Group #18080394 — subgroups

Subgroups — #18080394

Order 4864.

542 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14572716	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563631	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562060	C₂	1	2	yes	maximal
4	#14561493	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2536	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926568	C₂²	1	2	yes	—
10	C₂×#10597293	—	2	1	no	—
11	#11926313	—	2	1	no	—
12	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#398	C₄	1	2	yes	—
17	C₁₉×#394	C₄	1	2	yes	—
18	C₁₉×#388	—	2	2	no	—
19	C₁₉×#382	C₂²	1	1	yes	characteristic
20	C₁₉×#380	—	2	1	no	—
21	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₁₉×C₂²⋊Q₈	—	4	2	no	—
25	C₁₉×C₂²⋊Q₈	—	4	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	D₄	1	2	yes	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×#64520	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₁₉×#95	—	2	1	no	—
43	C₁₉×#95	C₂×C₄	1	2	yes	—
44	#10597293	—	4	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄×C₁₉⋊C₈	—	2	4	no	—
51	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	D₈	1	2	yes	—
56	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	4	4	no	—
74	C₄⋊C₄×C₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₂²⋊C₄×C₁₉	—	4	4	no	—
77	C₂²⋊C₄×C₁₉	—	4	4	no	—
78	C₂²⋊C₄×C₁₉	—	4	1	no	—
79	C₂²⋊C₄×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	2	2	no	—
81	C₄²×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	#41	1	2	yes	—
84	#64520	—	4	2	no	—
85	#64520	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	#9486	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	—	4	1	no	—
91	C₂³×C₁₉	—	4	1	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	4	1	no	—
94	C₂³×C₁₉	—	4	1	no	—
95	C₂³×C₁₉	—	4	1	no	—
96	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	Q₈×C₁₉	—	2	4	no	—
98	Q₈×C₁₉	—	2	4	no	—
99	D₄×C₁₉	—	2	4	no	—
100	D₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	—	4	1	no	—
113	C₂×C₄×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	—	8	2	no	—
115	C₂×C₄×C₁₉	#102	1	4	yes	—
116	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
117	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#121	1	2	yes	—
119	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
122	C₂×C₄×C₁₉	#135	1	2	yes	—
123	C₁₉⋊C₈	—	4	4	no	—
124	C₁₉⋊C₈	—	8	2	no	—
125	#2982	—	19	1	no	—
126	#2536	D₁₉	1	1	yes	characteristic
127	#1801	—	19	1	no	—
128	#1486	—	19	2	no	—
129	#1286	—	19	2	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	4	2	no	—
134	C₂²×C₁₉	—	4	2	no	—
135	C₂²×C₁₉	—	8	1	no	—
136	C₂²×C₁₉	—	8	1	no	—
137	C₂²×C₁₉	—	8	1	no	—
138	C₂²×C₁₉	—	8	1	no	—
139	C₂²×C₁₉	#386	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
141	C₂²×C₁₉	#416	1	1	yes	characteristic
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	2	4	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	4	2	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₄×C₁₉	—	8	1	no	—
149	C₄×C₁₉	#465	1	2	yes	—
150	C₄×C₁₉	#466	1	2	yes	—
151	C₂×C₂²⋊Q₈	—	2	1	no	—
152	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
154	C₈×Q₈	—	38	4	no	—
155	#431	—	19	2	no	—
156	#431	—	38	2	no	—
157	#423	—	19	2	no	—
158	C₂×#101	—	38	1	no	—
159	#398	Dic₁₉	1	2	yes	—
160	#394	Dic₁₉	1	2	yes	—
161	#388	—	2	2	no	—
162	#382	C₂×D₁₉	1	1	yes	characteristic
163	#380	—	2	1	no	—
164	#343	—	38	1	no	—
165	D₄⋊C₈	—	38	4	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	2	1	no	—
