—	2	4	no	—
19	#11926279	—	2	4	no	—
20	C₁₉×#432	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#335	—	2	1	no	—
23	C₁₉×#334	—	2	1	no	—
24	C₂×#64541	—	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	2	no	—
29	#10597376	—	2	2	no	—
30	C₂×C₄×Dic₁₉	—	2	1	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	C₂×D₁₅₂	—	2	1	no	—
33	C₂×D₁₅₂	—	2	1	no	—
34	#10597321	—	2	2	no	—
35	#10597320	C₂×C₄	1	2	yes	—
36	C₄×D₇₆	—	2	2	no	—
37	C₄×D₇₆	—	2	2	no	—
38	#10597315	C₂×C₄	1	2	yes	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₁₉×#97	—	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	C₁₉⋊#95	—	2	1	no	—
47	C₁₉⋊#95	D₄	1	2	yes	—
48	#10597278	—	2	2	no	—
49	#10597278	—	2	2	no	—
50	#10597275	—	2	1	no	—
51	#10597275	—	2	1	no	—
52	#10597272	—	2	4	no	—
53	C₈×Dic₁₉	—	2	4	no	—
54	#10597260	—	2	1	no	—
55	#10597260	D₄	1	2	yes	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂×C₂²⋊D₁₉	—	4	2	no	—
60	C₂²×Dic₁₉	—	2	2	no	—
61	#64541	—	8	4	no	—
62	C₂×D₇₆	—	2	2	no	—
63	C₂×D₇₆	—	2	2	no	—
64	C₂×D₇₆	—	2	2	no	—
65	C₂×C₄×D₁₉	—	4	2	no	—
66	C₂×Dic₃₈	—	2	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₉	#41	1	1	yes	characteristic
78	(C₂×D₁₉)⋊C₄	—	4	2	no	—
79	(C₂×D₁₉)⋊C₄	—	4	2	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	2	2	no	—
82	C₄×Dic₁₉	—	2	2	no	—
83	C₄×Dic₁₉	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	2	2	no	—
87	D₁₅₂	—	4	2	no	—
88	D₁₅₂	—	4	2	no	—
89	#9762	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	#121	1	1	yes	characteristic
91	C₂²×D₁₉	—	4	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
102	C₂²⋊D₁₉	—	8	4	no	—
103	C₂×Dic₁₉	—	2	4	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	D₇₆	—	4	2	no	—
108	D₇₆	—	4	2	no	—
109	D₇₆	—	8	2	no	—
110	D₇₆	—	8	2	no	—
111	C₄×D₁₉	—	8	4	no	—
112	Dic₃₈	—	8	2	no	—
113	C₈×C₁₉	—	2	1	no	—
114	C₈×C₁₉	—	2	1	no	—
115	C₈×C₁₉	—	8	2	no	—
116	C₈×C₁₉	#104	1	2	yes	—
117	C₈×C₁₉	#104	1	2	yes	—
118	C₁₉⋊C₈	—	2	4	no	—
119	#3169	—	19	1	no	—
120	#1726	—	19	1	no	—
121	#1568	D₁₉	1	1	yes	characteristic, complemented
122	#1530	—	19	2	no	—
123	#1505	—	19	2	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	#390	1	1	yes	characteristic
127	C₂²×C₁₉	#472	1	2	yes	—
128	C₂×D₁₉	—	8	2	no	—
129	C₂×D₁₉	—	8	2	no	—
130	C₂×D₁₉	—	8	2	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
137	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
138	Dic₁₉	—	4	4	no	—
139	Dic₁₉	—	8	2	no	—
140	#532	—	19	2	no	—
141	#500	—	19	1	no	—
142	#493	—	19	1	no	—
143	#486	—	19	2	no	—
144	#466	—	38	1	no	—
145	#466	—	38	1	no	—
146	C₄×D₈	—	38	1	no	—
147	C₄×D₈	—	38	1	no	—
148	#432	C₂×D₁₉	1	2	yes	—
149	C₂×#97	—	19	1	no	—
150	C₂×#97	—	38	1	no	—
151	C₂×C₄×C₈	—	38	1	no	—
152	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
153	#376	—	19	1	no	—
154	#335	—	2	1	no	—
155	#334	—	2	1	no	—
156	#329	—	38	4	no	—
157	#327	—	38	4	no	—
158	C₂×C₁₉	—	2	2	no	—
159	C₂×C₁₉	#1962	1	1	yes	characteristic
160	C₂×C₁₉	#1976	1	1	yes	characteristic
161	C₂×C₁₉	#1978	1	1	yes	characteristic
162	D₁₉	—	16	2	no	—
163	C₂×#41	—	38	2	no	—
164	C₂×D₈	—	38	1	no	—
165	C₂×D₈	—	38	1	no	—
166	C₂²×C₈	—	38	1	no	—
167	C₂²×C₈	D₇₆	1	1	yes	characteristic
168	C₂²×C₈	D₇₆	1	1	yes	characteristic
