Group #18071204 — subgroups

Subgroups — #18071204

Order 4864.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14571987	C₂	1	1	yes	maximal, characteristic
2	#14563703	C₂	1	1	yes	maximal, characteristic
3	#14561460	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597315	C₄	1	1	yes	characteristic
6	C₂×#10597370	C₄	1	2	yes	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	#11926450	C₂²	1	2	yes	—
9	#11926442	—	2	1	no	—
10	#11926442	—	2	1	no	—
11	#11926414	C₄	1	1	yes	characteristic
12	#11926404	—	2	1	no	—
13	#11926404	—	2	1	no	—
14	#11926299	—	2	1	no	—
15	#11926299	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
18	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
19	C₁₉×#336	C₂²	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	—	4	2	no	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
36	#10597370	—	4	4	no	—
37	C₂×Dic₁₉⋊C₄	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	#10597315	—	4	2	no	—
40	C₁₉×C₄⋊C₈	—	4	2	no	—
41	C₁₉×C₂²⋊C₈	—	4	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
45	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	1	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
58	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×Dic₁₉	—	2	2	no	—
63	C₂²×Dic₁₉	—	2	2	no	—
64	C₂×Dic₃₈	—	2	4	no	—
65	C₂×Dic₃₈	—	4	2	no	—
66	C₂×Dic₃₈	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	1	no	—
74	C₂²⋊Dic₁₉	—	4	4	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄⋊Dic₁₉	—	4	2	no	—
80	Dic₁₉⋊C₄	—	4	4	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	4	2	no	—
84	#7727	—	19	1	no	maximal, Sylow
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	—	2	1	no	—
91	C₂³×C₁₉	#103	1	2	yes	—
92	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	4	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	#99	1	2	yes	—
110	C₂×C₄×C₁₉	#100	1	2	yes	—
111	C₂×C₄×C₁₉	#103	1	2	yes	—
112	C₂×C₄×C₁₉	#131	1	2	yes	—
113	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#137	1	2	yes	—
116	C₂×Dic₁₉	—	4	2	no	—
117	C₂×Dic₁₉	—	4	2	no	—
118	C₂×Dic₁₉	—	4	2	no	—
119	C₂×Dic₁₉	—	4	2	no	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	Dic₃₈	—	8	4	no	—
123	C₈×C₁₉	—	8	2	no	—
124	C₁₉⋊C₈	—	8	2	no	—
125	#2857	—	19	1	no	—
126	#1817	—	19	1	no	—
127	#1797	D₁₉	1	1	yes	characteristic
128	#1272	—	19	4	no	—
129	C₂²×C₁₉	—	2	2	no	—
130	C₂²×C₁₉	—	2	2	no	—
131	C₂²×C₁₉	—	2	2	no	—
132	C₂²×C₁₉	—	4	1	no	—
133	C₂²×C₁₉	—	4	1	no	—
134	C₂²×C₁₉	—	4	1	no	—
135	C₂²×C₁₉	—	4	1	no	—
136	C₂²×C₁₉	#408	1	1	yes	characteristic
137	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
138	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
139	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
140	C₂²×C₁₉	#419	1	1	yes	characteristic
141	C₂²×C₁₉	#421	1	1	yes	characteristic
142	C₂²×C₁₉	#421	1	1	yes	characteristic
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	2	2	no	—
145	C₄×C₁₉	—	2	2	no	—
146	C₄×C₁₉	—	2	2	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	1	no	—
150	Dic₁₉	—	8	2	no	—
151	Dic₁₉	—	8	2	no	—
152	C₂×C₄⋊Q₈	—	19	1	no	—
153	C₂×C₂²⋊Q₈	—	19	2	no	—
154	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
155	C₂×C₄⋊C₈	—	2	1	no	—
156	C₂×C₂²⋊C₈	—	2	1	no	—
157	C₂×C₂²⋊C₈	—	38	1	no	—
158	#391	—	19	2	no	—
159	#389	—	38	1	no	—
160	#389	—	38	1	no	—
161	#384	—	19	1	no	—
162	#380	—	38	1	no	—
163	#380	—	38	1	no	—
164	#336	—	19	2	no	—
165	#336	—	38	1	no	—
166	#336	C₂×D₁₉	1	2	yes	—
167	C₂×C₁₉	—	4	2	no	—
168	C₂×C₁₉	#1471	1	1	yes	characteristic
169	C₂×C₁₉	#1481	1	1	yes	characteristic
170	C₂×C₁₉	#1497	1	1	yes	characteristic
