Group #18079967 — subgroups

Subgroups — #18079967

Order 4864.

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

normal subgroups only

This group has 554 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	#14572720	C₂	1	1	yes	maximal, characteristic, complemented
2	#14568634	C₂	1	1	yes	maximal, characteristic
3	#14562304	C₂	1	2	yes	maximal
4	#14561536	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	C₂×#10597393	—	2	1	no	—
8	#11926675	—	2	4	no	—
9	#11926601	—	2	2	no	—
10	#11926597	C₂²	1	2	yes	—
11	#11926461	C₄	1	4	yes	—
12	#11926446	—	2	2	no	—
13	#11926445	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926287	—	2	4	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₁₉×#101	—	2	1	no	—
19	C₁₉×#343	—	2	1	no	—
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	—	2	1	no	—
23	C₂²×D₇₆	C₂×C₄	1	2	yes	—
24	C₂×M₁₆×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	#10597393	—	4	4	no	—
32	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
33	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₄×Dic₁₉	—	2	1	no	—
36	#10597320	—	2	2	no	—
37	#10597320	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×#101	—	4	2	no	—
41	C₁₉⋊#95	C₂×C₄	1	2	yes	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	#10597260	—	2	4	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂³×D₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₈×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₁₉	—	2	2	no	—
58	C₂×D₇₆	—	2	4	no	—
59	C₂×D₇₆	—	4	4	no	—
60	C₂×D₇₆	—	4	1	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	—	4	1	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	1	no	—
65	C₂×D₇₆	—	4	1	no	—
66	C₂×D₇₆	—	8	2	no	—
67	M₁₆×C₁₉	—	4	2	no	—
68	M₁₆×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	C₂×D₄	1	2	yes	—
75	C₄²×C₁₉	#41	1	2	yes	—
76	(C₂×D₁₉)⋊C₄	—	4	8	no	—
77	(C₂×D₁₉)⋊C₄	—	8	4	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄×Dic₁₉	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	2	4	no	—
81	#9406	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×D₁₉	—	4	4	no	—
84	C₂²×D₁₉	—	4	4	no	—
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	2	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	Q₈×C₁₉	—	4	2	no	—
89	Q₈×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	4	1	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	2	yes	—
100	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
101	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	D₇₆	—	8	4	no	—
108	D₇₆	—	8	2	no	—
109	D₇₆	—	8	2	no	—
110	D₇₆	—	8	2	no	—
111	D₇₆	—	8	2	no	—
112	C₈×C₁₉	—	8	2	no	—
113	C₁₉⋊C₈	—	4	4	no	—
114	#2983	—	19	1	no	—
115	#2548	—	19	1	no	—
116	#1801	D₁₉	1	1	yes	characteristic, complemented
117	#1545	—	19	2	no	—
118	#1303	—	19	2	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	#386	1	1	yes	characteristic
122	C₂²×C₁₉	#417	1	1	yes	characteristic
123	C₂²×C₁₉	#418	1	1	yes	characteristic
124	C₂×D₁₉	—	8	4	no	—
125	C₂×D₁₉	—	8	4	no	—
126	C₂×D₁₉	—	8	2	no	—
127	C₂×D₁₉	—	8	2	no	—
128	C₂×D₁₉	—	8	2	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	2	no	—
131	C₄×C₁₉	—	4	2	no	—
132	C₄×C₁₉	—	4	2	no	—
133	C₄×C₁₉	#454	1	2	yes	—
134	C₄×C₁₉	#468	1	2	yes	—
135	C₄×C₁₉	#469	1	2	yes	—
136	Dic₁₉	—	8	2	no	—
137	C₂×#127	—	19	1	no	—
138	C₂×#124	—	38	1	no	—
139	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
