Group #18069848 — subgroups

Subgroups — #18069848

Order 4864.

328 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14563933	C₂	1	1	yes	maximal, characteristic
2	#14561973	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₄	1	1	yes	characteristic
5	#11926508	—	2	1	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
8	#11926299	—	2	1	no	—
9	#11926270	—	2	1	no	—
10	#11926268	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#423	—	2	1	no	—
13	C₂×C₁₉×#100	C₄	1	2	yes	—
14	C₁₉×#343	—	2	1	no	—
15	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	—	2	2	no	—
19	C₄×D₄×C₁₉	—	4	1	no	—
20	C₄×D₄×C₁₉	—	4	1	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×#64520	—	4	2	no	—
26	C₂×#64520	—	4	1	no	—
27	C₂×#64520	—	4	1	no	—
28	C₂²×C₁₉⋊C₈	—	2	1	no	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₁₉×C₄⋊C₈	—	4	1	no	—
31	C₁₉×C₄⋊C₈	—	4	1	no	—
32	C₁₉×#100	—	4	2	no	—
33	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
37	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
38	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×D₄×C₁₉	—	2	1	no	—
40	C₂×D₄×C₁₉	—	2	1	no	—
41	C₂×D₄×C₁₉	—	4	1	no	—
42	C₂×D₄×C₁₉	—	4	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	M₁₆×C₁₉	—	4	2	no	—
57	M₁₆×C₁₉	—	4	2	no	—
58	C₂×C₈×C₁₉	—	4	2	no	—
59	C₄⋊C₄×C₁₉	—	4	1	no	—
60	C₂²⋊C₄×C₁₉	—	4	1	no	—
61	C₂²⋊C₄×C₁₉	—	4	1	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	#64520	—	4	2	no	—
65	#64520	—	4	2	no	—
66	#64520	—	8	1	no	—
67	#64520	—	8	1	no	—
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	#7321	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	—	2	1	no	—
77	C₂³×C₁₉	—	2	1	no	—
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	2	1	no	—
81	C₂³×C₁₉	—	2	1	no	—
82	C₂³×C₁₉	—	4	1	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	#95	1	1	yes	characteristic
87	D₄×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	8	1	no	—
105	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
109	C₈×C₁₉	—	8	2	no	—
110	C₁₉⋊C₈	—	4	2	no	—
111	C₁₉⋊C₈	—	8	1	no	—
112	C₁₉⋊C₈	—	8	2	no	—
113	#1870	—	19	1	no	—
114	#1800	D₁₉	1	1	yes	characteristic
115	#1465	—	19	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	4	2	no	—
119	C₂²×C₁₉	—	4	1	no	—
120	C₂²×C₁₉	—	4	1	no	—
121	C₂²×C₁₉	—	4	1	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	8	1	no	—
126	C₂²×C₁₉	—	8	1	no	—
127	C₂²×C₁₉	—	8	1	no	—
128	C₂²×C₁₉	#342	1	1	yes	characteristic
129	C₂²×C₁₉	#343	1	1	yes	characteristic
130	C₂²×C₁₉	#344	1	1	yes	characteristic
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	1	no	—
134	C₄×C₁₉	—	4	1	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	—	4	1	no	—
137	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
138	C₄×C₁₉	#352	1	1	yes	characteristic
139	C₂²×M₁₆	—	19	1	no	—
140	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
141	#423	—	2	1	no	—
142	C₂×#100	Dic₁₉	1	2	yes	—
143	#407	—	38	1	no	—
144	C₂×C₂²⋊C₈	—	19	1	no	—
145	C₂×C₂²⋊C₈	—	38	1	no	—
146	#343	—	2	1	no	—
147	#336	—	38	1	no	—
148	#324	—	38	1	no	—
149	#323	—	19	2	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	—	2	1	no	—
152	C₂×C₁₉	—	8	1	no	—
153	C₂×C₁₉	—	8	1	no	—
