Group #18074102 — subgroups

Subgroups — #18074102

Order 4864.

686 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 167 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	#14564572	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	#14562325	C₂	1	2	yes	maximal
4	#14562090	C₂	1	2	yes	maximal
5	C₁₉×#3502	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#10597293	—	2	1	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	#11926313	—	2	1	no	—
11	#11926299	—	2	2	no	—
12	#11926293	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
15	Q₈²×C₁₉	—	2	2	no	—
16	C₁₉×#557	—	2	2	no	—
17	C₁₉×#557	—	2	4	no	—
18	C₁₉×#544	—	2	1	no	—
19	C₁₉×#544	C₄	1	4	yes	—
20	C₁₉×#533	—	2	2	no	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#519	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	2	no	—
27	C₁₉×C₄⋊Q₈	—	2	4	no	—
28	C₁₉×C₄⋊Q₈	—	2	8	no	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
31	C₁₉×#125	—	2	4	no	—
32	C₁₉×#125	—	2	4	no	—
33	C₁₉×#125	—	2	8	no	—
34	C₁₉×#125	—	2	2	no	—
35	C₁₉×C₂²⋊Q₈	—	2	4	no	—
36	C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
38	C₄×Q₈×C₁₉	—	2	4	no	—
39	C₄×Q₈×C₁₉	—	2	4	no	—
40	C₄×Q₈×C₁₉	—	2	4	no	—
41	C₄×Q₈×C₁₉	—	2	4	no	—
42	C₄×Q₈×C₁₉	—	2	2	no	—
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×Q₈×C₁₉	D₄	1	4	yes	—
46	C₁₉×#117	—	2	4	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	2	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64520	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	#10597293	—	4	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄×C₁₉⋊C₈	—	2	2	no	—
60	C₂×Q₈×C₁₉	—	2	4	no	—
61	C₂×Q₈×C₁₉	—	2	2	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
65	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
66	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	—	2	8	no	—
76	C₄⋊C₄×C₁₉	—	2	4	no	—
77	C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
84	C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₄²×C₁₉	—	2	8	no	—
86	C₄²×C₁₉	—	2	2	no	—
87	C₄²×C₁₉	—	2	2	no	—
88	C₄²×C₁₉	—	2	4	no	—
89	C₄²×C₁₉	C₂×D₄	1	2	yes	—
90	C₄²×C₁₉	C₂×D₄	1	2	yes	—
91	#64520	—	4	2	no	—
92	#64520	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	2	2	no	—
94	C₂×C₁₉⋊C₈	—	4	1	no	—
95	C₂×C₁₉⋊C₈	—	4	1	no	—
96	C₂×C₁₉⋊C₈	—	4	2	no	—
97	C₂×C₁₉⋊C₈	—	4	1	no	—
98	C₂×C₁₉⋊C₈	—	4	2	no	—
99	#8356	—	19	1	no	maximal, Sylow
100	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	Q₈×C₁₉	—	2	4	no	—
102	Q₈×C₁₉	—	2	4	no	—
103	Q₈×C₁₉	—	4	4	no	—
104	Q₈×C₁₉	—	4	2	no	—
105	Q₈×C₁₉	—	4	2	no	—
106	Q₈×C₁₉	—	8	4	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	4	no	—
112	C₂×C₄×C₁₉	—	2	4	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	#103	1	4	yes	—
117	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
118	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#120	1	2	yes	—
120	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#137	1	2	yes	—
124	C₁₉⋊C₈	—	4	2	no	—
125	C₁₉⋊C₈	—	8	2	no	—
126	C₁₉⋊C₈	—	8	1	no	—
127	#3502	D₁₉	1	1	yes	characteristic
128	#1984	—	19	1	no	—
129	#1801	—	19	1	no	—
130	#1550	—	19	2	no	—
131	#1493	—	19	2	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	2	1	no	—
134	C₂²×C₁₉	#379	1	1	yes	characteristic
135	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
136	C₂²×C₁₉	#419	1	1	yes	characteristic
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	4	no	—
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	4	4	no	—
141	C₄×C₁₉	—	4	2	no	—
142	C₄×C₁₉	—	4	4	no	—
143	C₄×C₁₉	#448	1	2	yes	—
144	C₄×C₁₉	#451	1	2	yes	—
145	C₄×C₁₉	#454	1	1	yes	characteristic
146	C₄×C₁₉	#456	1	1	yes	characteristic
147	Q₈²	—	2	2	no	—
148	#557	—	2	2	no	—
149	#557	—	2	4	no	—
150	#544	—	2	1	no	—
151	#544	Dic₁₉	1	4	yes	—
152	#533	—	2	2	no	—
153	#533	C₂×D₁₉	1	2	yes	—
