Group #18073890 — subgroups

Subgroups — #18073890

Order 4864.

1154 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 171 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, complemented
2	C₂×#11926268	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	4	no	—
6	#11926268	—	2	8	no	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂×C₁₉×#124	—	2	8	no	—
10	C₂×C₁₉×#124	—	2	4	no	—
11	C₂²×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
15	C₂²×Q₈×C₁₉	—	2	4	no	—
16	C₂²×Q₈×C₁₉	—	2	2	no	—
17	C₂²×Q₈×C₁₉	—	4	4	no	—
18	C₂²×D₄×C₁₉	—	2	4	no	—
19	C₂²×D₄×C₁₉	—	2	2	no	—
20	C₂²×D₄×C₁₉	—	4	4	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₁₉×#124	—	2	32	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
30	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
31	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
32	C₂×C₄²×C₁₉	—	2	4	no	—
33	C₂×C₄²×C₁₉	D₄	1	4	yes	—
34	C₂²×C₁₉⋊C₈	—	2	4	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
36	C₂⁴×C₁₉	—	2	2	no	—
37	C₂⁴×C₁₉	—	2	2	no	—
38	C₂⁴×C₁₉	—	2	8	no	—
39	C₂⁴×C₁₉	—	4	4	no	—
40	C₂⁴×C₁₉	—	4	4	no	—
41	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	—
42	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	—	2	8	no	—
44	C₂×Q₈×C₁₉	—	4	16	no	—
45	C₂×Q₈×C₁₉	—	4	4	no	—
46	C₂×Q₈×C₁₉	—	4	4	no	—
47	C₂×D₄×C₁₉	—	2	8	no	—
48	C₂×D₄×C₁₉	—	4	16	no	—
49	C₂×D₄×C₁₉	—	4	4	no	—
50	C₂×D₄×C₁₉	—	4	4	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	4	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	4	no	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
64	C₂²⋊C₄×C₁₉	—	2	16	no	—
65	C₂²⋊C₄×C₁₉	—	2	16	no	—
66	C₄²×C₁₉	—	2	8	no	—
67	C₂×C₁₉⋊C₈	—	4	8	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	#8305	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	—	2	2	no	—
72	C₂³×C₁₉	—	2	4	no	—
73	C₂³×C₁₉	—	2	8	no	—
74	C₂³×C₁₉	—	4	4	no	—
75	C₂³×C₁₉	—	4	4	no	—
76	C₂³×C₁₉	—	4	4	no	—
77	C₂³×C₁₉	—	4	4	no	—
78	C₂³×C₁₉	—	4	4	no	—
79	C₂³×C₁₉	—	4	4	no	—
80	C₂³×C₁₉	—	4	4	no	—
81	C₂³×C₁₉	—	4	4	no	—
82	C₂³×C₁₉	—	8	16	no	—
83	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
84	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂³×C₁₉	#131	1	4	yes	—
86	Q₈×C₁₉	—	4	16	no	—
87	D₄×C₁₉	—	4	16	no	—
88	C₂×C₄×C₁₉	—	2	8	no	—
89	C₂×C₄×C₁₉	—	2	2	no	—
90	C₂×C₄×C₁₉	—	2	4	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	4	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	—	4	4	no	—
100	C₂×C₄×C₁₉	#100	1	4	yes	—
101	C₂×C₄×C₁₉	#120	1	4	yes	—
102	C₁₉⋊C₈	—	8	4	no	—
103	C₂²×#124	D₁₉	1	1	yes	characteristic
104	#1817	—	19	2	no	—
105	C₂×#323	—	19	4	no	—
106	C₂²×C₁₉	—	2	8	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	4	4	no	—
110	C₂²×C₁₉	—	4	4	no	—
111	C₂²×C₁₉	—	4	4	no	—
112	C₂²×C₁₉	—	8	8	no	—
113	C₂²×C₁₉	—	8	8	no	—
114	C₂²×C₁₉	—	8	8	no	—
115	C₂²×C₁₉	#379	1	1	yes	characteristic
116	C₂²×C₁₉	#408	1	4	yes	—
117	C₂²×C₁₉	#408	1	2	yes	—
118	C₂²×C₁₉	#410	1	2	yes	—
119	C₂²×C₁₉	C₂×#100	1	2	yes	—
120	C₄×C₁₉	—	2	4	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	—	4	2	no	—
123	C₄×C₁₉	—	4	4	no	—
124	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
125	C₂³×D₄	Dic₁₉	1	1	yes	characteristic
126	C₂×#124	—	2	8	no	—
127	C₂×#124	—	2	4	no	—
128	C₂²×C₂²⋊C₄	Dic₁₉	1	2	yes	—
129	C₂²×C₂²⋊C₄	C₂×D₁₉	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	#323	—	38	8	no	—