154	C₂×C₁₉	#1305	1	1	yes	characteristic
155	C₂×C₁₉	#1390	1	1	yes	characteristic
156	C₂×C₁₉	#1392	1	1	yes	characteristic
157	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
158	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
159	C₂³×C₄	D₇₆	1	1	yes	characteristic
160	C₂×M₁₆	—	2	2	no	—
161	C₂×M₁₆	—	76	2	no	—
162	C₂×M₁₆	—	76	1	no	—
163	C₂×M₁₆	—	76	1	no	—
164	C₂²×C₈	—	38	1	no	—
165	C₂²×C₈	—	38	1	no	—
166	C₄×D₄	—	4	1	no	—
167	C₄×D₄	—	4	1	no	—
168	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	4	1	no	—
173	C₄⋊C₈	—	4	1	no	—
174	#100	—	4	2	no	—
175	C₂²⋊C₈	—	38	2	no	—
176	C₂²⋊C₈	—	76	2	no	—
177	C₂²⋊C₈	—	76	1	no	—
178	C₂²⋊C₈	—	76	1	no	—
179	C₁₉	#7321	1	1	yes	characteristic, complemented, Sylow
180	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
181	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
182	C₂×D₄	—	2	1	no	—
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	4	1	no	—
185	C₂×D₄	—	4	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	—	4	1	no	—
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
195	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
196	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
197	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
198	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
199	M₁₆	—	4	2	no	—
200	M₁₆	—	4	2	no	—
201	M₁₆	—	76	2	no	—
202	M₁₆	—	76	2	no	—
203	M₁₆	—	152	1	no	—
204	M₁₆	—	152	1	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	38	2	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	1	no	—
209	C₂×C₈	—	76	2	no	—
210	C₂×C₈	—	76	1	no	—
211	C₂×C₈	—	76	1	no	—
212	C₂×C₈	—	76	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₂²⋊C₄	—	4	1	no	—
215	C₂²⋊C₄	—	4	1	no	—
216	C₄²	—	2	1	no	—
217	C₄²	—	2	1	no	—
218	C₂³	—	2	1	no	—
219	C₂³	—	2	1	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	2	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	1	no	—
224	C₂³	—	4	1	no	—
225	C₂³	—	4	1	no	—
226	C₂³	—	4	1	no	—
227	C₂³	—	4	1	no	—
228	C₂³	C₁₉⋊#95	1	1	yes	characteristic
229	D₄	—	4	2	no	—
230	D₄	—	4	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	8	1	no	—
247	C₂×C₄	#10597263	1	1	yes	characteristic
248	C₂×C₄	#10597263	1	1	yes	characteristic
249	C₂×C₄	#10597290	1	1	yes	characteristic
250	C₂×C₄	#10597293	1	1	yes	characteristic
251	C₈	—	8	2	no	—
252	C₈	—	76	2	no	—
253	C₈	—	152	1	no	—
254	C₈	—	152	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	4	2	no	—
258	C₂²	—	4	1	no	—
259	C₂²	—	4	1	no	—
260	C₂²	—	4	1	no	—
261	C₂²	—	4	1	no	—
262	C₂²	—	4	1	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	—	8	1	no	—
266	C₂²	—	8	1	no	—
267	C₂²	#11926310	1	1	yes	characteristic
268	C₂²	#11926313	1	1	yes	characteristic
269	C₂²	#11926314	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	4	1	no	—
274	C₄	—	4	1	no	—
275	C₄	—	4	1	no	—
276	C₄	#11926332	1	1	yes	characteristic
277	C₄	#11926335	1	1	yes	characteristic
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	—	8	1	no	—
281	C₂	—	8	1	no	—
282	C₂	#14561541	1	1	yes	characteristic
283	C₂	#14561754	1	1	yes	characteristic
284	C₂	#14561757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563933

