Group #18070828 — subgroups

Subgroups — #18070828

Order 4864.

646 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14563615	C₂	1	2	yes	maximal
2	#14561461	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#391	—	2	2	no	—
11	C₁₉×#391	C₄	1	2	yes	—
12	C₁₉×#391	C₂²	1	2	yes	—
13	C₂×C₁₉×#95	—	2	2	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	—	2	1	no	—
16	C₂²×Q₈×C₁₉	—	4	2	no	—
17	C₂²×Q₈×C₁₉	—	4	2	no	—
18	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	—	2	1	no	—
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	—	4	2	no	—
27	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₁₉⋊C₈	—	2	4	no	—
31	C₁₉×#95	—	2	4	no	—
32	C₁₉×#95	—	2	4	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
34	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	4	16	no	—
39	C₂×Q₈×C₁₉	—	4	2	no	—
40	C₂×Q₈×C₁₉	—	4	2	no	—
41	C₂×Q₈×C₁₉	—	4	2	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
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	4	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	4	no	—
55	C₂²×C₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	—
59	C₂²×C₄×C₁₉	Q₁₆	1	4	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₄²×C₁₉	—	2	4	no	—
65	C₄²×C₁₉	—	4	1	no	—
66	C₄²×C₁₉	—	4	1	no	—
67	C₂×C₁₉⋊C₈	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	C₂×C₁₉⋊C₈	—	4	4	no	—
70	#7643	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	—	2	1	no	—
72	C₂³×C₁₉	—	2	1	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	#100	1	2	yes	—
75	C₂³×C₁₉	#103	1	4	yes	—
76	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₁₉	—	4	4	no	—
78	Q₈×C₁₉	—	4	8	no	—
79	Q₈×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	2	8	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	4	4	no	—
92	C₂×C₄×C₁₉	—	4	8	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	—	8	4	no	—
98	C₂×C₄×C₁₉	#99	1	2	yes	—
99	C₂×C₄×C₁₉	#103	1	4	yes	—
100	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
101	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
102	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
103	C₁₉⋊C₈	—	8	4	no	—
104	C₂×#391	D₁₉	1	1	yes	characteristic
105	#1797	—	19	2	no	—
106	#1272	—	19	4	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	4	no	—
109	C₂²×C₁₉	—	2	4	no	—
110	C₂²×C₁₉	—	2	2	no	—
111	C₂²×C₁₉	#333	1	4	yes	—
112	C₂²×C₁₉	#407	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
115	C₂²×C₁₉	C₂×#103	1	2	yes	—
116	C₂²×C₁₉	#421	1	2	yes	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	4	4	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
125	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
126	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
127	C₂×C₄⋊C₈	—	38	2	no	—
128	C₂×C₂²⋊C₈	—	38	2	no	—
129	#391	—	2	2	no	—
130	#391	Dic₁₉	1	2	yes	—
131	#391	C₂×D₁₉	1	2	yes	—
132	C₂×#95	—	2	2	no	—
133	#336	—	19	4	no	—
134	C₂×C₁₉	—	2	4	no	—
135	C₂×C₁₉	#1462	1	1	yes	characteristic
136	C₂×C₁₉	#1487	1	2	yes	—
137	C₂×C₁₉	#1520	1	2	yes	—
138	C₂×C₁₉	#1533	1	1	yes	characteristic
139	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
140	C₂²×Q₈	—	2	4	no	—
141	C₂²×Q₈	—	2	1	no	—
142	C₂²×Q₈	—	4	2	no	—
143	C₂²×Q₈	—	4	2	no	—
144	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
145	C₂³×C₄	—	2	1	no	—
146	C₂³×C₄	—	2	1	no	—
147	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
148	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
149	C₂²×C₈	—	38	4	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	4	2	no	—
152	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
153	C₂×C₄²	—	4	2	no	—
154	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
156	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
157	C₄⋊C₈	—	76	4	no	—
158	C₂²⋊C₈	—	76	4	no	—
159	#95	—	2	4	no	—
160	#95	—	2	4	no	—
161	C₁₉	#7643	1	1	yes	characteristic, complemented, Sylow
162	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
163	C₂×Q₈	—	2	4	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	16	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	#64520	1	4	yes	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	—	4	2	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	4	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	#64527	1	4	yes	—
184	C₂²×C₄	#64528	1	4	yes	—
185	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
186	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
189	C₂×C₈	—	76	4	no	—
190	C₂×C₈	—	76	4	no	—
191	C₂×C₈	—	76	4	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₄²	—	2	4	no	—
195	C₄²	—	4	1	no	—
196	C₄²	—	4	1	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	#10597290	1	2	yes	—
201	C₂³	#10597292	1	4	yes	—
202	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
203	Q₈	—	4	4	no	—
204	Q₈	—	4	8	no	—
205	Q₈	—	4	4	no	—
206	C₂×C₄	—	2	8	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	4	8	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	8	4	no	—
224	C₂×C₄	#10597291	1	2	yes	—
225	C₂×C₄	#10597292	1	4	yes	—
226	C₂×C₄	C₂×#64520	1	2	yes	—
227	C₂×C₄	C₂×#64527	1	2	yes	—
228	C₂×C₄	C₂×#64528	1	2	yes	—
229	C₈	—	152	4	no	—
230	C₂²	—	2	4	no	—
231	C₂²	—	2	4	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	2	no	—
234	C₂²	#11926293	1	4	yes	—
235	C₂²	#11926508	1	1	yes	characteristic
236	C₂²	C₂×#10597291	1	1	yes	characteristic
237	C₂²	C₂×#10597290	1	1	yes	characteristic
238	C₂²	C₂×#10597292	1	2	yes	—
239	C₂²	#11926561	1	2	yes	—
240	C₄	—	2	2	no	—
241	C₄	—	2	2	no	—
242	C₄	—	2	4	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	2	no	—
245	C₄	—	4	4	no	—
246	C₄	—	8	2	no	—
247	C₂	—	2	4	no	—
248	C₂	#14561962	1	1	yes	characteristic
249	C₂	#14562064	1	2	yes	—
250	C₂	#14562207	1	2	yes	—
251	C₂	#14562259	1	1	yes	characteristic
252	C₂	C₂×#11926293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563615