134	C₂×C₁₉	—	2	4	no	—
135	C₂×C₁₉	—	8	4	no	—
136	C₂×C₁₉	#1469	1	4	yes	—
137	C₂×C₁₉	#1780	1	1	yes	characteristic
138	C₂×C₁₉	#1782	1	1	yes	characteristic
139	C₂×C₁₉	#1783	1	1	yes	characteristic
140	C₂⁵	C₂×Dic₁₉	1	2	yes	—
141	C₂²×Q₈	—	2	4	no	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×Q₈	—	4	4	no	—
144	C₂²×D₄	—	2	4	no	—
145	C₂²×D₄	—	2	2	no	—
146	C₂²×D₄	—	4	4	no	—
147	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
148	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
149	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
150	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
151	C₂²×C₈	—	38	4	no	—
152	#124	—	2	32	no	—
153	C₂×C₂²⋊C₄	—	2	4	no	—
154	C₂×C₂²⋊C₄	—	2	4	no	—
155	C₂×C₂²⋊C₄	—	2	4	no	—
156	C₂×C₂²⋊C₄	—	2	4	no	—
157	C₂×C₂²⋊C₄	—	2	4	no	—
158	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	8	yes	—
159	C₂×C₄²	—	2	4	no	—
160	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
161	C₂²⋊C₈	—	38	8	no	—
162	C₁₉	#8305	1	1	yes	characteristic, complemented, Sylow
163	C₂⁴	—	2	2	no	—
164	C₂⁴	—	2	2	no	—
165	C₂⁴	—	2	8	no	—
166	C₂⁴	—	4	4	no	—
167	C₂⁴	—	4	4	no	—
168	C₂⁴	C₂²⋊Dic₁₉	1	4	yes	—
169	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
170	C₂×Q₈	—	2	8	no	—
171	C₂×Q₈	—	4	16	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂×Q₈	—	4	4	no	—
174	C₂×D₄	—	2	8	no	—
175	C₂×D₄	—	4	16	no	—
176	C₂×D₄	—	4	4	no	—
177	C₂×D₄	—	4	4	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	4	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	4	no	—
186	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
187	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
188	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
189	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
190	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
191	C₂×C₈	—	76	8	no	—
192	C₂×C₈	—	76	4	no	—
193	C₂²⋊C₄	—	2	16	no	—
194	C₂²⋊C₄	—	2	16	no	—
195	C₄²	—	2	8	no	—
196	C₂³	—	2	2	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	2	4	no	—
199	C₂³	—	2	8	no	—
200	C₂³	—	4	4	no	—
201	C₂³	—	4	4	no	—
202	C₂³	—	4	4	no	—
203	C₂³	—	4	4	no	—
204	C₂³	—	4	4	no	—
205	C₂³	—	4	4	no	—
206	C₂³	—	4	4	no	—
207	C₂³	—	4	4	no	—
208	C₂³	—	8	16	no	—
209	C₂³	#10597394	1	4	yes	—
210	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
211	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
212	Q₈	—	4	16	no	—
213	D₄	—	4	16	no	—
214	C₂×C₄	—	2	8	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	4	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	#10597290	1	4	yes	—
227	C₂×C₄	#10597399	1	4	yes	—
228	C₈	—	152	4	no	—
229	C₂²	—	2	8	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	4	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	4	4	no	—
235	C₂²	—	8	8	no	—
236	C₂²	—	8	8	no	—
237	C₂²	—	8	8	no	—
238	C₂²	#11926400	1	1	yes	characteristic
239	C₂²	#11926511	1	4	yes	—
240	C₂²	#11926511	1	2	yes	—
241	C₂²	#11926518	1	2	yes	—
242	C₂²	C₂×#10597290	1	2	yes	—
243	C₄	—	2	4	no	—
244	C₄	—	2	4	no	—
245	C₄	—	4	2	no	—
246	C₄	—	4	4	no	—
247	C₂	—	2	4	no	—
248	C₂	—	8	4	no	—
249	C₂	#14561987	1	4	yes	—
250	C₂	#14563547	1	1	yes	characteristic
251	C₂	#14563553	1	1	yes	characteristic
252	C₂	#14563556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal, complemented

