Group #18075947 — subgroups

Subgroups — #18075947

Order 4864.

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

normal subgroups only

This group has 526 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	#14566042	C₂	1	1	yes	maximal, characteristic
2	#14563397	C₂	1	1	yes	maximal, characteristic
3	#14561517	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1749	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597372	C₄	1	2	yes	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×#10597260	C₂²	1	2	yes	—
8	#11926414	C₄	1	1	yes	characteristic
9	#11926414	C₄	1	1	yes	characteristic
10	#11926410	C₂²	1	2	yes	—
11	#11926404	—	2	1	no	—
12	#11926404	—	2	1	no	—
13	C₄×C₄⋊Dic₁₉	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	—	2	1	no	—
15	#11926299	—	2	1	no	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₁₉×#97	C₂²	1	2	yes	—
19	C₁₉×#336	—	2	1	no	—
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×C₈×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	—	2	4	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
30	#10597372	—	4	4	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	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄×Dic₁₉	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₁₉×C₂²⋊C₈	—	2	4	no	—
40	C₁₉×#97	—	2	4	no	—
41	C₁₉⋊#95	—	2	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	#10597260	—	2	4	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	—	2	2	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₁₉	—	2	2	no	—
62	C₂²×Dic₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	—	2	2	no	—
67	C₄²×C₁₉	—	2	2	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	#41	1	4	yes	—
70	C₂²⋊Dic₁₉	—	4	4	no	—
71	C₄⋊Dic₁₉	—	4	2	no	—
72	C₄⋊Dic₁₉	—	4	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄×Dic₁₉	—	4	4	no	—
78	C₂×C₁₉⋊C₈	—	2	4	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	#8721	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	1	no	—
83	C₂³×C₁₉	—	2	1	no	—
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	#101	1	2	yes	—
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	—	2	8	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	—	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	—	4	4	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	#100	1	2	yes	—
106	C₂×C₄×C₁₉	#104	1	2	yes	—
107	C₂×C₄×C₁₉	#104	1	2	yes	—
108	C₂×C₄×C₁₉	#117	1	2	yes	—
109	C₂×C₄×C₁₉	#123	1	2	yes	—
110	C₂×C₄×C₁₉	#123	1	2	yes	—
111	C₂×Dic₁₉	—	4	2	no	—
112	C₂×Dic₁₉	—	4	2	no	—
113	C₂×Dic₁₉	—	4	2	no	—
114	C₂×Dic₁₉	—	4	2	no	—
115	C₂×Dic₁₉	—	4	2	no	—
116	C₂×Dic₁₉	—	4	2	no	—
117	C₈×C₁₉	—	4	4	no	—
118	C₁₉⋊C₈	—	4	4	no	—
119	#2285	—	19	1	no	—
120	#1749	—	19	1	no	—
121	#1749	D₁₉	1	1	yes	characteristic
122	#1295	—	19	4	no	—
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	—	4	1	no	—
128	C₂²×C₁₉	—	4	1	no	—
129	C₂²×C₁₉	—	4	1	no	—
130	C₂²×C₁₉	#381	1	1	yes	characteristic
131	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
132	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
133	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
134	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
135	C₂²×C₁₉	#421	1	1	yes	characteristic
136	C₂²×C₁₉	#421	1	1	yes	characteristic
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	—	2	2	no	—
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	Dic₁₉	—	8	2	no	—
144	Dic₁₉	—	8	2	no	—
145	C₂×#117	—	19	2	no	—
146	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
147	C₂×C₂²⋊C₈	—	2	1	no	—
148	C₂×C₂²⋊C₈	—	38	1	no	—
149	C₂×#97	—	19	2	no	—
150	C₂×#97	C₂×D₁₉	1	2	yes	—
151	#384	—	19	1	no	—