168	C₂×C₁₉	—	8	2	no	—
169	C₂×C₁₉	#1891	1	1	yes	characteristic
170	C₂×C₁₉	#1893	1	1	yes	characteristic
171	C₂×C₁₉	#1912	1	1	yes	characteristic
172	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
173	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂³×C₄	—	2	1	no	—
175	C₂×M₁₆	—	38	2	no	—
176	C₂²⋊Q₈	—	4	2	no	—
177	C₂²⋊Q₈	—	4	2	no	—
178	C₄×Q₈	—	2	2	no	—
179	C₄×Q₈	—	2	2	no	—
180	C₄×D₄	—	2	2	no	—
181	C₄×D₄	—	2	2	no	—
182	C₂×C₄⋊C₄	—	2	2	no	—
183	C₂×C₄⋊C₄	—	2	1	no	—
184	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
186	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
187	C₂×C₂²⋊C₄	—	2	2	no	—
188	C₂×C₂²⋊C₄	—	2	2	no	—
189	C₂×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	C₄⋊C₈	—	38	4	no	—
193	C₄⋊C₈	—	38	2	no	—
194	C₄⋊C₈	—	38	2	no	—
195	C₄⋊C₈	—	38	2	no	—
196	#101	—	76	2	no	—
197	C₂²⋊C₈	—	38	2	no	—
198	C₄×C₈	—	19	4	no	—
199	C₄×C₈	—	38	4	no	—
200	#95	—	2	2	no	—
201	#95	—	2	1	no	—
202	#95	C₂×Dic₁₉	1	2	yes	—
203	C₁₉	#9486	1	1	yes	characteristic, complemented, Sylow
204	C₂⁴	—	2	1	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	#64525	1	2	yes	—
208	C₂×Q₈	#64526	1	2	yes	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	—	4	1	no	—
215	C₂²×C₄	—	4	2	no	—
216	C₂²×C₄	—	4	2	no	—
217	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
218	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
219	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
222	M₁₆	—	76	2	no	—
223	M₁₆	—	76	2	no	—
224	C₂×C₈	—	38	4	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	2	4	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₄⋊C₄	—	4	1	no	—
230	C₄⋊C₄	—	4	1	no	—
231	C₄⋊C₄	—	4	4	no	—
232	C₂²⋊C₄	—	4	4	no	—
233	C₂²⋊C₄	—	4	1	no	—
234	C₂²⋊C₄	—	4	1	no	—
235	C₂²⋊C₄	—	4	4	no	—
236	C₄²	—	2	2	no	—
237	C₄²	—	2	2	no	—
238	C₄²	D₄×D₁₉	1	2	yes	—
239	C₄²	#64543	1	2	yes	—
240	C₂³	—	2	2	no	—
241	C₂³	—	4	1	no	—
242	C₂³	—	4	1	no	—
243	C₂³	—	4	1	no	—
244	C₂³	—	4	1	no	—
245	C₂³	—	4	1	no	—
246	C₂³	—	4	1	no	—
247	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
248	Q₈	—	2	4	no	—
249	Q₈	—	2	4	no	—
250	D₄	—	2	4	no	—
251	D₄	—	4	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	1	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	1	no	—
263	C₂×C₄	—	4	1	no	—
264	C₂×C₄	—	8	2	no	—
265	C₂×C₄	—	8	2	no	—
266	C₂×C₄	#10597289	1	4	yes	—
267	C₂×C₄	C₂×#64525	1	1	yes	characteristic
268	C₂×C₄	C₂×#64526	1	1	yes	characteristic
269	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
270	C₂×C₄	#10597381	1	1	yes	characteristic
271	C₂×C₄	#10597383	1	1	yes	characteristic
272	C₂×C₄	#10597385	1	2	yes	—
273	C₂×C₄	#10597396	1	2	yes	—
274	C₈	—	76	4	no	—
275	C₈	—	152	2	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	4	2	no	—
279	C₂²	—	4	2	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	8	1	no	—
282	C₂²	—	8	1	no	—
283	C₂²	—	8	1	no	—
284	C₂²	—	8	1	no	—
285	C₂²	#11926424	1	1	yes	characteristic
286	C₂²	C₂×#10597289	1	1	yes	characteristic
287	C₂²	#11926540	1	1	yes	characteristic
288	C₄	—	2	1	no	—
289	C₄	—	2	1	no	—
290	C₄	—	2	2	no	—
291	C₄	—	2	4	no	—
292	C₄	—	4	2	no	—
293	C₄	—	8	2	no	—
294	C₄	—	8	1	no	—
295	C₄	#11926771	1	2	yes	—
296	C₄	#11926778	1	2	yes	—
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	8	2	no	—
300	C₂	#14564054	1	1	yes	characteristic
301	C₂	#14564064	1	1	yes	characteristic
302	C₂	#14564173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic, complemented

