Group #18073961 — subgroups

Subgroups — #18073961

Order 4864.

930 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 203 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	#14562030	C₂	1	4	yes	maximal, complemented
2	#14561949	C₂	1	2	yes	maximal
3	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic
4	#11926597	C₂²	1	4	yes	—
5	Q₈⋊(C₁₉⋊C₈)	—	2	8	no	—
6	#11926270	—	2	2	no	—
7	#11926268	—	2	2	no	—
8	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
9	C₁₉×#519	—	2	8	no	—
10	C₂×C₄×Q₈×C₁₉	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×#117	—	2	2	no	—
14	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₂²×Q₈×C₁₉	—	2	4	no	—
17	C₂²×Q₈×C₁₉	—	2	4	no	—
18	C₂²×Q₈×C₁₉	—	2	1	no	—
19	C₂²×Q₈×C₁₉	—	2	2	no	—
20	C₂²×Q₈×C₁₉	C₈	1	4	yes	complemented
21	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Q₈×C₁₉	—	2	16	no	—
25	C₄×Q₈×C₁₉	—	2	4	no	—
26	C₄×Q₈×C₁₉	—	2	4	no	—
27	C₄×Q₈×C₁₉	—	2	4	no	—
28	C₄×Q₈×C₁₉	D₄	1	8	yes	—
29	C₁₉×#117	—	2	16	no	—
30	C₁₉×#117	—	2	4	no	—
31	C₁₉×#117	—	2	4	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
38	C₂×C₄²×C₁₉	—	2	2	no	—
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₄×C₁₉⋊C₈	—	2	4	no	—
46	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×Q₈×C₁₉	—	2	4	no	—
48	C₂×Q₈×C₁₉	—	2	16	no	—
49	C₂×Q₈×C₁₉	—	2	4	no	—
50	C₂×Q₈×C₁₉	—	2	16	no	—
51	C₂×Q₈×C₁₉	—	2	4	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂×Q₈×C₁₉	C₂×C₈	1	4	yes	—
57	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
58	C₂²×C₄×C₁₉	—	2	4	no	—
59	C₂²×C₄×C₁₉	—	2	4	no	—
60	C₂²×C₄×C₁₉	—	2	4	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
71	C₄⋊C₄×C₁₉	—	2	8	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	8	no	—
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
76	C₂²⋊C₄×C₁₉	—	2	4	no	—
77	C₂²⋊C₄×C₁₉	—	2	4	no	—
78	C₄²×C₁₉	—	2	8	no	—
79	C₄²×C₁₉	—	2	4	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	8	no	—
82	C₄²×C₁₉	C₂×D₄	1	4	yes	—
83	C₂×C₁₉⋊C₈	—	4	4	no	—
84	#8323	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	—	2	1	no	—
86	C₂³×C₁₉	—	2	1	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	Q₈×C₁₉	—	2	16	no	—
91	Q₈×C₁₉	—	2	4	no	—
92	Q₈×C₁₉	—	2	4	no	—
93	Q₈×C₁₉	—	2	4	no	—
94	Q₈×C₁₉	C₂²⋊C₈	1	8	yes	—
95	C₂×C₄×C₁₉	—	2	16	no	—
96	C₂×C₄×C₁₉	—	2	4	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	4	no	—
99	C₂×C₄×C₁₉	—	2	4	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	2	4	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	4	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
109	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
110	C₂×C₄×C₁₉	#120	1	4	yes	—
111	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
113	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
114	C₁₉⋊C₈	—	8	4	no	—
115	C₂×#519	D₁₉	1	1	yes	characteristic
116	#1479	—	19	4	no	—
117	#1458	—	19	2	no	—
118	C₂²×C₁₉	—	2	2	no	—
119	C₂²×C₁₉	—	2	2	no	—
120	C₂²×C₁₉	—	4	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	2	no	—
123	C₂²×C₁₉	#379	1	1	yes	characteristic
124	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₂²×C₁₉	#407	1	1	yes	characteristic
126	C₄×C₁₉	—	2	4	no	—
127	C₄×C₁₉	—	2	8	no	—
128	C₄×C₁₉	—	2	2	no	—
129	C₄×C₁₉	—	4	2	no	—
130	C₄×C₁₉	—	4	4	no	—
131	C₄×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
132	C₄×C₁₉	#407	1	2	yes	—
133	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
134	#519	—	2	8	no	—
135	C₂×C₄×Q₈	—	2	2	no	—
136	C₂×C₄×Q₈	Dic₁₉	1	2	yes	—
137	C₂×C₄×Q₈	C₂×D₁₉	1	2	yes	—