154	#519	—	2	1	no	—
155	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
156	#423	—	19	2	no	—
157	C₂×C₄⋊C₈	—	19	1	no	—
158	C₂×#101	—	38	1	no	—
159	C₂×C₄×C₈	—	19	1	no	—
160	#343	—	38	1	no	—
161	#336	—	38	2	no	—
162	#333	—	38	2	no	—
163	#332	—	38	2	no	—
164	Q₈⋊C₈	—	38	4	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	#1787	1	1	yes	characteristic
168	C₂×C₁₉	#1791	1	1	yes	characteristic
169	C₂×C₁₉	#1793	1	1	yes	characteristic
170	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₂×M₁₆	—	38	2	no	—
172	C₂²×C₈	—	38	1	no	—
173	C₂²×C₈	—	38	1	no	—
174	C₄⋊Q₈	—	2	2	no	—
175	C₄⋊Q₈	—	2	2	no	—
176	C₄⋊Q₈	—	2	4	no	—
177	C₄⋊Q₈	—	2	8	no	—
178	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
179	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
180	#125	—	2	4	no	—
181	#125	—	2	4	no	—
182	#125	—	2	8	no	—
183	#125	—	2	2	no	—
184	C₂²⋊Q₈	—	2	4	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	C₂×Dic₁₉	1	4	yes	—
187	C₄×Q₈	—	2	4	no	—
188	C₄×Q₈	—	2	4	no	—
189	C₄×Q₈	—	2	4	no	—
190	C₄×Q₈	—	2	4	no	—
191	C₄×Q₈	—	2	2	no	—
192	C₄×Q₈	—	2	2	no	—
193	C₄×Q₈	—	2	2	no	—
194	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
195	#117	—	2	4	no	—
196	#117	—	2	2	no	—
197	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
198	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
199	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
200	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
201	C₄⋊C₈	—	38	2	no	—
202	C₄⋊C₈	—	38	2	no	—
203	C₄⋊C₈	—	38	2	no	—
204	#101	—	76	2	no	—
205	C₄×C₈	—	38	2	no	—
206	C₁₉	#8356	1	1	yes	characteristic, complemented, Sylow
207	C₂×Q₈	—	2	4	no	—
208	C₂×Q₈	—	2	2	no	—
209	C₂×Q₈	—	2	2	no	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	#64527	1	2	yes	—
212	C₂×Q₈	#64528	1	2	yes	—
213	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
214	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
215	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
216	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
219	M₁₆	—	76	2	no	—
220	M₁₆	—	76	2	no	—
221	C₂×C₈	—	38	2	no	—
222	C₂×C₈	—	76	1	no	—
223	C₂×C₈	—	76	1	no	—
224	C₂×C₈	—	76	2	no	—
225	C₂×C₈	—	76	1	no	—
226	C₂×C₈	—	76	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	2	4	no	—
230	C₄⋊C₄	—	2	8	no	—
231	C₄⋊C₄	—	2	4	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₄²	—	2	8	no	—
241	C₄²	—	2	2	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	4	no	—
244	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
245	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
246	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
247	Q₈	—	2	4	no	—
248	Q₈	—	2	4	no	—
249	Q₈	—	4	4	no	—
250	Q₈	—	4	2	no	—
251	Q₈	—	4	2	no	—
252	Q₈	—	8	4	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	#10597292	1	4	yes	—
263	C₂×C₄	C₂×#64527	1	1	yes	characteristic
264	C₂×C₄	#10597388	1	2	yes	—
265	C₂×C₄	C₂×#64528	1	1	yes	characteristic
266	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
267	C₂×C₄	#10597399	1	1	yes	characteristic
268	C₂×C₄	#10597399	1	2	yes	—
269	C₂×C₄	#10597399	1	1	yes	characteristic
270	C₈	—	76	2	no	—
271	C₈	—	152	2	no	—
272	C₈	—	152	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	1	no	—
275	C₂²	#11926400	1	1	yes	characteristic
276	C₂²	C₂×#10597292	1	1	yes	characteristic
277	C₂²	#11926553	1	1	yes	characteristic
278	C₄	—	2	2	no	—
279	C₄	—	2	1	no	—
280	C₄	—	2	4	no	—
281	C₄	—	4	2	no	—
282	C₄	—	4	4	no	—
283	C₄	—	4	4	no	—
284	C₄	#11926683	1	2	yes	—
285	C₄	#11926700	1	2	yes	—
286	C₄	#11926717	1	1	yes	characteristic
287	C₄	#11926727	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	#14563570	1	1	yes	characteristic
291	C₂	#14563586	1	1	yes	characteristic
292	C₂	#14563594	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564572