140	#446	—	38	4	no	—
141	#432	—	38	2	no	—
142	#431	—	19	2	no	—
143	#423	C₂×D₁₉	1	2	yes	—
144	C₂×#101	—	2	1	no	—
145	#394	—	19	4	no	—
146	#390	—	38	1	no	—
147	#390	—	38	2	no	—
148	C₄×C₄⋊C₄	—	19	1	no	—
149	#343	—	2	1	no	—
150	#331	—	38	4	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	#1888	1	1	yes	characteristic
154	C₂×C₁₉	#1895	1	1	yes	characteristic
155	C₂×C₁₉	#1914	1	1	yes	characteristic
156	D₁₉	—	16	2	no	—
157	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
158	C₂²×D₄	—	19	2	no	—
159	C₂²×D₄	—	38	1	no	—
160	C₂²×D₄	—	38	1	no	—
161	C₂×M₁₆	—	2	2	no	—
162	#127	—	38	2	no	—
163	#127	—	38	2	no	—
164	#124	—	76	4	no	—
165	C₄×Q₈	—	2	2	no	—
166	C₄×Q₈	—	2	2	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	—	38	4	no	—
171	C₂×C₂²⋊C₄	—	38	4	no	—
172	C₂×C₄²	—	38	1	no	—
173	C₂×C₄²	D₇₆	1	2	yes	—
174	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	—	2	2	no	—
177	C₄⋊C₈	—	19	4	no	—
178	C₄⋊C₈	—	38	4	no	—
179	#101	—	4	2	no	—
180	C₂²⋊C₈	—	38	2	no	—
181	#97	—	38	4	no	—
182	C₄×C₈	—	38	2	no	—
183	#95	—	19	2	no	—
184	C₁₉	#9406	1	1	yes	characteristic, complemented, Sylow
185	C₂⁴	—	38	2	no	—
186	C₂×Q₈	—	2	1	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×Q₈	—	2	1	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×D₄	—	38	4	no	—
191	C₂×D₄	—	76	4	no	—
192	C₂×D₄	—	76	1	no	—
193	C₂×D₄	—	76	2	no	—
194	C₂×D₄	—	76	1	no	—
195	C₂×D₄	—	76	2	no	—
196	C₂×D₄	—	76	1	no	—
197	C₂×D₄	—	76	1	no	—
198	C₂×D₄	—	152	2	no	—
199	C₂²×C₄	—	38	2	no	—
200	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
201	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
202	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	M₁₆	—	4	2	no	—
206	M₁₆	—	4	2	no	—
207	C₂×C₈	—	4	2	no	—
208	C₂×C₈	—	38	4	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₂²⋊C₄	—	76	8	no	—
213	C₂²⋊C₄	—	152	4	no	—
214	C₄²	—	2	2	no	—
215	C₄²	—	2	2	no	—
216	C₄²	—	76	2	no	—
217	C₄²	D₄×D₁₉	1	2	yes	—
218	C₄²	#64543	1	2	yes	—
219	C₂³	—	76	4	no	—
220	C₂³	—	76	4	no	—
221	C₂³	—	76	2	no	—
222	C₂³	—	76	2	no	—
223	C₂³	—	76	2	no	—
224	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
225	Q₈	—	4	2	no	—
226	Q₈	—	4	2	no	—
227	D₄	—	152	4	no	—
228	D₄	—	152	2	no	—
229	D₄	—	152	2	no	—
230	D₄	—	152	2	no	—
231	D₄	—	152	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	—	76	2	no	—
241	C₂×C₄	—	76	2	no	—
242	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
243	C₂×C₄	#10597328	1	1	yes	characteristic
244	C₂×C₄	#10597332	1	1	yes	characteristic
245	C₂×C₄	#10597378	1	1	yes	characteristic
246	C₂×C₄	#10597385	1	2	yes	—
247	C₂×C₄	#10597388	1	1	yes	characteristic
248	C₂×C₄	#10597395	1	2	yes	—
249	C₈	—	8	2	no	—
250	C₈	—	76	4	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	152	4	no	—
254	C₂²	—	152	4	no	—
255	C₂²	—	152	2	no	—
256	C₂²	—	152	2	no	—
257	C₂²	—	152	2	no	—
258	C₂²	#11926421	1	1	yes	characteristic
259	C₂²	#11926543	1	1	yes	characteristic
260	C₂²	#11926548	1	1	yes	characteristic
261	C₄	—	2	2	no	—
262	C₄	—	2	1	no	—
263	C₄	—	4	2	no	—
264	C₄	—	4	2	no	—
265	C₄	—	152	2	no	—
266	C₄	#11926719	1	2	yes	—
267	C₄	#11926792	1	2	yes	—
268	C₄	#11926795	1	2	yes	—
269	C₂	—	2	1	no	—
270	C₂	—	2	1	no	—
271	C₂	—	304	2	no	—
272	C₂	#14564036	1	1	yes	characteristic
273	C₂	#14564071	1	1	yes	characteristic
274	C₂	#14564180	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic, complemented