171	C₂×C₁₉	#1511	1	1	yes	characteristic
172	C₂×C₁₉	#1520	1	1	yes	characteristic
173	C₂×C₁₉	#1536	1	1	yes	characteristic
174	C₂×C₁₉	#1548	1	1	yes	characteristic
175	C₂²×Q₈	—	19	2	no	—
176	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
177	C₂³×C₄	D₇₆	1	1	yes	characteristic
178	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	—	38	2	no	—
181	C₄⋊Q₈	—	76	2	no	—
182	C₂²⋊Q₈	—	76	4	no	—
183	C₂×C₄⋊C₄	—	19	2	no	—
184	C₂×C₄⋊C₄	—	38	2	no	—
185	C₂×C₄⋊C₄	—	38	1	no	—
186	C₂×C₄⋊C₄	—	38	1	no	—
187	C₂×C₄⋊C₄	—	38	1	no	—
188	C₂×C₄⋊C₄	—	38	1	no	—
189	C₂×C₂²⋊C₄	—	38	2	no	—
190	C₂×C₄²	—	4	2	no	—
191	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
192	C₂×C₄²	D₇₆	1	1	yes	characteristic
193	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
194	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	C₄⋊C₈	—	4	2	no	—
196	C₂²⋊C₈	—	4	2	no	—
197	C₂²⋊C₈	—	76	2	no	—
198	#95	—	38	2	no	—
199	#95	—	38	2	no	—
200	C₁₉	#7727	1	1	yes	characteristic, complemented, Sylow
201	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂×Q₈	—	38	4	no	—
203	C₂×Q₈	—	76	2	no	—
204	C₂×Q₈	—	76	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	—	4	1	no	—
213	C₂²×C₄	—	38	2	no	—
214	C₂²×C₄	—	38	2	no	—
215	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
216	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
218	C₂²×C₄	#64526	1	2	yes	—
219	C₂²×C₄	#64528	1	2	yes	—
220	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
222	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂×C₈	—	4	2	no	—
224	C₂×C₈	—	4	2	no	—
225	C₂×C₈	—	4	2	no	—
226	C₂×C₈	—	76	2	no	—
227	C₂×C₈	—	76	2	no	—
228	C₂×C₈	—	76	2	no	—
229	C₄⋊C₄	—	76	2	no	—
230	C₄⋊C₄	—	76	2	no	—
231	C₄⋊C₄	—	76	2	no	—
232	C₄⋊C₄	—	76	2	no	—
233	C₄⋊C₄	—	76	2	no	—
234	C₄⋊C₄	—	76	4	no	—
235	C₂²⋊C₄	—	76	4	no	—
236	C₄²	—	2	2	no	—
237	C₄²	—	2	2	no	—
238	C₄²	—	4	1	no	—
239	C₄²	—	4	1	no	—
240	C₂³	—	2	1	no	—
241	C₂³	—	2	1	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	—	2	1	no	—
246	C₂³	#10597267	1	2	yes	—
247	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
248	Q₈	—	152	4	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	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂×C₄	—	76	2	no	—
266	C₂×C₄	—	76	2	no	—
267	C₂×C₄	—	76	2	no	—
268	C₂×C₄	—	76	2	no	—
269	C₂×C₄	—	76	2	no	—
270	C₂×C₄	—	76	2	no	—
271	C₂×C₄	#10597263	1	2	yes	—
272	C₂×C₄	#10597267	1	2	yes	—
273	C₂×C₄	#10597280	1	2	yes	—
274	C₂×C₄	#10597347	1	2	yes	—
275	C₂×C₄	#10597355	1	2	yes	—
276	C₂×C₄	C₂×#64526	1	1	yes	characteristic
277	C₂×C₄	C₂×#64528	1	1	yes	characteristic
278	C₈	—	8	2	no	—
279	C₈	—	152	2	no	—
280	C₂²	—	2	2	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	4	1	no	—
284	C₂²	—	4	1	no	—
285	C₂²	—	4	1	no	—
286	C₂²	—	4	1	no	—
287	C₂²	#11926510	1	1	yes	characteristic
288	C₂²	C₂×#10597263	1	1	yes	characteristic
289	C₂²	C₂×#10597280	1	1	yes	characteristic
290	C₂²	C₂×#10597267	1	1	yes	characteristic
291	C₂²	#11926554	1	1	yes	characteristic
292	C₂²	#11926560	1	1	yes	characteristic
293	C₂²	#11926562	1	1	yes	characteristic
294	C₄	—	2	2	no	—
295	C₄	—	2	2	no	—
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	2	2	no	—
299	C₄	—	2	2	no	—
300	C₄	—	2	2	no	—
301	C₄	—	152	2	no	—
302	C₄	—	152	2	no	—
303	C₂	—	4	2	no	—
304	C₂	#14561994	1	1	yes	characteristic
305	C₂	#14562037	1	1	yes	characteristic
306	C₂	#14562109	1	1	yes	characteristic
307	C₂	#14562169	1	1	yes	characteristic
308	C₂	#14562206	1	1	yes	characteristic
309	C₂	#14562269	1	1	yes	characteristic
310	C₂	#14562317	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571987