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14562325

C₂

yes

maximal

#14562090

C₂

yes

maximal

C₁₉×#3502

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597293

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

Q₈²×C₁₉

—

C₁₉×#557

—

C₁₉×#557

—

C₁₉×#544

—

C₁₉×#544

C₄

yes

—

C₁₉×#533

—

C₁₉×#533

C₂²

yes

—

C₁₉×#519

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597293

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8356

—

maximal, Sylow

100

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

101

Q₈×C₁₉

—

102

Q₈×C₁₉

—

103

Q₈×C₁₉

—

104

Q₈×C₁₉

—

105

Q₈×C₁₉

—

106

Q₈×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

—

114

C₂×C₄×C₁₉

—

115

C₂×C₄×C₁₉

—

116

C₂×C₄×C₁₉

#103

yes

—

117

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

118

C₂×C₄×C₁₉

#120

yes

characteristic

119

C₂×C₄×C₁₉

#120

yes

—

120

C₂×C₄×C₁₉

#120

yes

characteristic

121

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

122

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

123

C₂×C₄×C₁₉

#137

yes

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

#3502

D₁₉

yes

characteristic

128

#1984

—

129

#1801

—

130

#1550

—

131

#1493

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

#379

yes

characteristic

135

C₂²×C₁₉

C₂×#103

yes

characteristic

136

C₂²×C₁₉

#419

yes

characteristic

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

#448

yes

—

144

C₄×C₁₉

#451

yes

—

145

C₄×C₁₉

#454

yes

characteristic

146

C₄×C₁₉

#456

yes

characteristic

147

Q₈²

—

148

#557

—

149

#557

—

150

#544

—

151

#544

Dic₁₉

yes

—

152

#533

—

153

#533

C₂×D₁₉

yes

—

154

#519

—

155

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

156

#423

—

157

C₂×C₄⋊C₈

—

158

C₂×#101

—

159

C₂×C₄×C₈

—

160

#343

—

161

#336

—

162

#333

—

163

#332

—

164

Q₈⋊C₈

—

165

C₂×C₁₉

—

166

C₂×C₁₉

—

167

C₂×C₁₉

#1787

yes

characteristic

168

C₂×C₁₉

#1791

yes

characteristic

169

C₂×C₁₉

#1793

yes

characteristic

170

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

171

C₂×M₁₆

—

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

179

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

180

#125

—

181

#125

—

182

#125

—

183

#125

—

184

C₂²⋊Q₈

—

185

C₂²⋊Q₈

—

186

C₂²⋊Q₈

C₂×Dic₁₉

yes

—

187

C₄×Q₈

—

188

C₄×Q₈

—

189

C₄×Q₈

—

190

C₄×Q₈

—

191

C₄×Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

C₂²⋊D₁₉

yes

—

195

#117

—

196

#117

—

197

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

198

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

199

C₂×C₄²

C₂²⋊D₁₉

yes

—

200

C₂×C₄²

C₂²×D₁₉

yes

characteristic

201

C₄⋊C₈

—

202

C₄⋊C₈

—

203

C₄⋊C₈

—

204

#101

—

205

C₄×C₈

—

206

C₁₉

#8356

yes

characteristic, complemented, Sylow

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

#64527

yes

—

212

C₂×Q₈

#64528

yes

—

213

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

214

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

215

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

216

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

217

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

218

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

219

M₁₆

—

220

M₁₆

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

239

C₂²⋊C₄

—

240

C₄²

—

241

C₄²

—

242

C₄²

—

243

C₄²

—

244

C₄²

C₂×C₂²⋊D₁₉

yes

—

245

C₄²

C₂×C₂²⋊D₁₉

yes

—

246

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

247

Q₈

—

248

Q₈

—

249

Q₈

—

250

Q₈

—

251

Q₈

—

252

Q₈

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

#10597292

yes

—

263

C₂×C₄

C₂×#64527

yes

characteristic

264

C₂×C₄

#10597388

yes

—

265

C₂×C₄

C₂×#64528

yes

characteristic

266

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

267

C₂×C₄

#10597399

yes

characteristic

268

C₂×C₄

#10597399

yes

—

269

C₂×C₄

#10597399

yes

characteristic

270

C₈

—

271

C₈

—

152

—

272

C₈

—

152

—

273

C₂²

—

274

C₂²

—

275

C₂²

#11926400

yes

characteristic

276

C₂²

C₂×#10597292

yes

characteristic

277

C₂²

#11926553

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

284

C₄

#11926683

yes

—

285

C₄

#11926700

yes

—

286

C₄

#11926717

yes

characteristic

287

C₄

#11926727

yes

characteristic

288

C₂

—

289

C₂

—

290

C₂

#14563570

yes

characteristic

291

C₂

#14563586

yes

characteristic

292

C₂

#14563594

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3502	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3502	D₁₉
hypocenter	C₁₉	#8356
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3502

C₂

socle

C₂²×C₁₉

#379

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

N	H ≅ G/N	type
206. C₁₉	#8356	semidirect

H ≅ G/N

type

206. C₁₉

#8356

semidirect

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

subgroup	index
#14564572	2
#14563631	2
#14562325	2
#14562090	2
C₁₉×#3502	2
#8356	19

subgroup

index

C₁₉×#3502

Subgroups — #18074102

Conjugacy classes of subgroups

Complements

Maximal subgroups