Group #18071117 — subgroups

Subgroups — #18071117

Order 4864.

500 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 119 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	1	yes	maximal, characteristic
2	#14563397	C₂	1	1	yes	maximal, characteristic
3	#14561458	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×#10597260	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	C₂²	1	2	yes	—
10	#11926299	C₂²	1	2	yes	—
11	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#391	—	2	1	no	—
15	C₁₉×#389	—	2	1	no	—
16	C₁₉×#389	C₂²	1	2	yes	—
17	C₁₉×#384	C₄	1	1	yes	characteristic
18	C₁₉×#380	—	2	1	no	—
19	C₁₉×#380	C₄	1	2	yes	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₁₉×C₄⋊Q₈	—	4	2	no	—
25	C₁₉×C₂²⋊Q₈	—	4	4	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	4	2	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₂²×C₁₉⋊C₈	—	2	2	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	—	2	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
44	#10597260	—	4	2	no	—
45	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×Q₈×C₁₉	—	4	2	no	—
47	C₂×Q₈×C₁₉	—	4	2	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	4	no	—
72	C₂²⋊C₄×C₁₉	—	4	4	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₂×C₁₉⋊C₈	—	2	4	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#7708	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	1	no	—
85	C₂³×C₁₉	—	2	1	no	—
86	C₂³×C₁₉	—	2	1	no	—
87	C₂³×C₁₉	—	2	1	no	—
88	C₂³×C₁₉	—	2	1	no	—
89	C₂³×C₁₉	—	2	1	no	—
90	C₂³×C₁₉	#101	1	2	yes	—
91	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	Q₈×C₁₉	—	8	4	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	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	4	4	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	2	no	—
115	C₂×C₄×C₁₉	#99	1	2	yes	—
116	C₂×C₄×C₁₉	#104	1	2	yes	—
117	C₂×C₄×C₁₉	#131	1	2	yes	—
118	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
119	C₂×C₄×C₁₉	#137	1	2	yes	—
120	C₁₉⋊C₈	—	4	4	no	—
121	C₁₉⋊C₈	—	8	2	no	—
122	#2857	D₁₉	1	1	yes	characteristic
123	#1817	—	19	1	no	—
124	#1749	—	19	1	no	—
125	#1271	—	19	4	no	—
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	2	2	no	—
128	C₂²×C₁₉	—	2	2	no	—
129	C₂²×C₁₉	—	4	1	no	—
130	C₂²×C₁₉	—	4	1	no	—
131	C₂²×C₁₉	—	4	1	no	—
132	C₂²×C₁₉	—	4	1	no	—
133	C₂²×C₁₉	#408	1	1	yes	characteristic
134	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
135	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
136	C₂²×C₁₉	#418	1	1	yes	characteristic
137	C₂²×C₁₉	#419	1	1	yes	characteristic
138	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
139	C₂²×C₁₉	#421	1	1	yes	characteristic
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
149	C₂×C₂²⋊Q₈	—	2	1	no	—
150	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
151	C₂×C₂²⋊C₈	—	38	1	no	—
152	C₂×C₂²⋊C₈	—	38	1	no	—
153	C₂×#97	—	38	1	no	—
154	#391	—	2	1	no	—
155	#389	—	2	1	no	—
156	#389	C₂×D₁₉	1	2	yes	—
157	#384	Dic₁₉	1	1	yes	characteristic
158	#380	—	2	1	no	—
159	#380	Dic₁₉	1	2	yes	—
160	#336	—	19	2	no	—
161	#336	—	19	2	no	—
162	#336	—	38	1	no	—
163	C₂×C₁₉	—	4	2	no	—
164	C₂×C₁₉	#1472	1	1	yes	characteristic
165	C₂×C₁₉	#1484	1	1	yes	characteristic
166	C₂×C₁₉	#1497	1	1	yes	characteristic
167	C₂×C₁₉	#1508	1	1	yes	characteristic
168	C₂×C₁₉	#1510	1	1	yes	characteristic