138	C₂×#117	—	2	2	no	—
139	C₂×#117	Dic₁₉	1	1	yes	characteristic
140	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
141	#431	—	19	4	no	—
142	Q₈⋊C₈	—	38	8	no	—
143	#324	—	38	2	no	—
144	#323	—	38	2	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	4	2	no	—
148	C₂×C₁₉	#1779	1	1	yes	characteristic
149	C₂×C₁₉	#1796	1	2	yes	—
150	C₂²×Q₈	—	2	4	no	—
151	C₂²×Q₈	—	2	4	no	—
152	C₂²×Q₈	—	2	2	no	—
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×Q₈	C₁₉⋊C₈	1	4	yes	complemented
155	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
156	C₂³×C₄	—	2	1	no	—
157	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
158	C₄×Q₈	—	2	16	no	—
159	C₄×Q₈	—	2	4	no	—
160	C₄×Q₈	—	2	4	no	—
161	C₄×Q₈	—	2	4	no	—
162	C₄×Q₈	C₂²⋊D₁₉	1	8	yes	—
163	#117	—	2	16	no	—
164	#117	—	2	4	no	—
165	#117	—	2	4	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
169	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
170	C₂×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
172	C₂×C₄²	—	2	2	no	—
173	C₂×C₄²	—	2	1	no	—
174	C₂×C₄²	—	2	2	no	—
175	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
177	C₄⋊C₈	—	38	4	no	—
178	C₂²⋊C₈	—	38	4	no	—
179	C₄×C₈	—	38	4	no	—
180	C₁₉	#8323	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
182	C₂×Q₈	—	2	4	no	—
183	C₂×Q₈	—	2	16	no	—
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	2	16	no	—
186	C₂×Q₈	—	2	2	no	—
187	C₂×Q₈	—	2	4	no	—
188	C₂×Q₈	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	C₂×C₁₉⋊C₈	1	4	yes	—
191	C₂×Q₈	#64520	1	4	yes	—
192	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
193	C₂²×C₄	—	2	4	no	—
194	C₂²×C₄	—	2	4	no	—
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	—	2	4	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
201	C₂²×C₄	#64520	1	2	yes	—
202	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
204	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
206	C₂×C₈	—	76	4	no	—
207	C₄⋊C₄	—	2	8	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	8	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
212	C₂²⋊C₄	—	2	4	no	—
213	C₂²⋊C₄	—	2	4	no	—
214	C₄²	—	2	8	no	—
215	C₄²	—	2	4	no	—
216	C₄²	—	2	2	no	—
217	C₄²	—	2	8	no	—
218	C₄²	C₂×C₂²⋊D₁₉	1	4	yes	—
219	C₂³	—	2	1	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	4	2	no	—
222	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
223	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
224	Q₈	—	2	16	no	—
225	Q₈	—	2	4	no	—
226	Q₈	—	2	4	no	—
227	Q₈	—	2	4	no	—
228	Q₈	C₂²⋊(C₁₉⋊C₈)	1	8	yes	—
229	C₂×C₄	—	2	16	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	4	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
243	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
244	C₂×C₄	C₂×#64520	1	2	yes	—
245	C₂×C₄	C₂×#64520	1	1	yes	characteristic
246	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
247	C₂×C₄	#10597399	1	4	yes	—
248	C₈	—	152	4	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	4	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	#11926400	1	1	yes	characteristic
255	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
256	C₂²	#11926508	1	1	yes	characteristic
257	C₄	—	2	4	no	—
258	C₄	—	2	8	no	—
259	C₄	—	2	2	no	—
260	C₄	—	4	4	no	—
261	C₄	—	4	2	no	—
262	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
263	C₄	#11926508	1	2	yes	—
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	—	4	2	no	—
267	C₂	#14563545	1	1	yes	characteristic
268	C₂	#14563610	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562030