#14568634

C₂

yes

maximal, characteristic

#14562304

C₂

yes

maximal

#14561536

C₂

yes

maximal, complemented

C₁₉×#1801

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

—

C₂²

yes

—

#11926461

C₄

yes

—

#11926446

—

#11926445

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926287

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₂×C₁₉×#101

—

C₁₉×#343

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597393

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

#10597320

—

#10597320

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉⋊#95

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

#9406

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

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

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

100

C₂×C₄×C₁₉

#123

yes

characteristic

101

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₁₉

#137

yes

characteristic

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

D₇₆

—

108

D₇₆

—

109

D₇₆

—

110

D₇₆

—

111

D₇₆

—

112

C₈×C₁₉

—

113

C₁₉⋊C₈

—

114

#2983

—

115

#2548

—

116

#1801

D₁₉

yes

characteristic, complemented

117

#1545

—

118

#1303

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#386

yes

characteristic

122

C₂²×C₁₉

#417

yes

characteristic

123

C₂²×C₁₉

#418

yes

characteristic

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₂×D₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

#454

yes

—

134

C₄×C₁₉

#468

yes

—

135

C₄×C₁₉

#469

yes

—

136

Dic₁₉

—

137

C₂×#127

—

138

C₂×#124

—

139

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

140

#446

—

141

#432

—

142

#431

—

143

#423

C₂×D₁₉

yes

—

144

C₂×#101

—

145

#394

—

146

#390

—

147

#390

—

148

C₄×C₄⋊C₄

—

149

#343

—

150

#331

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#1888

yes

characteristic

154

C₂×C₁₉

#1895

yes

characteristic

155

C₂×C₁₉

#1914

yes

characteristic

156

D₁₉

—

157

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

158

C₂²×D₄

—

159

C₂²×D₄

—

160

C₂²×D₄

—

161

C₂×M₁₆

—

162

#127

—

163

#127

—

164

#124

—

165

C₄×Q₈

—

166

C₄×Q₈

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₄×D₁₉

yes

—

169

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

—

172

C₂×C₄²

—

173

C₂×C₄²

D₇₆

yes

—

174

C₂×C₄²

C₂²×D₁₉

yes

characteristic

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

#101

—

180

C₂²⋊C₈

—

181

#97

—

182

C₄×C₈

—

183

#95

—

184

C₁₉

#9406

yes

characteristic, complemented, Sylow

185

C₂⁴

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

152

—

199

C₂²×C₄

—

200

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

201

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

202

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

203

C₂²×C₄

C₂×D₇₆

yes

characteristic

204

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

205

M₁₆

—

206

M₁₆

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

152

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

D₄×D₁₉

yes

—

218

C₄²

#64543

yes

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

225

Q₈

—

226

Q₈

—

227

D₄

—

152

—

228

D₄

—

152

—

229

D₄

—

152

—

230

D₄

—

152

—

231

D₄

—

152

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

243

C₂×C₄

#10597328

yes

characteristic

244

C₂×C₄

#10597332

yes

characteristic

245

C₂×C₄

#10597378

yes

characteristic

246

C₂×C₄

#10597385

yes

—

247

C₂×C₄

#10597388

yes

characteristic

248

C₂×C₄

#10597395

yes

—

249

C₈

—

250

C₈

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

152

—

254

C₂²

—

152

—

255

C₂²

—

152

—

256

C₂²

—

152

—

257

C₂²

—

152

—

258

C₂²

#11926421

yes

characteristic

259

C₂²

#11926543

yes

characteristic

260

C₂²

#11926548

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

—

265

C₄

—

152

—

266

C₄

#11926719

yes

—

267

C₄

#11926792

yes

—

268

C₄

#11926795

yes

—

269

C₂

—

270

C₂

—

271

C₂

—

304

—

272

C₂

#14564036

yes

characteristic

273

C₂

#14564071

yes

characteristic

274

C₂

#14564180

yes

characteristic

	subgroup	G/H
center	C₂²	#11926421
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1801	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1801	D₁₉
hypocenter	C₁₉	#9406
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#11926421

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1801

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
1. #14572720	C₂	semidirect
4. #14561536	C₂	semidirect
5. C₁₉×#1801	C₂	semidirect
116. #1801	D₁₉	semidirect
184. C₁₉	#9406	semidirect

H ≅ G/N

type

1. #14572720

C₂

semidirect

4. #14561536

C₂

semidirect

5. C₁₉×#1801

C₂

semidirect

116. #1801

D₁₉

semidirect

184. C₁₉

#9406

semidirect

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

subgroup	index
#14572720	2
#14568634	2
#14562304	2
#14561536	2
C₁₉×#1801	2
#9406	19

subgroup

index

C₁₉×#1801

Subgroups — #18079967

Conjugacy classes of subgroups

Complements

Maximal subgroups