169	C₂×C₁₉	#1531	1	1	yes	characteristic
170	C₂×C₁₉	#1556	1	1	yes	characteristic
171	C₂²×Q₈	—	2	1	no	—
172	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
173	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
174	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
175	C₂²×C₈	—	38	2	no	—
176	C₂²×C₈	—	38	2	no	—
177	C₄⋊Q₈	—	4	2	no	—
178	C₂²⋊Q₈	—	4	4	no	—
179	C₂×C₄⋊C₄	—	2	1	no	—
180	C₂×C₄⋊C₄	—	2	1	no	—
181	C₂×C₄⋊C₄	—	2	1	no	—
182	C₂×C₄⋊C₄	—	2	2	no	—
183	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
184	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
185	C₂×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₄²	—	4	2	no	—
187	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
188	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
190	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
191	C₂²⋊C₈	—	38	4	no	—
192	C₂²⋊C₈	—	76	2	no	—
193	#97	—	76	2	no	—
194	#95	—	2	2	no	—
195	#95	—	2	2	no	—
196	C₁₉	#7708	1	1	yes	characteristic, complemented, Sylow
197	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
198	C₂×Q₈	—	4	2	no	—
199	C₂×Q₈	—	4	2	no	—
200	C₂×Q₈	—	4	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	4	1	no	—
210	C₂²×C₄	—	4	1	no	—
211	C₂²×C₄	—	4	1	no	—
212	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
213	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
214	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
216	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂×C₈	—	38	4	no	—
219	C₂×C₈	—	76	2	no	—
220	C₂×C₈	—	76	2	no	—
221	C₂×C₈	—	76	2	no	—
222	C₂×C₈	—	76	2	no	—
223	C₂×C₈	—	76	2	no	—
224	C₄⋊C₄	—	2	4	no	—
225	C₄⋊C₄	—	4	2	no	—
226	C₄⋊C₄	—	4	2	no	—
227	C₄⋊C₄	—	4	2	no	—
228	C₄⋊C₄	—	4	4	no	—
229	C₄⋊C₄	—	4	2	no	—
230	C₂²⋊C₄	—	4	4	no	—
231	C₄²	—	2	2	no	—
232	C₄²	—	2	2	no	—
233	C₄²	—	4	1	no	—
234	C₄²	—	4	1	no	—
235	C₂³	—	2	1	no	—
236	C₂³	—	2	1	no	—
237	C₂³	—	2	1	no	—
238	C₂³	—	2	1	no	—
239	C₂³	—	2	1	no	—
240	C₂³	—	2	1	no	—
241	C₂³	#10597293	1	2	yes	—
242	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
243	Q₈	—	8	4	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	4	4	no	—
258	C₂×C₄	—	4	4	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	#10597291	1	2	yes	—
267	C₂×C₄	#10597294	1	2	yes	—
268	C₂×C₄	#10597378	1	2	yes	—
269	C₂×C₄	#10597388	1	2	yes	—
270	C₂×C₄	#10597394	1	2	yes	—
271	C₈	—	76	4	no	—
272	C₈	—	152	2	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	4	1	no	—
277	C₂²	—	4	1	no	—
278	C₂²	—	4	1	no	—
279	C₂²	—	4	1	no	—
280	C₂²	#11926511	1	1	yes	characteristic
281	C₂²	C₂×#10597291	1	1	yes	characteristic
282	C₂²	C₂×#10597293	1	1	yes	characteristic
283	C₂²	#11926549	1	1	yes	characteristic
284	C₂²	#11926553	1	1	yes	characteristic
285	C₂²	C₂×#10597294	1	1	yes	characteristic
286	C₂²	#11926561	1	1	yes	characteristic
287	C₄	—	2	2	no	—
288	C₄	—	2	2	no	—
289	C₄	—	2	2	no	—
290	C₄	—	2	2	no	—
291	C₄	—	2	2	no	—
292	C₄	—	4	1	no	—
293	C₄	—	8	2	no	—
294	C₄	—	8	2	no	—
295	C₂	—	4	2	no	—
296	C₂	#14561999	1	1	yes	characteristic
297	C₂	#14562052	1	1	yes	characteristic
298	C₂	#14562108	1	1	yes	characteristic
299	C₂	#14562155	1	1	yes	characteristic
300	C₂	#14562164	1	1	yes	characteristic
301	C₂	#14562250	1	1	yes	characteristic
302	C₂	#14562352	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal, characteristic