C₂

yes

maximal, characteristic

#14563703

C₂

yes

maximal, characteristic

#14561460

C₂

yes

maximal, complemented

C₁₉×#1797

C₂

yes

maximal, characteristic

C₂×#10597315

C₄

yes

characteristic

C₂×#10597370

C₄

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926450

C₂²

yes

—

#11926442

—

#11926442

—

#11926414

C₄

yes

—

—

—

C₂²

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₂²⋊C₈

—

C₁₉×#336

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×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

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

—

#10597315

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

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

SD₁₆

yes

—

C₂²×C₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7727

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

#99

yes

—

110

C₂×C₄×C₁₉

#100

yes

—

111

C₂×C₄×C₁₉

#103

yes

—

112

C₂×C₄×C₁₉

#131

yes

—

113

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

114

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

115

C₂×C₄×C₁₉

#137

yes

—

116

C₂×Dic₁₉

—

117

C₂×Dic₁₉

—

118

C₂×Dic₁₉

—

119

C₂×Dic₁₉

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

Dic₃₈

—

123

C₈×C₁₉

—

124

C₁₉⋊C₈

—

125

#2857

—

126

#1817

—

127

#1797

D₁₉

yes

characteristic

128

#1272

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

#408

yes

characteristic

137

C₂²×C₁₉

C₂×#99

yes

characteristic

138

C₂²×C₁₉

C₂×#100

yes

characteristic

139

C₂²×C₁₉

C₂×#103

yes

characteristic

140

C₂²×C₁₉

#419

yes

characteristic

141

C₂²×C₁₉

#421

yes

characteristic

142

C₂²×C₁₉

#421

yes

characteristic

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

Dic₁₉

—

151

Dic₁₉

—

152

C₂×C₄⋊Q₈

—

153

C₂×C₂²⋊Q₈

—

154

C₂²×C₄²

C₂×D₁₉

yes

characteristic

155

C₂×C₄⋊C₈

—

156

C₂×C₂²⋊C₈

—

157

C₂×C₂²⋊C₈

—

158

#391

—

159

#389

—

160

#389

—

161

#384

—

162

#380

—

163

#380

—

164

#336

—

165

#336

—

166

#336

C₂×D₁₉

yes

—

167

C₂×C₁₉

—

168

C₂×C₁₉

#1471

yes

characteristic

169

C₂×C₁₉

#1481

yes

characteristic

170

C₂×C₁₉

#1497

yes

characteristic

171

C₂×C₁₉

#1511

yes

characteristic

172

C₂×C₁₉

#1520

yes

characteristic

173

C₂×C₁₉

#1536

yes

characteristic

174

C₂×C₁₉

#1548

yes

characteristic

175

C₂²×Q₈

—

176

C₂³×C₄

C₄×D₁₉

yes

characteristic

177

C₂³×C₄

D₇₆

yes

characteristic

178

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

179

C₂²×C₈

—

180

C₂²×C₈

—

181

C₄⋊Q₈

—

182

C₂²⋊Q₈

—

183

C₂×C₄⋊C₄

—

184

C₂×C₄⋊C₄

—

185

C₂×C₄⋊C₄

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄⋊C₄

—

189

C₂×C₂²⋊C₄

—

190

C₂×C₄²

—

191

C₂×C₄²

C₄×D₁₉

yes

characteristic