C₂

yes

maximal

#14561461

C₂

yes

maximal, complemented

C₂×C₁₉×#391

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

C₂²

yes

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#391

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₂×C₁₉×#95

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

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

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7643

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

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

—

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

#99

yes

—

C₂×C₄×C₁₉

#103

yes

—

100

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

101

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

102

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

103

C₁₉⋊C₈

—

104

C₂×#391

D₁₉

yes

characteristic

105

#1797

—

106

#1272

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#333

yes

—

112

C₂²×C₁₉

#407

yes

characteristic

113

C₂²×C₁₉

C₂×#99

yes

characteristic

114

C₂²×C₁₉

C₂×#100

yes

characteristic

115

C₂²×C₁₉

C₂×#103

yes

—

116

C₂²×C₁₉

#421

yes

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₂³×Q₈

Dic₁₉

yes

characteristic

125

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

126

C₂²×C₄²

C₂×D₁₉

yes

characteristic

127

C₂×C₄⋊C₈

—

128

C₂×C₂²⋊C₈

—

129

#391

—

130

#391

Dic₁₉

yes

—

131

#391

C₂×D₁₉

yes

—

132

C₂×#95

—

133

#336

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1462

yes

characteristic

136

C₂×C₁₉

#1487

yes

—

137

C₂×C₁₉

#1520

yes

—

138

C₂×C₁₉

#1533

yes

characteristic

139

C₂×C₁₉

C₂×#333

yes

characteristic

140

C₂²×Q₈

—

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

C₂×Dic₁₉

yes

—

145

C₂³×C₄

—

146

C₂³×C₄

—

147

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

148

C₂³×C₄

C₂²⋊D₁₉

yes

—

149

C₂²×C₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

155

C₂×C₄²

C₂²⋊D₁₉

yes

—

156

C₂×C₄²

C₂²×D₁₉

yes

characteristic

157

C₄⋊C₈

—

158

C₂²⋊C₈

—

159

#95

—

160

#95

—

161

C₁₉

#7643

yes

characteristic, complemented, Sylow

162

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

#64520

yes

—

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

#64527

yes

—

184

C₂²×C₄

#64528

yes

—

185

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

186

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

187

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

188

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

#10597290

yes

—

201

C₂³

#10597292

yes

—

202

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

C₂×C₄

—

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

#10597291

yes

—

225

C₂×C₄

#10597292

yes

—

226

C₂×C₄

C₂×#64520

yes

—

227

C₂×C₄

C₂×#64527

yes

—

228

C₂×C₄

C₂×#64528

yes

—

229

C₈

—

152

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

#11926293

yes

—

235

C₂²

#11926508

yes

characteristic

236

C₂²

C₂×#10597291

yes

characteristic

237

C₂²

C₂×#10597290

yes

characteristic

238

C₂²

C₂×#10597292

yes

—

239

C₂²

#11926561

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₂

—

248

C₂

#14561962

yes

characteristic

249

C₂

#14562064

yes

—

250

C₂

#14562207

yes

—

251

C₂

#14562259

yes

characteristic

252

C₂

C₂×#11926293

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#391	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#391	D₁₉
hypocenter	C₁₉	#7643
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#391

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

N	H ≅ G/N	type
2. #14561461	C₂	semidirect
161. C₁₉	#7643	semidirect

H ≅ G/N

type

2. #14561461

C₂

semidirect

161. C₁₉

#7643

semidirect

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

subgroup	index
#14563615	2
#14561461	2
C₂×C₁₉×#391	2
#7643	19

subgroup

index

#14563615

#14561461

C₂×C₁₉×#391

#7643

Subgroups — #18070828

Conjugacy classes of subgroups

Complements

Maximal subgroups