169	C₄⋊Q₈	—	19	2	no	—
170	#127	—	19	2	no	—
171	#124	—	38	2	no	—
172	#121	—	38	2	no	—
173	#121	—	38	2	no	—
174	C₄×D₄	—	38	2	no	—
175	C₄×D₄	—	38	2	no	—
176	C₂×C₄²	—	38	1	no	—
177	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
178	#107	—	38	1	no	—
179	#107	—	38	1	no	—
180	C₄⋊C₈	—	2	2	no	—
181	#102	—	38	2	no	—
182	#102	—	38	2	no	—
183	C₂²⋊C₈	—	2	2	no	—
184	#97	—	2	2	no	—
185	#97	—	19	2	no	—
186	#97	—	38	4	no	—
187	#97	—	38	1	no	—
188	C₄×C₈	—	38	4	no	—
189	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
190	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
191	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
192	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
193	#95	—	19	2	no	—
194	#95	—	38	1	no	—
195	C₁₉	#9762	1	1	yes	characteristic, complemented, Sylow
196	#41	—	152	4	no	—
197	C₂×Q₈	—	38	2	no	—
198	C₂×D₄	—	38	2	no	—
199	C₂×D₄	—	38	2	no	—
200	C₂×D₄	—	38	2	no	—
201	C₂×D₄	—	76	2	no	—
202	C₂²×C₄	—	38	2	no	—
203	C₂²×C₄	—	76	2	no	—
204	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
205	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
206	C₂²×C₄	#64545	1	1	yes	characteristic
207	D₈	—	76	2	no	—
208	D₈	—	76	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	4	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	—	38	2	no	—
214	C₂×C₈	—	38	2	no	—
215	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
218	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
219	C₄⋊C₄	—	38	2	no	—
220	C₄⋊C₄	—	38	2	no	—
221	C₂²⋊C₄	—	76	2	no	—
222	C₂²⋊C₄	—	76	2	no	—
223	C₄²	—	38	2	no	—
224	C₄²	—	38	2	no	—
225	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
226	C₄²	D₄×D₁₉	1	1	yes	characteristic
227	C₄²	#64545	1	1	yes	characteristic
228	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂³	—	76	2	no	—
230	C₂³	#10597341	1	1	yes	characteristic
231	Q₈	—	152	2	no	—
232	D₄	—	76	2	no	—
233	D₄	—	76	2	no	—
234	D₄	—	152	2	no	—
235	D₄	—	152	2	no	—
236	D₄	—	152	4	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	38	4	no	—
242	C₂×C₄	—	76	2	no	—
243	C₂×C₄	—	76	2	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	152	4	no	—
246	C₂×C₄	#10597339	1	1	yes	characteristic
247	C₂×C₄	#10597339	1	1	yes	characteristic
248	C₂×C₄	#10597341	1	1	yes	characteristic
249	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
250	C₂×C₄	#10597386	1	1	yes	characteristic
251	C₂×C₄	#10597393	1	1	yes	characteristic
252	C₈	—	2	1	no	—
253	C₈	—	2	1	no	—
254	C₈	—	8	2	no	—
255	C₈	—	38	4	no	—
256	C₈	#10597282	1	2	yes	—
257	C₈	#10597282	1	2	yes	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	152	2	no	—
261	C₂²	—	152	2	no	—
262	C₂²	—	152	2	no	—
263	C₂²	#11926445	1	1	yes	characteristic
264	C₂²	#11926815	1	2	yes	—
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	1	no	—
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	—	76	4	no	—
271	C₄	—	152	2	no	—
272	C₄	C₂×#10597282	1	1	yes	characteristic
273	C₄	C₂×#10597282	1	1	yes	characteristic
274	C₂	—	2	2	no	—
275	C₂	—	304	2	no	—
276	C₂	#14564462	1	1	yes	characteristic
277	C₂	#14564531	1	1	yes	characteristic
278	C₂	#14564543	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574214

