Group #18073883 — subgroups

Subgroups — #18073883

Order 4864.

1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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	#14563703	C₂	1	2	yes	maximal
2	C₂×#11926270	C₂	1	4	yes	maximal
3	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	4	no	—
6	#11926270	—	2	8	no	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₉	—	2	8	no	—
9	C₂×C₄×Q₈×C₁₉	—	2	4	no	—
10	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₉	C₄	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	2	no	—
16	C₂²×Q₈×C₁₉	—	2	2	no	—
17	C₂²×Q₈×C₁₉	—	2	4	no	—
18	C₂²×Q₈×C₁₉	C₈	1	4	yes	complemented
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₄×Q₈×C₁₉	—	2	32	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	—	2	4	no	—
32	C₂×C₄²×C₁₉	—	2	4	no	—
33	C₂×C₄²×C₁₉	—	2	4	no	—
34	C₂×C₄²×C₁₉	D₄	1	4	yes	—
35	C₂²×C₁₉⋊C₈	—	2	4	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
37	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Q₈×C₁₉	—	2	8	no	—
39	C₂×Q₈×C₁₉	—	2	16	no	—
40	C₂×Q₈×C₁₉	—	2	8	no	—
41	C₂×Q₈×C₁₉	—	2	16	no	—
42	C₂×Q₈×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	2	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
59	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
60	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
61	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
62	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
65	C₄⋊C₄×C₁₉	—	2	8	no	—
66	C₄⋊C₄×C₁₉	—	2	16	no	—
67	C₄²×C₁₉	—	2	16	no	—
68	C₄²×C₁₉	—	2	8	no	—
69	C₂×C₁₉⋊C₈	—	4	8	no	—
70	C₂×C₁₉⋊C₈	—	4	4	no	—
71	#8303	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
75	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
77	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
79	Q₈×C₁₉	—	2	32	no	—
80	C₂×C₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	—	2	4	no	—
86	C₂×C₄×C₁₉	—	2	4	no	—
87	C₂×C₄×C₁₉	—	2	4	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	4	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	4	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	4	no	—
95	C₂×C₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	4	4	no	—
98	C₂×C₄×C₁₉	—	4	4	no	—
99	C₂×C₄×C₁₉	C₂²⋊C₈	1	8	yes	—
100	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
101	C₂×C₄×C₁₉	#101	1	4	yes	—
102	C₂×C₄×C₁₉	#120	1	4	yes	—
103	C₁₉⋊C₈	—	8	4	no	—
104	C₂²×C₄×Q₈	D₁₉	1	1	yes	characteristic
105	#1817	—	19	2	no	—
106	C₂×#324	—	19	4	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	4	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	#379	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
114	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
115	C₂²×C₁₉	#407	1	2	yes	—
116	C₂²×C₁₉	#407	1	1	yes	characteristic
117	C₂²×C₁₉	#410	1	2	yes	—
118	C₂²×C₁₉	C₂×#101	1	2	yes	—
119	C₄×C₁₉	—	2	8	no	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	—	2	4	no	—
123	C₄×C₁₉	—	4	4	no	—
124	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
125	C₂×C₄×Q₈	—	2	8	no	—
126	C₂×C₄×Q₈	—	2	4	no	—
127	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
128	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
129	C₂²×C₄²	Dic₁₉	1	2	yes	—
130	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
131	C₂×C₂²⋊C₈	—	19	4	no	—
132	#336	—	38	4	no	—
133	#324	—	38	8	no	—
134	C₂×C₁₉	—	2	2	no	—
135	C₂×C₁₉	—	2	2	no	—
136	C₂×C₁₉	#1461	1	2	yes	—
137	C₂×C₁₉	#1467	1	2	yes	—
138	C₂×C₁₉	#1779	1	1	yes	characteristic
139	C₂×C₁₉	#1782	1	1	yes	characteristic
140	C₂×C₁₉	#1784	1	1	yes	characteristic
141	C₂²×Q₈	—	2	4	no	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×Q₈	—	2	4	no	—
144	C₂²×Q₈	—	2	2	no	—
145	C₂²×Q₈	C₁₉⋊C₈	1	4	yes	complemented
146	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
147	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
148	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
149	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
150	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
151	C₂²×C₈	—	38	4	no	—
152	C₄×Q₈	—	2	32	no	—
153	C₂×C₄⋊C₄	—	2	4	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	4	no	—
156	C₂×C₄⋊C₄	—	2	4	no	—
157	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	8	yes	—
158	C₂×C₄²	—	2	4	no	—
159	C₂×C₄²	—	2	4	no	—
160	C₂×C₄²	—	2	4	no	—
161	C₂×C₄²	—	2	4	no	—
162	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
163	C₂²⋊C₈	—	38	8	no	—
164	C₁₉	#8303	1	1	yes	characteristic, complemented, Sylow
165	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
166	C₂×Q₈	—	2	8	no	—
167	C₂×Q₈	—	2	16	no	—
168	C₂×Q₈	—	2	8	no	—
169	C₂×Q₈	—	2	16	no	—
170	C₂×Q₈	—	2	8	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	4	4	no	—
183	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
184	C₂²×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
185	C₂²×C₄	#64520	1	2	yes	—
186	C₂²×C₄	#64520	1	4	yes	—
187	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
188	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
189	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
190	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
191	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
192	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
193	C₂×C₈	—	76	8	no	—
194	C₂×C₈	—	76	4	no	—
195	C₄⋊C₄	—	2	8	no	—
196	C₄⋊C₄	—	2	16	no	—
197	C₄²	—	2	16	no	—
198	C₄²	—	2	8	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	2	no	—
201	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
202	C₂³	C₂×#64520	1	1	yes	characteristic
203	C₂³	C₂×#64520	1	2	yes	—
204	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
205	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
206	Q₈	—	2	32	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	4	no	—
225	C₂×C₄	—	4	4	no	—
226	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	8	yes	—
227	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
228	C₂×C₄	#10597293	1	4	yes	—
229	C₂×C₄	#10597399	1	4	yes	—
230	C₈	—	152	4	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	4	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	2	no	—
236	C₂²	#11926400	1	1	yes	characteristic
237	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
238	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
239	C₂²	#11926508	1	2	yes	—
240	C₂²	#11926508	1	1	yes	characteristic
241	C₂²	#11926518	1	2	yes	—
242	C₂²	C₂×#10597293	1	2	yes	—
243	C₄	—	2	8	no	—
244	C₄	—	2	4	no	—
245	C₄	—	2	4	no	—
246	C₄	—	2	4	no	—
247	C₄	—	4	4	no	—
248	C₂	—	2	2	no	—
249	C₂	—	2	2	no	—
250	C₂	#14561959	1	2	yes	—
251	C₂	#14561979	1	2	yes	—
252	C₂	#14563545	1	1	yes	characteristic
253	C₂	#14563553	1	1	yes	characteristic
254	C₂	#14563559	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal

C₂×#11926270

C₂

yes

maximal

C₂²×C₄×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926270

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

—

C₂×C₄×Q₈×C₁₉

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₈

yes

complemented

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8303

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂²×C₈

yes

characteristic

C₂³×C₁₉

C₂×M₁₆

yes

characteristic

C₂³×C₁₉

C₂×M₁₆

yes

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

100

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

101

C₂×C₄×C₁₉

#101

yes

—

102

C₂×C₄×C₁₉

#120

yes

—

103

C₁₉⋊C₈

—

104

C₂²×C₄×Q₈

D₁₉

yes

characteristic

105

#1817

—

106

C₂×#324

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

#379

yes

characteristic

113

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

—

114

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

115

C₂²×C₁₉

#407

yes

—

116

C₂²×C₁₉

#407

yes

characteristic

117

C₂²×C₁₉

#410

yes

—

118

C₂²×C₁₉

C₂×#101

yes

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₂³×Q₈

Dic₁₉

yes

characteristic

125

C₂×C₄×Q₈

—

126

C₂×C₄×Q₈

—

127

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

128

C₂²×C₄⋊C₄

C₂×D₁₉

yes

—

129

C₂²×C₄²

Dic₁₉

yes

—

130

C₂²×C₄²

C₂×D₁₉

yes

characteristic

131

C₂×C₂²⋊C₈

—

132

#336

—

133

#324

—

134

C₂×C₁₉

—

135

C₂×C₁₉

—

136

C₂×C₁₉

#1461

yes

—

137

C₂×C₁₉

#1467

yes

—

138

C₂×C₁₉

#1779

yes

characteristic

139

C₂×C₁₉

#1782

yes

characteristic

140

C₂×C₁₉

#1784

yes

characteristic

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

—

145

C₂²×Q₈

C₁₉⋊C₈

yes

complemented

146

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

147

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

148

C₂³×C₄

C₂×Dic₁₉

yes

—

149

C₂³×C₄

C₂×Dic₁₉

yes

—

150

C₂³×C₄

C₂²×D₁₉

yes

characteristic

151

C₂²×C₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

—

161

C₂×C₄²

—

162

C₂×C₄²

C₂²⋊D₁₉

yes

—

163

C₂²⋊C₈

—

164

C₁₉

#8303

yes

characteristic, complemented, Sylow

165

C₂⁴

C₂²×Dic₁₉

yes

characteristic

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

184

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

185

C₂²×C₄

#64520

yes

—

186

C₂²×C₄

#64520

yes

—

187

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

188

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

189

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

190

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

191

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

192

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₂³

—

200

C₂³

—

201

C₂³

C₂²×C₁₉⋊C₈

yes

characteristic

202

C₂³

C₂×#64520

yes

characteristic

203

C₂³

C₂×#64520

yes

—

204

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

205

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

206

Q₈

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

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

C₂²⋊(C₁₉⋊C₈)

yes

—

227

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

228

C₂×C₄

#10597293

yes

—

229

C₂×C₄

#10597399

yes

—

230

C₈

—

152

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

#11926400

yes

characteristic

237

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

—

238

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

239

C₂²

#11926508

yes

—

240

C₂²

#11926508

yes

characteristic

241

C₂²

#11926518

yes

—

242

C₂²

C₂×#10597293

yes

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₂

—

249

C₂

—

250

C₂

#14561959

yes

—

251

C₂

#14561979

yes

—

252

C₂

#14563545

yes

characteristic

253

C₂

#14563553

yes

characteristic

254

C₂

#14563559

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₄×Q₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×C₄×Q₈	D₁₉
hypocenter	C₁₉	#8303
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂³×C₁₉

C₂²×C₈

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂²×C₄×Q₈×C₁₉

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²×C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×C₄×Q₈

D₁₉

hypocenter

C₁₉

#8303

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

N	H ≅ G/N	type
18. C₂²×Q₈×C₁₉	C₈	semidirect
145. C₂²×Q₈	C₁₉⋊C₈	semidirect
164. C₁₉	#8303	semidirect

H ≅ G/N

type

18. C₂²×Q₈×C₁₉

C₈

semidirect

145. C₂²×Q₈

C₁₉⋊C₈

semidirect

164. C₁₉

#8303

semidirect

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

subgroup	index
#14563703	2
C₂×#11926270	2
C₂²×C₄×Q₈×C₁₉	2
#8303	19

subgroup

index

#14563703

C₂×#11926270

C₂²×C₄×Q₈×C₁₉

#8303

Subgroups — #18073883

Conjugacy classes of subgroups

Complements

Maximal subgroups