C₂

yes

maximal, characteristic

#14561973

C₂

yes

maximal, characteristic

C₁₉×#1800

C₂

yes

maximal, characteristic

C₂²×#64520

C₄

yes

characteristic

#11926508

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

—

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#423

—

C₂×C₁₉×#100

C₄

yes

—

C₁₉×#343

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#100

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₄²

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

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

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7321

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

D₄×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

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

#99

yes

characteristic

106

C₂×C₄×C₁₉

#99

yes

characteristic

107

C₂×C₄×C₁₉

#100

yes

characteristic

108

C₂×C₄×C₁₉

#101

yes

characteristic

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₁₉⋊C₈

—

112

C₁₉⋊C₈

—

113

#1870

—

114

#1800

D₁₉

yes

characteristic

115

#1465

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#342

yes

characteristic

129

C₂²×C₁₉

#343

yes

characteristic

130

C₂²×C₁₉

#344

yes

characteristic

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

138

C₄×C₁₉

#352

yes

characteristic

139

C₂²×M₁₆

—

140

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

141

#423

—

142

C₂×#100

Dic₁₉

yes

—

143

#407

—

144

C₂×C₂²⋊C₈

—

145

C₂×C₂²⋊C₈

—

146

#343

—

147

#336

—

148

#324

—

149

#323

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#1305

yes

characteristic

155

C₂×C₁₉

#1390

yes

characteristic

156

C₂×C₁₉

#1392

yes

characteristic

157

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

158

C₂³×C₄

C₄×D₁₉

yes

characteristic

159

C₂³×C₄

D₇₆

yes

characteristic

160

C₂×M₁₆

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂²×C₈

—

165

C₂²×C₈

—

166

C₄×D₄

—

167

C₄×D₄

—

168

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

169

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

170

C₂×C₂²⋊C₄

C₄×D₁₉

yes

characteristic

171

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#100

—

175

C₂²⋊C₈

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

C₁₉

#7321

yes

characteristic, complemented, Sylow

180

C₂⁴

C₄×Dic₁₉

yes

characteristic

181

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

195

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

196

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

197

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

198

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

M₁₆

—

152

—

204

M₁₆

—

152

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

216

C₄²

—

217

C₄²

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

C₁₉⋊#95

yes

characteristic

229

D₄

—

230

D₄

—

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

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

#10597263

yes

characteristic

248

C₂×C₄

#10597263

yes

characteristic

249

C₂×C₄

#10597290

yes

characteristic

250

C₂×C₄

#10597293

yes

characteristic

251

C₈

—

252

C₈

—

253

C₈

—

152

—

254

C₈

—

152

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

#11926310

yes

characteristic

268

C₂²

#11926313

yes

characteristic

269

C₂²

#11926314

yes

characteristic

270

C₄

—

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

#11926332

yes

characteristic

277

C₄

#11926335

yes

characteristic

278

C₂

—

279

C₂

—

280

C₂

—

281

C₂

—

282

C₂

#14561541

yes

characteristic

283

C₂

#14561754

yes

characteristic

284

C₂

#14561757

yes

characteristic

	subgroup	G/H
center	C₂²	#11926310
commutator	C₂⁴×C₁₉	C₄²
Frattini	C₂×C₄×D₄	C₂×D₁₉
Fitting	C₁₉×#1800	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄×D₄×C₁₉	C₂²
hypercenter	#1800	D₁₉
hypocenter	C₁₉	#7321
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ #1800

subgroup

G/H

center

C₂²

#11926310

commutator

C₂⁴×C₁₉

C₄²

Frattini

C₂×C₄×D₄

C₂×D₁₉

Fitting

C₁₉×#1800

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ #1800

N	H ≅ G/N	type
179. C₁₉	#7321	semidirect

H ≅ G/N

type

179. C₁₉

#7321

semidirect

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

subgroup	index
#14563933	2
#14561973	2
C₁₉×#1800	2
#7321	19

subgroup

index

#14563933

#14561973

C₁₉×#1800

#7321

Subgroups — #18069848

Conjugacy classes of subgroups

Complements

Maximal subgroups