C₂×#11926268

C₂

yes

maximal, complemented

C₂²×C₁₉×#124

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

#11926268

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂³×D₄×C₁₉

C₄

yes

characteristic

C₂×C₁₉×#124

—

C₂×C₁₉×#124

—

C₂²×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂²×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂⁵×C₁₉

C₂×C₄

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#124

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×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

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8305

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#131

yes

—

Q₈×C₁₉

—

D₄×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

—

100

C₂×C₄×C₁₉

#100

yes

—

101

C₂×C₄×C₁₉

#120

yes

—

102

C₁₉⋊C₈

—

103

C₂²×#124

D₁₉

yes

characteristic

104

#1817

—

105

C₂×#323

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

#379

yes

characteristic

116

C₂²×C₁₉

#408

yes

—

117

C₂²×C₁₉

#408

yes

—

118

C₂²×C₁₉

#410

yes

—

119

C₂²×C₁₉

C₂×#100

yes

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₂³×Q₈

Dic₁₉

yes

characteristic

125

C₂³×D₄

Dic₁₉

yes

characteristic

126

C₂×#124

—

127

C₂×#124

—

128

C₂²×C₂²⋊C₄

Dic₁₉

yes

—

129

C₂²×C₂²⋊C₄

C₂×D₁₉

yes

—

130

C₂²×C₄²

C₂×D₁₉

yes

characteristic

131

C₂×C₂²⋊C₈

—

132

#336

—

133

#323

—

134

C₂×C₁₉

—

135

C₂×C₁₉

—

136

C₂×C₁₉

#1469

yes

—

137

C₂×C₁₉

#1780

yes

characteristic

138

C₂×C₁₉

#1782

yes

characteristic

139

C₂×C₁₉

#1783

yes

characteristic

140

C₂⁵

C₂×Dic₁₉

yes

—

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×D₄

—

145

C₂²×D₄

—

146

C₂²×D₄

—

147

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

148

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

149

C₂³×C₄

C₂×Dic₁₉

yes

—

150

C₂³×C₄

C₂²×D₁₉

yes

characteristic

151

C₂²×C₈

—

152

#124

—

153

C₂×C₂²⋊C₄

—

154

C₂×C₂²⋊C₄

—

155

C₂×C₂²⋊C₄

—

156

C₂×C₂²⋊C₄

—

157

C₂×C₂²⋊C₄

—

158

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

159

C₂×C₄²

—

160

C₂×C₄²

C₂²⋊D₁₉

yes

—

161

C₂²⋊C₈

—

162

C₁₉

#8305

yes

characteristic, complemented, Sylow

163

C₂⁴

—

164

C₂⁴

—

165

C₂⁴

—

166

C₂⁴

—

167

C₂⁴

—

168

C₂⁴

C₂²⋊Dic₁₉

yes

—

169

C₂⁴

C₂²×Dic₁₉

yes

characteristic

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

187

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

188

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

189

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

190

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

#10597394

yes

—

210

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

211

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

212

Q₈

—

213

D₄

—

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

#10597290

yes

—

227

C₂×C₄

#10597399

yes

—

228

C₈

—

152

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

#11926400

yes

characteristic

239

C₂²

#11926511

yes

—

240

C₂²

#11926511

yes

—

241

C₂²

#11926518

yes

—

242

C₂²

C₂×#10597290

yes

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₂

—

248

C₂

—

249

C₂

#14561987

yes

—

250

C₂

#14563547

yes

characteristic

251

C₂

#14563553

yes

characteristic

252

C₂

#14563556

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₁₉	C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#124	D₁₉
hypocenter	C₁₉	#8305
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂²×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×D₄×C₁₉

C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×#124

D₁₉

hypocenter

C₁₉

#8305

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#124

N	H ≅ G/N	type
1. #14563703	C₂	semidirect
2. C₂×#11926268	C₂	semidirect
162. C₁₉	#8305	semidirect

H ≅ G/N

type

1. #14563703

C₂

semidirect

2. C₂×#11926268

C₂

semidirect

162. C₁₉

#8305

semidirect

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

subgroup	index
#14563703	2
C₂×#11926268	2
C₂²×C₁₉×#124	2
#8305	19

subgroup

index

#14563703

C₂×#11926268

C₂²×C₁₉×#124

#8305

Subgroups — #18073890

Conjugacy classes of subgroups

Complements

Maximal subgroups