#14563397

C₂

yes

maximal, characteristic

#14561458

C₂

yes

maximal, complemented

C₁₉×#2857

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

—

#11926299

C₂²

yes

—

#11926299

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊Q₈

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#389

C₂²

yes

—

C₁₉×#384

C₄

yes

characteristic

C₁₉×#380

—

C₁₉×#380

C₄

yes

—

C₂²×Q₈×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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×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

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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7708

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×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

—

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

#99

yes

—

116

C₂×C₄×C₁₉

#104

yes

—

117

C₂×C₄×C₁₉

#131

yes

—

118

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

119

C₂×C₄×C₁₉

#137

yes

—

120

C₁₉⋊C₈

—

121

C₁₉⋊C₈

—

122

#2857

D₁₉

yes

characteristic

123

#1817

—

124

#1749

—

125

#1271

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

#408

yes

characteristic

134

C₂²×C₁₉

C₂×#99

yes

characteristic

135

C₂²×C₁₉

C₂×#101

yes

characteristic

136

C₂²×C₁₉

#418

yes

characteristic

137

C₂²×C₁₉

#419

yes

characteristic

138

C₂²×C₁₉

C₂×#104

yes

characteristic

139

C₂²×C₁₉

#421

yes

characteristic

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

149

C₂×C₂²⋊Q₈

—

150

C₂²×C₄²

C₂×D₁₉

yes

characteristic

151

C₂×C₂²⋊C₈

—

152

C₂×C₂²⋊C₈

—

153

C₂×#97

—

154

#391

—

155

#389

—

156

#389

C₂×D₁₉

yes

—

157

#384

Dic₁₉

yes

characteristic

158

#380

—

159

#380

Dic₁₉

yes

—

160

#336

—

161

#336

—

162

#336

—

163

C₂×C₁₉

—

164

C₂×C₁₉

#1472

yes

characteristic

165

C₂×C₁₉

#1484

yes

characteristic

166

C₂×C₁₉

#1497

yes

characteristic

167

C₂×C₁₉

#1508

yes

characteristic

168

C₂×C₁₉

#1510

yes

characteristic

169

C₂×C₁₉

#1531

yes

characteristic

170

C₂×C₁₉

#1556

yes

characteristic

171

C₂²×Q₈

—

172

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

173

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

174

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

175

C₂²×C₈

—

176

C₂²×C₈

—

177

C₄⋊Q₈

—

178

C₂²⋊Q₈

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

—

182

C₂×C₄⋊C₄

—

183

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

184

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

185

C₂×C₂²⋊C₄

—

186

C₂×C₄²

—

187

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

188

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

189

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

190

C₂×C₄²

C₂²×D₁₉

yes

characteristic

191

C₂²⋊C₈

—

192

C₂²⋊C₈

—

193

#97

—

194

#95

—

195

#95

—

196

C₁₉

#7708

yes

characteristic, complemented, Sylow

197

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

—

212

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

213

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

214

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

215

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

216

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

217

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₂²⋊C₄

—

231

C₄²

—

232

C₄²

—

233

C₄²

—

234

C₄²

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

—

240

C₂³

—

241

C₂³

#10597293

yes

—

242

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

243

Q₈

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

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

#10597291

yes

—

267

C₂×C₄

#10597294

yes

—

268

C₂×C₄

#10597378

yes

—

269

C₂×C₄

#10597388

yes

—

270

C₂×C₄

#10597394

yes

—

271

C₈

—

272

C₈

—

152

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

#11926511

yes

characteristic

281

C₂²

C₂×#10597291

yes

characteristic

282

C₂²

C₂×#10597293

yes

characteristic

283

C₂²

#11926549

yes

characteristic

284

C₂²

#11926553

yes

characteristic

285

C₂²

C₂×#10597294

yes

characteristic

286

C₂²

#11926561

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

295

C₂

—

296

C₂

#14561999

yes

characteristic

297

C₂

#14562052

yes

characteristic

298

C₂

#14562108

yes

characteristic

299

C₂

#14562155

yes

characteristic

300

C₂

#14562164

yes

characteristic

301

C₂

#14562250

yes

characteristic

302

C₂

#14562352

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2857	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2857	D₁₉
hypocenter	C₁₉	#7708
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2857

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2857

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2857

N	H ≅ G/N	type
3. #14561458	C₂	semidirect
196. C₁₉	#7708	semidirect

H ≅ G/N

type

3. #14561458

C₂

semidirect

196. C₁₉

#7708

semidirect

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

subgroup	index
#14563703	2
#14563397	2
#14561458	2
C₁₉×#2857	2
#7708	19

subgroup

index

C₁₉×#2857

Subgroups — #18071117

Conjugacy classes of subgroups

Complements

Maximal subgroups