Group #18079925 — subgroups

Subgroups — #18079925

Order 4864.

730 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14572659	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563627	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562303	C₂	1	2	yes	maximal, complemented
4	#14561538	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2541	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597290	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	#11926313	—	2	1	no	—
12	#11926288	—	2	4	no	—
13	C₂×C₁₉×#127	—	2	1	no	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#392	C₄	1	4	yes	—
18	C₁₉×#390	—	2	1	no	—
19	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	—	2	4	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	2	yes	—
26	C₁₉×#127	—	2	2	no	—
27	C₁₉×#127	—	2	2	no	—
28	C₁₉×#127	—	4	2	no	—
29	C₁₉×#127	—	4	2	no	—
30	C₁₉×#121	—	4	8	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₄×D₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
36	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×#64520	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	4	no	—
41	C₁₉×#95	C₂×C₄	1	2	yes	—
42	#10597290	—	4	2	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
48	C₄×C₁₉⋊C₈	—	2	2	no	—
49	C₂⁴×C₁₉	—	2	2	no	—
50	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	4	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	4	4	no	—
55	C₂×D₄×C₁₉	—	4	8	no	—
56	C₂×D₄×C₁₉	—	4	8	no	—
57	C₂×D₄×C₁₉	—	4	1	no	—
58	C₂×D₄×C₁₉	—	4	2	no	—
59	C₂×D₄×C₁₉	—	4	1	no	—
60	C₂×D₄×C₁₉	—	4	1	no	—
61	C₂×D₄×C₁₉	—	4	1	no	—
62	C₂×D₄×C₁₉	—	4	2	no	—
63	C₂×D₄×C₁₉	—	8	4	no	—
64	C₂×D₄×C₁₉	—	8	2	no	—
65	C₂×D₄×C₁₉	D₈	1	2	yes	—
66	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	4	4	no	—
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₂²⋊C₄×C₁₉	—	2	4	no	—
78	C₂²⋊C₄×C₁₉	—	4	8	no	—
79	C₄²×C₁₉	—	4	1	no	—
80	C₄²×C₁₉	—	4	1	no	—
81	C₄²×C₁₉	C₂×D₄	1	2	yes	—
82	C₄²×C₁₉	#41	1	2	yes	—
83	#64520	—	4	2	no	—
84	#64520	—	4	2	no	—
85	C₂×C₁₉⋊C₈	—	2	4	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	8	4	no	—
88	#9397	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	—	2	2	no	—
91	C₂³×C₁₉	—	4	2	no	—
92	C₂³×C₁₉	—	4	2	no	—
93	C₂³×C₁₉	—	4	4	no	—
94	C₂³×C₁₉	—	4	4	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	—	4	2	no	—
98	C₂³×C₁₉	#102	1	4	yes	—
99	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	D₄×C₁₉	—	2	4	no	—
101	D₄×C₁₉	—	2	4	no	—
102	D₄×C₁₉	—	8	4	no	—
103	D₄×C₁₉	—	8	2	no	—
104	D₄×C₁₉	—	8	16	no	—
105	D₄×C₁₉	—	8	2	no	—
106	D₄×C₁₉	—	8	2	no	—
107	D₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	4	no	—
110	C₂×C₄×C₁₉	—	2	2	no	—
111	C₂×C₄×C₁₉	—	4	1	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	4	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	8	2	no	—
117	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#121	1	2	yes	—
120	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#135	1	2	yes	—
124	C₁₉⋊C₈	—	4	4	no	—
125	C₁₉⋊C₈	—	8	2	no	—
126	#2972	—	19	1	no	—
127	#2541	D₁₉	1	1	yes	characteristic
128	#1800	—	19	1	no	—
129	#1545	—	19	2	no	—
130	#1303	—	19	2	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	2	4	no	—
134	C₂²×C₁₉	—	4	4	no	—
135	C₂²×C₁₉	—	4	2	no	—
136	C₂²×C₁₉	—	4	2	no	—
137	C₂²×C₁₉	—	8	2	no	—
138	C₂²×C₁₉	—	8	4	no	—
139	C₂²×C₁₉	—	8	4	no	—
140	C₂²×C₁₉	—	8	2	no	—
141	C₂²×C₁₉	—	8	2	no	—
142	C₂²×C₁₉	—	8	2	no	—
143	C₂²×C₁₉	#386	1	1	yes	characteristic
144	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
145	C₂²×C₁₉	#416	1	1	yes	characteristic
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	—	4	4	no	—
149	C₄×C₁₉	—	4	2	no	—
150	C₄×C₁₉	#453	1	2	yes	—
151	C₄×C₁₉	#465	1	2	yes	—
152	C₄×C₁₉	#466	1	2	yes	—
153	C₂×#127	—	2	1	no	—
154	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
155	C₂×#121	—	2	2	no	—
156	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
157	C₈×D₄	—	38	4	no	—