152	#384	—	19	1	no	—
153	#382	—	19	2	no	—
154	#380	—	38	1	no	—
155	#380	—	38	1	no	—
156	C₄×C₄⋊C₄	—	38	1	no	—
157	C₄×C₄⋊C₄	—	38	1	no	—
158	#336	—	2	1	no	—
159	#336	—	38	1	no	—
160	C₂×C₁₉	—	4	2	no	—
161	C₂×C₁₉	#1525	1	1	yes	characteristic
162	C₂×C₁₉	#1531	1	1	yes	characteristic
163	C₂×C₁₉	#1531	1	1	yes	characteristic
164	C₂×C₁₉	#1536	1	1	yes	characteristic
165	C₂×C₁₉	#1821	1	1	yes	characteristic
166	C₂×C₁₉	#1826	1	1	yes	characteristic
167	C₂×C₁₉	#1826	1	1	yes	characteristic
168	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
169	C₂³×C₄	D₇₆	1	1	yes	characteristic
170	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
171	C₂²×C₈	—	2	2	no	—
172	C₂²×C₈	—	38	2	no	—
173	#117	—	76	4	no	—
174	C₂×C₄⋊C₄	—	19	2	no	—
175	C₂×C₄⋊C₄	—	19	2	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	—	38	1	no	—
179	C₂×C₄⋊C₄	—	38	1	no	—
180	C₂×C₂²⋊C₄	—	38	2	no	—
181	C₂×C₄²	—	2	4	no	—
182	C₂×C₄²	—	38	2	no	—
183	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
184	C₂×C₄²	D₇₆	1	1	yes	characteristic
185	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
187	C₂²⋊C₈	—	2	4	no	—
188	C₂²⋊C₈	—	38	4	no	—
189	#97	—	2	4	no	—
190	#97	—	38	4	no	—
191	#95	—	38	2	no	—
192	#95	—	38	2	no	—
193	C₁₉	#8721	1	1	yes	characteristic, complemented, Sylow
194	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
195	C₂²×C₄	—	2	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	4	1	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	—	38	2	no	—
205	C₂²×C₄	—	38	2	no	—
206	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
211	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
212	C₂×C₈	—	2	4	no	—
213	C₂×C₈	—	4	2	no	—
214	C₂×C₈	—	4	2	no	—
215	C₂×C₈	—	38	4	no	—
216	C₂×C₈	—	76	2	no	—
217	C₂×C₈	—	76	2	no	—
218	C₄⋊C₄	—	76	2	no	—
219	C₄⋊C₄	—	76	2	no	—
220	C₄⋊C₄	—	76	2	no	—
221	C₄⋊C₄	—	76	2	no	—
222	C₄⋊C₄	—	76	2	no	—
223	C₄⋊C₄	—	76	2	no	—
224	C₂²⋊C₄	—	76	4	no	—
225	C₄²	—	2	2	no	—
226	C₄²	—	2	2	no	—
227	C₄²	—	2	2	no	—
228	C₄²	—	76	4	no	—
229	C₄²	#64543	1	4	yes	—
230	C₂³	—	2	1	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	2	1	no	—
233	C₂³	—	2	1	no	—
234	C₂³	—	2	1	no	—
235	C₂³	—	2	1	no	—
236	C₂³	#10597281	1	2	yes	—
237	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
238	C₂×C₄	—	2	8	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	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	—	4	4	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	76	2	no	—
254	C₂×C₄	—	76	2	no	—
255	C₂×C₄	—	76	2	no	—
256	C₂×C₄	—	76	2	no	—
257	C₂×C₄	—	76	2	no	—
258	C₂×C₄	—	76	2	no	—
259	C₂×C₄	#10597262	1	2	yes	—
260	C₂×C₄	#10597280	1	2	yes	—
261	C₂×C₄	#10597282	1	2	yes	—
262	C₂×C₄	#10597323	1	2	yes	—
263	C₂×C₄	#10597332	1	2	yes	—
264	C₂×C₄	#10597381	1	2	yes	—
265	C₈	—	4	4	no	—
266	C₈	—	76	4	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	2	no	—
270	C₂²	—	4	1	no	—
271	C₂²	—	4	1	no	—
272	C₂²	—	4	1	no	—
273	C₂²	—	4	1	no	—
274	C₂²	#11926405	1	1	yes	characteristic
275	C₂²	C₂×#10597280	1	1	yes	characteristic
276	C₂²	C₂×#10597281	1	1	yes	characteristic
277	C₂²	C₂×#10597282	1	1	yes	characteristic
278	C₂²	C₂×#10597262	1	1	yes	characteristic
279	C₂²	#11926560	1	1	yes	characteristic
280	C₂²	#11926562	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	152	2	no	—
288	C₄	—	152	2	no	—
289	C₂	—	4	2	no	—
290	C₂	#14562226	1	1	yes	characteristic
291	C₂	#14562249	1	1	yes	characteristic
292	C₂	#14562251	1	1	yes	characteristic
293	C₂	#14562269	1	1	yes	characteristic
294	C₂	#14563713	1	1	yes	characteristic
295	C₂	#14563732	1	1	yes	characteristic
296	C₂	#14563735	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566042