C₂

yes

maximal, complemented

#14561949

C₂

yes

maximal

C₂×C₁₉×#519

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

Q₈⋊(C₁₉⋊C₈)

—

#11926270

—

#11926268

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₁₉×#519

—

C₂×C₄×Q₈×C₁₉

—

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

—

C₂×C₁₉×#117

—

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₈

yes

complemented

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(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

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

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

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₂×C₁₉⋊C₈

—

#8323

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

109

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

110

C₂×C₄×C₁₉

#120

yes

—

111

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

112

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

113

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

114

C₁₉⋊C₈

—

115

C₂×#519

D₁₉

yes

characteristic

116

#1479

—

117

#1458

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#379

yes

characteristic

124

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

125

C₂²×C₁₉

#407

yes

characteristic

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

C₂×C₂²⋊C₈

yes

—

132

C₄×C₁₉

#407

yes

—

133

C₂³×Q₈

Dic₁₉

yes

characteristic

134

#519

—

135

C₂×C₄×Q₈

—

136

C₂×C₄×Q₈

Dic₁₉

yes

—

137

C₂×C₄×Q₈

C₂×D₁₉

yes

—

138

C₂×#117

—

139

C₂×#117

Dic₁₉

yes

characteristic

140

C₂×#117

C₂×D₁₉

yes

characteristic

141

#431

—

142

Q₈⋊C₈

—

143

#324

—

144

#323

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1779

yes

characteristic

149

C₂×C₁₉

#1796

yes

—

150

C₂²×Q₈

—

151

C₂²×Q₈

—

152

C₂²×Q₈

—

153

C₂²×Q₈

—

154

C₂²×Q₈

C₁₉⋊C₈

yes

complemented

155

C₂²×Q₈

C₂×Dic₁₉

yes

—

156

C₂³×C₄

—

157

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

158

C₄×Q₈

—

159

C₄×Q₈

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

C₂²⋊D₁₉

yes

—

163

#117

—

164

#117

—

165

#117

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

169

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

172

C₂×C₄²

—

173

C₂×C₄²

—

174

C₂×C₄²

—

175

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

176

C₂×C₄²

C₂²×D₁₉

yes

characteristic

177

C₄⋊C₈

—

178

C₂²⋊C₈

—

179

C₄×C₈

—

180

C₁₉

#8323

yes

characteristic, complemented, Sylow

181

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

C₂×C₁₉⋊C₈

yes

—

191

C₂×Q₈

#64520

yes

—

192

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

201

C₂²×C₄

#64520

yes

—

202

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

203

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

204

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

205

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

206

C₂×C₈

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

—

218

C₄²

C₂×C₂²⋊D₁₉

yes

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

—

223

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

Q₈

—

228

Q₈

C₂²⋊(C₁₉⋊C₈)

yes

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

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⋊(C₁₉⋊C₈)

yes

—

243

C₂×C₄

C₂²×C₁₉⋊C₈

yes

characteristic

244

C₂×C₄

C₂×#64520

yes

—

245

C₂×C₄

C₂×#64520

yes

characteristic

246

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

247

C₂×C₄

#10597399

yes

—

248

C₈

—

152

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926400

yes

characteristic

255

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

256

C₂²

#11926508

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

C₂×C₂²⋊(C₁₉⋊C₈)

yes

—

263

C₄

#11926508

yes

—

264

C₂

—

265

C₂

—

266

C₂

—

267

C₂

#14563545

yes

characteristic

268

C₂

#14563610

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#519	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#519	D₁₉
hypocenter	C₁₉	#8323
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#519

subgroup

G/H

center

C₂²

#11926400

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#519

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#519

N	H ≅ G/N	type
1. #14562030	C₂	semidirect
20. C₂²×Q₈×C₁₉	C₈	semidirect
154. C₂²×Q₈	C₁₉⋊C₈	semidirect
180. C₁₉	#8323	semidirect

H ≅ G/N

type

1. #14562030

C₂

semidirect

20. C₂²×Q₈×C₁₉

C₈

semidirect

154. C₂²×Q₈

C₁₉⋊C₈

semidirect

180. C₁₉

#8323

semidirect

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

subgroup	index
#14562030	2
#14561949	2
C₂×C₁₉×#519	2
#8323	19

subgroup

index

#14562030

#14561949

C₂×C₁₉×#519

#8323

Subgroups — #18073961

Conjugacy classes of subgroups

Complements

Maximal subgroups