158	#431	—	19	2	no	—
159	#423	—	19	2	no	—
160	C₂×#100	—	38	1	no	—
161	C₂×C₂²⋊C₈	—	38	2	no	—
162	#392	Dic₁₉	1	4	yes	—
163	#390	—	2	1	no	—
164	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
165	#343	—	38	1	no	—
166	#331	—	38	4	no	—
167	C₂×C₁₉	—	2	1	no	—
168	C₂×C₁₉	—	2	1	no	—
169	C₂×C₁₉	—	4	4	no	—
170	C₂×C₁₉	—	16	2	no	—
171	C₂×C₁₉	#1887	1	1	yes	characteristic
172	C₂×C₁₉	#1893	1	1	yes	characteristic
173	C₂×C₁₉	#1914	1	1	yes	characteristic
174	C₂²×D₄	—	2	4	no	—
175	C₂²×D₄	—	2	1	no	—
176	C₂²×D₄	—	2	1	no	—
177	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
178	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
179	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
180	C₂×M₁₆	—	38	2	no	—
181	C₂²×C₈	—	38	4	no	—
182	#127	—	2	2	no	—
183	#127	—	2	2	no	—
184	#127	—	4	2	no	—
185	#127	—	4	2	no	—
186	#121	—	4	8	no	—
187	C₄×D₄	—	2	2	no	—
188	C₄×D₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	—	2	4	no	—
192	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
193	C₂×C₄²	—	2	1	no	—
194	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	C₄⋊C₈	—	19	4	no	—
196	C₄⋊C₈	—	38	2	no	—
197	C₄⋊C₈	—	38	2	no	—
198	#100	—	76	2	no	—
199	C₂²⋊C₈	—	38	4	no	—
200	C₂²⋊C₈	—	38	2	no	—
201	C₄×C₈	—	38	2	no	—
202	#95	C₂×Dic₁₉	1	2	yes	—
203	C₁₉	#9397	1	1	yes	characteristic, complemented, Sylow
204	C₂⁴	—	2	2	no	—
205	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
206	C₂×D₄	—	2	4	no	—
207	C₂×D₄	—	2	2	no	—
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	4	4	no	—
210	C₂×D₄	—	4	8	no	—
211	C₂×D₄	—	4	8	no	—
212	C₂×D₄	—	4	1	no	—
213	C₂×D₄	—	4	1	no	—
214	C₂×D₄	—	4	1	no	—
215	C₂×D₄	—	4	1	no	—
216	C₂×D₄	—	4	2	no	—
217	C₂×D₄	—	4	2	no	—
218	C₂×D₄	—	8	4	no	—
219	C₂×D₄	—	8	2	no	—
220	C₂×D₄	#64525	1	2	yes	—
221	C₂×D₄	#64526	1	2	yes	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	4	4	no	—
226	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
227	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	M₁₆	—	76	2	no	—
231	M₁₆	—	76	2	no	—
232	C₂×C₈	—	38	4	no	—
233	C₂×C₈	—	76	2	no	—
234	C₂×C₈	—	152	4	no	—
235	C₄⋊C₄	—	2	4	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₂²⋊C₄	—	2	4	no	—
238	C₂²⋊C₄	—	4	8	no	—
239	C₄²	—	4	1	no	—
240	C₄²	—	4	1	no	—
241	C₄²	D₄×D₁₉	1	2	yes	—
242	C₄²	#64543	1	2	yes	—
243	C₂³	—	2	2	no	—
244	C₂³	—	2	2	no	—
245	C₂³	—	4	2	no	—
246	C₂³	—	4	2	no	—
247	C₂³	—	4	4	no	—
248	C₂³	—	4	4	no	—
249	C₂³	—	4	2	no	—
250	C₂³	—	4	2	no	—
251	C₂³	—	4	2	no	—
252	C₂³	#10597289	1	4	yes	—
253	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
254	D₄	—	2	4	no	—
255	D₄	—	2	4	no	—
256	D₄	—	8	4	no	—
257	D₄	—	8	2	no	—
258	D₄	—	8	16	no	—
259	D₄	—	8	2	no	—
260	D₄	—	8	2	no	—
261	D₄	—	8	2	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	8	2	no	—
271	C₂×C₄	C₂×#64525	1	1	yes	characteristic
272	C₂×C₄	C₂×#64526	1	1	yes	characteristic
273	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
274	C₂×C₄	#10597381	1	1	yes	characteristic
275	C₂×C₄	#10597383	1	1	yes	characteristic
276	C₂×C₄	#10597385	1	2	yes	—
277	C₂×C₄	#10597396	1	2	yes	—
278	C₈	—	76	4	no	—
279	C₈	—	152	2	no	—
280	C₂²	—	2	1	no	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	4	no	—
283	C₂²	—	4	4	no	—
284	C₂²	—	4	2	no	—
285	C₂²	—	4	2	no	—
286	C₂²	—	8	2	no	—
287	C₂²	—	8	4	no	—
288	C₂²	—	8	4	no	—
289	C₂²	—	8	2	no	—
290	C₂²	—	8	2	no	—
291	C₂²	—	8	2	no	—
292	C₂²	#11926424	1	1	yes	characteristic
293	C₂²	C₂×#10597289	1	1	yes	characteristic
294	C₂²	#11926540	1	1	yes	characteristic
295	C₄	—	2	2	no	—
296	C₄	—	2	1	no	—
297	C₄	—	4	4	no	—
298	C₄	—	4	2	no	—
299	C₄	#11926711	1	2	yes	—
300	C₄	#11926771	1	2	yes	—
301	C₄	#11926778	1	2	yes	—
302	C₂	—	2	1	no	—
303	C₂	—	2	1	no	—
304	C₂	—	4	4	no	—
305	C₂	—	16	2	no	—
306	C₂	#14564034	1	1	yes	characteristic
307	C₂	#14564064	1	1	yes	characteristic
308	C₂	#14564183	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic, complemented