C₂

yes

maximal, characteristic

#14563397

C₂

yes

maximal, characteristic

#14561517

C₂

yes

maximal, complemented

C₁₉×#1749

C₂

yes

maximal, characteristic

C₂×#10597372

C₄

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

C₂²

yes

—

#11926414

C₄

yes

characteristic

#11926414

C₄

yes

characteristic

#11926410

C₂²

yes

—

#11926404

—

#11926404

—

C₄×C₄⋊Dic₁₉

—

C₄×C₄⋊Dic₁₉

—

#11926299

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

—

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

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

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

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×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

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8721

—

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

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

#100

yes

—

106

C₂×C₄×C₁₉

#104

yes

—

107

C₂×C₄×C₁₉

#104

yes

—

108

C₂×C₄×C₁₉

#117

yes

—

109

C₂×C₄×C₁₉

#123

yes

—

110

C₂×C₄×C₁₉

#123

yes

—

111

C₂×Dic₁₉

—

112

C₂×Dic₁₉

—

113

C₂×Dic₁₉

—

114

C₂×Dic₁₉

—

115

C₂×Dic₁₉

—

116

C₂×Dic₁₉

—

117

C₈×C₁₉

—

118

C₁₉⋊C₈

—

119

#2285

—

120

#1749

—

121

#1749

D₁₉

yes

characteristic

122

#1295

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

#381

yes

characteristic

131

C₂²×C₁₉

C₂×#100

yes

characteristic

132

C₂²×C₁₉

C₂×#101

yes

characteristic

133

C₂²×C₁₉

C₂×#104

yes

characteristic

134

C₂²×C₁₉

C₂×#104

yes

characteristic

135

C₂²×C₁₉

#421

yes

characteristic

136

C₂²×C₁₉

#421

yes

characteristic

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

Dic₁₉

—

144

Dic₁₉

—

145

C₂×#117

—

146

C₂²×C₄²

C₂×D₁₉

yes

characteristic

147

C₂×C₂²⋊C₈

—

148

C₂×C₂²⋊C₈

—

149

C₂×#97

—

150

C₂×#97

C₂×D₁₉

yes

—

151

#384

—

152

#384

—

153

#382

—

154

#380

—

155

#380

—

156

C₄×C₄⋊C₄

—

157

C₄×C₄⋊C₄

—

158

#336

—

159

#336

—

160

C₂×C₁₉

—

161

C₂×C₁₉

#1525

yes

characteristic

162

C₂×C₁₉

#1531

yes

characteristic

163

C₂×C₁₉

#1531

yes

characteristic

164

C₂×C₁₉

#1536

yes

characteristic

165

C₂×C₁₉

#1821

yes

characteristic

166

C₂×C₁₉

#1826

yes

characteristic

167

C₂×C₁₉

#1826

yes

characteristic

168

C₂³×C₄

C₄×D₁₉

yes

characteristic

169

C₂³×C₄

D₇₆

yes

characteristic

170

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

171

C₂²×C₈

—

172

C₂²×C₈

—

173

#117

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

179

C₂×C₄⋊C₄

—

180

C₂×C₂²⋊C₄

—

181

C₂×C₄²

—

182

C₂×C₄²

—

183

C₂×C₄²

C₄×D₁₉

yes

characteristic

184

C₂×C₄²

D₇₆

yes

characteristic

185

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

186

C₂×C₄²

C₂²×D₁₉

yes

characteristic

187

C₂²⋊C₈

—

188

C₂²⋊C₈

—

189

#97

—

190

#97

—

191

#95

—

192

#95

—

193

C₁₉

#8721

yes

characteristic, complemented, Sylow

194

C₂⁴

(C₂×D₁₉)⋊C₄

yes

characteristic

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

207

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

208

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

209

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

210

C₂²×C₄

C₂×D₇₆

yes

characteristic

211

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₂²⋊C₄

—

225

C₄²

—

226

C₄²

—

227

C₄²

—

228

C₄²

—

229

C₄²

#64543

yes

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

#10597281

yes

—

237

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

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

—

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

#10597262

yes

—

260

C₂×C₄

#10597280

yes

—

261

C₂×C₄

#10597282

yes

—

262

C₂×C₄

#10597323

yes

—

263

C₂×C₄

#10597332

yes

—

264

C₂×C₄

#10597381

yes

—

265

C₈

—

266

C₈

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

#11926405

yes

characteristic

275

C₂²

C₂×#10597280

yes

characteristic

276

C₂²

C₂×#10597281

yes

characteristic

277

C₂²

C₂×#10597282

yes

characteristic

278

C₂²

C₂×#10597262

yes

characteristic

279

C₂²

#11926560

yes

characteristic

280

C₂²

#11926562

yes

characteristic

281

C₄

—

282

C₄

—

283

C₄

—

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

152

—

288

C₄

—

152

—

289

C₂

—

290

C₂

#14562226

yes

characteristic

291

C₂

#14562249

yes

characteristic

292

C₂

#14562251

yes

characteristic

293

C₂

#14562269

yes

characteristic

294

C₂

#14563713

yes

characteristic

295

C₂

#14563732

yes

characteristic

296

C₂

#14563735

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1749	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1749	D₁₉
hypocenter	C₁₉	#8721
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1749

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1749

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 ◁ #1749

N	H ≅ G/N	type
3. #14561517	C₂	semidirect
193. C₁₉	#8721	semidirect

H ≅ G/N

type

3. #14561517

C₂

semidirect

193. C₁₉

#8721

semidirect

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

subgroup	index
#14566042	2
#14563397	2
#14561517	2
C₁₉×#1749	2
#8721	19

subgroup

index

C₁₉×#1749

Subgroups — #18075947

Conjugacy classes of subgroups

Complements

Maximal subgroups