C₂

yes

maximal, characteristic

#14563321

C₂

yes

maximal, characteristic, complemented

#14562247

C₂

yes

maximal, complemented

#14562144

C₂

yes

maximal, complemented

C₁₉×#1568

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

#11926891

C₄

yes

complemented

#11926780

—

#11926780

—

C₄×D₁₅₂

—

C₄×D₁₅₂

—

C₂×#10597260

C₂²

yes

characteristic

C₂×#10597272

—

C₂×C₈×Dic₁₉

—

#11926390

C₂²

yes

characteristic

#11926283

—

#11926279

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

#10597321

—

#10597320

C₂×C₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

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

C₁₉⋊#95

—

C₁₉⋊#95

D₄

yes

—

—

—

—

—

—

C₈×Dic₁₉

—

#10597260

—

#10597260

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

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×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

characteristic

100

C₂×C₄×C₁₉

#124

yes

characteristic

101

C₂×C₄×C₁₉

#127

yes

characteristic

102

C₂²⋊D₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

D₇₆

—

108

D₇₆

—

109

D₇₆

—

110

D₇₆

—

111

C₄×D₁₉

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₈×C₁₉

—

116

C₈×C₁₉

#104

yes

—

117

C₈×C₁₉

#104

yes

—

118

C₁₉⋊C₈

—

119

#3169

—

120

#1726

—

121

#1568

D₁₉

yes

characteristic, complemented

122

#1530

—

123

#1505

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#390

yes

characteristic

127

C₂²×C₁₉

#472

yes

—

128

C₂×D₁₉

—

129

C₂×D₁₉

—

130

C₂×D₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

C₂×#104

yes

characteristic

137

C₄×C₁₉

C₂×#104

yes

characteristic

138

Dic₁₉

—

139

Dic₁₉

—

140

#532

—

141

#500

—

142

#493

—

143

#486

—

144

#466

—

145

#466

—

146

C₄×D₈

—

147

C₄×D₈

—

148

#432

C₂×D₁₉

yes

—

149

C₂×#97

—

150

C₂×#97

—

151

C₂×C₄×C₈

—

152

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

153

#376

—

154

#335

—

155

#334

—

156

#329

—

157

#327

—

158

C₂×C₁₉

—

159

C₂×C₁₉

#1962

yes

characteristic

160

C₂×C₁₉

#1976

yes

characteristic

161

C₂×C₁₉

#1978

yes

characteristic

162

D₁₉

—

163

C₂×#41

—

164

C₂×D₈

—

165

C₂×D₈

—

166

C₂²×C₈

—

167

C₂²×C₈

D₇₆

yes

characteristic

168

C₂²×C₈

D₇₆

yes

characteristic

169

C₄⋊Q₈

—

170

#127

—

171

#124

—

172

#121

—

173

#121

—

174

C₄×D₄

—

175

C₄×D₄

—

176

C₂×C₄²

—

177

C₂×C₄²

C₂²×D₁₉

yes

characteristic

178

#107

—

179

#107

—

180

C₄⋊C₈

—

181

#102

—

182

#102

—

183

C₂²⋊C₈

—

184

#97

—

185

#97

—

186

#97

—

187

#97

—

188

C₄×C₈

—

189

C₄×C₈

C₄×D₁₉

yes

characteristic

190

C₄×C₈

C₄×D₁₉

yes

characteristic

191

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

192

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

193

#95

—

194

#95

—

195

C₁₉

#9762

yes

characteristic, complemented, Sylow

196

#41

—

152

—

197

C₂×Q₈

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

C₂×D₇₆

yes

characteristic

205

C₂²×C₄

D₄×D₁₉

yes

characteristic

206

C₂²×C₄

#64545

yes

characteristic

207

D₈

—

208

D₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

216

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

217

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

218

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₂²⋊C₄

—

222

C₂²⋊C₄

—

223

C₄²

—

224

C₄²

—

225

C₄²

C₂×C₄×D₁₉

yes

characteristic

226

C₄²

D₄×D₁₉

yes

characteristic

227

C₄²

#64545

yes

characteristic

228

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂³

—

230

C₂³

#10597341

yes

characteristic

231

Q₈

—

152

—

232

D₄

—

233

D₄

—

234

D₄

—

152

—

235

D₄

—

152

—

236

D₄

—

152

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

152

—

246

C₂×C₄

#10597339

yes

characteristic

247

C₂×C₄

#10597339

yes

characteristic

248

C₂×C₄

#10597341

yes

characteristic

249

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

250

C₂×C₄

#10597386

yes

characteristic

251

C₂×C₄

#10597393

yes

characteristic

252

C₈

—

253

C₈

—

254

C₈

—

255

C₈

—

256

C₈

#10597282

yes

—

257

C₈

#10597282

yes

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

152

—

261

C₂²

—

152

—

262

C₂²

—

152

—

263

C₂²

#11926445

yes

characteristic

264

C₂²

#11926815

yes

—

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

152

—

272

C₄

C₂×#10597282

yes

characteristic

273

C₄

C₂×#10597282

yes

characteristic

274

C₂

—

275

C₂

—

304

—

276

C₂

#14564462

yes

characteristic

277

C₂

#14564531

yes

characteristic

278

C₂

#14564543

yes

characteristic

	subgroup	G/H
center	C₂²	#11926445
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#390
prime radical	#14574214	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#9762
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926445

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
2. #14563321	C₂	semidirect
3. #14562247	C₂	semidirect
4. #14562144	C₂	semidirect
5. C₁₉×#1568	C₂	semidirect
7. #11926949	C₄	semidirect
8. #11926921	C₄	semidirect
9. #11926891	C₄	semidirect
121. #1568	D₁₉	semidirect
195. C₁₉	#9762	semidirect

H ≅ G/N

type

2. #14563321

C₂

semidirect

3. #14562247

C₂

semidirect

4. #14562144

C₂

semidirect

5. C₁₉×#1568

C₂

semidirect

7. #11926949

C₄

semidirect

8. #11926921

C₄

semidirect

9. #11926891

C₄

semidirect

121. #1568

D₁₉

semidirect

195. C₁₉

#9762

semidirect

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

subgroup	index
#14574214	2
#14563321	2
#14562247	2
#14562144	2
C₁₉×#1568	2
#9762	19

subgroup

index

C₁₉×#1568

Subgroups — #18081945

Conjugacy classes of subgroups

Complements

Maximal subgroups