#14563631

C₂

yes

maximal, characteristic, complemented

#14562060

C₂

yes

maximal

#14561493

C₂

yes

maximal, complemented

C₁₉×#2536

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

D₄⋊(C₁₉⋊C₈)

—

C₂×C₁₉×C₂²⋊Q₈

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#398

C₄

yes

—

C₁₉×#394

C₄

yes

—

C₁₉×#388

—

C₁₉×#382

C₂²

yes

characteristic

C₁₉×#380

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

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

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

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9486

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

100

D₄×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

—

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

#102

yes

—

116

C₂×C₄×C₁₉

C₄×D₄

yes

—

117

C₂×C₄×C₁₉

#120

yes

characteristic

118

C₂×C₄×C₁₉

#121

yes

—

119

C₂×C₄×C₁₉

#123

yes

characteristic

120

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

121

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

122

C₂×C₄×C₁₉

#135

yes

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

#2982

—

126

#2536

D₁₉

yes

characteristic

127

#1801

—

128

#1486

—

129

#1286

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

#386

yes

characteristic

140

C₂²×C₁₉

C₂×#102

yes

characteristic

141

C₂²×C₁₉

#416

yes

characteristic

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

#465

yes

—

150

C₄×C₁₉

#466

yes

—

151

C₂×C₂²⋊Q₈

—

152

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

153

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

154

C₈×Q₈

—

155

#431

—

156

#431

—

157

#423

—

158

C₂×#101

—

159

#398

Dic₁₉

yes

—

160

#394

Dic₁₉

yes

—

161

#388

—

162

#382

C₂×D₁₉

yes

characteristic

163

#380

—

164

#343

—

165

D₄⋊C₈

—

166

C₂×C₁₉

—

167

C₂×C₁₉

—

168

C₂×C₁₉

—

169

C₂×C₁₉

#1891

yes

characteristic

170

C₂×C₁₉

#1893

yes

characteristic

171

C₂×C₁₉

#1912

yes

characteristic

172

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

173

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

174

C₂³×C₄

—

175

C₂×M₁₆

—

176

C₂²⋊Q₈

—

177

C₂²⋊Q₈

—

178

C₄×Q₈

—

179

C₄×Q₈

—

180

C₄×D₄

—

181

C₄×D₄

—

182

C₂×C₄⋊C₄

—

183

C₂×C₄⋊C₄

—

184

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

185

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

186

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

187

C₂×C₂²⋊C₄

—

188

C₂×C₂²⋊C₄

—

189

C₂×C₂²⋊C₄

—

190

C₂×C₄²

C₂²⋊D₁₉

yes

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

C₄⋊C₈

—

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

C₄⋊C₈

—

196

#101

—

197

C₂²⋊C₈

—

198

C₄×C₈

—

199

C₄×C₈

—

200

#95

—

201

#95

—

202

#95

C₂×Dic₁₉

yes

—

203

C₁₉

#9486

yes

characteristic, complemented, Sylow

204

C₂⁴

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

#64525

yes

—

208

C₂×Q₈

#64526

yes

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

218

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

219

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

220

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

221

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

222

M₁₆

—

223

M₁₆

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₂²⋊C₄

—

233

C₂²⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₄²

—

237

C₄²

—

238

C₄²

D₄×D₁₉

yes

—

239

C₄²

#64543

yes

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

248

Q₈

—

249

Q₈

—

250

D₄

—

251

D₄

—

252

C₂×C₄

—

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

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

#10597289

yes

—

267

C₂×C₄

C₂×#64525

yes

characteristic

268

C₂×C₄

C₂×#64526

yes

characteristic

269

C₂×C₄

D₄×Dic₁₉

yes

—

270

C₂×C₄

#10597381

yes

characteristic

271

C₂×C₄

#10597383

yes

characteristic

272

C₂×C₄

#10597385

yes

—

273

C₂×C₄

#10597396

yes

—

274

C₈

—

275

C₈

—

152

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

#11926424

yes

characteristic

286

C₂²

C₂×#10597289

yes

characteristic

287

C₂²

#11926540

yes

characteristic

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

295

C₄

#11926771

yes

—

296

C₄

#11926778

yes

—

297

C₂

—

298

C₂

—

299

C₂

—

300

C₂

#14564054

yes

characteristic

301

C₂

#14564064

yes

characteristic

302

C₂

#14564173

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2536	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2536	D₁₉
hypocenter	C₁₉	#9486
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2536

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2536

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2536

N	H ≅ G/N	type
1. #14572716	C₂	semidirect
2. #14563631	C₂	semidirect
4. #14561493	C₂	semidirect
203. C₁₉	#9486	semidirect

H ≅ G/N

type

1. #14572716

C₂

semidirect

2. #14563631

C₂

semidirect

4. #14561493

C₂

semidirect

203. C₁₉

#9486

semidirect

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

subgroup	index
#14572716	2
#14563631	2
#14562060	2
#14561493	2
C₁₉×#2536	2
#9486	19

subgroup

index

C₁₉×#2536

Subgroups — #18080394

Conjugacy classes of subgroups

Complements

Maximal subgroups