192

C₂×C₄²

D₇₆

yes

characteristic

193

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

194

C₂×C₄²

C₂²×D₁₉

yes

characteristic

195

C₄⋊C₈

—

196

C₂²⋊C₈

—

197

C₂²⋊C₈

—

198

#95

—

199

#95

—

200

C₁₉

#7727

yes

characteristic, complemented, Sylow

201

C₂⁴

(C₂×D₁₉)⋊C₄

yes

characteristic

202

C₂×Q₈

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

216

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

217

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

218

C₂²×C₄

#64526

yes

—

219

C₂²×C₄

#64528

yes

—

220

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

221

C₂²×C₄

C₂×D₇₆

yes

characteristic

222

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₂²⋊C₄

—

236

C₄²

—

237

C₄²

—

238

C₄²

—

239

C₄²

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

#10597267

yes

—

247

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

248

Q₈

—

152

—

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

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

#10597263

yes

—

272

C₂×C₄

#10597267

yes

—

273

C₂×C₄

#10597280

yes

—

274

C₂×C₄

#10597347

yes

—

275

C₂×C₄

#10597355

yes

—

276

C₂×C₄

C₂×#64526

yes

characteristic

277

C₂×C₄

C₂×#64528

yes

characteristic

278

C₈

—

279

C₈

—

152

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

#11926510

yes

characteristic

288

C₂²

C₂×#10597263

yes

characteristic

289

C₂²

C₂×#10597280

yes

characteristic

290

C₂²

C₂×#10597267

yes

characteristic

291

C₂²

#11926554

yes

characteristic

292

C₂²

#11926560

yes

characteristic

293

C₂²

#11926562

yes

characteristic

294

C₄

—

295

C₄

—

296

C₄

—

297

C₄

—

298

C₄

—

299

C₄

—

300

C₄

—

301

C₄

—

152

—

302

C₄

—

152

—

303

C₂

—

304

C₂

#14561994

yes

characteristic

305

C₂

#14562037

yes

characteristic

306

C₂

#14562109

yes

characteristic

307

C₂

#14562169

yes

characteristic

308

C₂

#14562206

yes

characteristic

309

C₂

#14562269

yes

characteristic

310

C₂

#14562317

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1797	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1797	D₁₉
hypocenter	C₁₉	#7727
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1797

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1797

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 ◁ #1797

N	H ≅ G/N	type
3. #14561460	C₂	semidirect
200. C₁₉	#7727	semidirect

H ≅ G/N

type

3. #14561460

C₂

semidirect

200. C₁₉

#7727

semidirect

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

subgroup	index
#14571987	2
#14563703	2
#14561460	2
C₁₉×#1797	2
#7727	19

subgroup

index

C₁₉×#1797

Subgroups — #18071204

Conjugacy classes of subgroups

Complements

Maximal subgroups