#14563627

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal, complemented

#14561538

C₂

yes

maximal, complemented

C₁₉×#2541

C₂

yes

maximal, characteristic

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926313

—

#11926288

—

C₂×C₁₉×#127

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#121

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#392

C₄

yes

—

C₁₉×#390

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

C₂×C₄

yes

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₈

yes

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

—

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

—

C₂×C₁₉⋊C₈

—

#9397

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×C₁₉

—

106

D₄×C₁₉

—

107

D₄×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

—

117

C₂×C₄×C₁₉

C₄×D₄

yes

—

118

C₂×C₄×C₁₉

#120

yes

characteristic

119

C₂×C₄×C₁₉

#121

yes

—

120

C₂×C₄×C₁₉

#123

yes

characteristic

121

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

122

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

123

C₂×C₄×C₁₉

#135

yes

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

#2972

—

127

#2541

D₁₉

yes

characteristic

128

#1800

—

129

#1545

—

130

#1303

—

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

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

#386

yes

characteristic

144

C₂²×C₁₉

C₂×#102

yes

characteristic

145

C₂²×C₁₉

#416

yes

characteristic

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

#453

yes

—

151

C₄×C₁₉

#465

yes

—

152

C₄×C₁₉

#466

yes

—

153

C₂×#127

—

154

C₂×#127

C₂×D₁₉

yes

characteristic

155

C₂×#121

—

156

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

157

C₈×D₄

—

158

#431

—

159

#423

—

160

C₂×#100

—

161

C₂×C₂²⋊C₈

—

162

#392

Dic₁₉

yes

—

163

#390

—

164

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

165

#343

—

166

#331

—

167

C₂×C₁₉

—

168

C₂×C₁₉

—

169

C₂×C₁₉

—

170

C₂×C₁₉

—

171

C₂×C₁₉

#1887

yes

characteristic

172

C₂×C₁₉

#1893

yes

characteristic

173

C₂×C₁₉

#1914

yes

characteristic

174

C₂²×D₄

—

175

C₂²×D₄

—

176

C₂²×D₄

—

177

C₂²×D₄

C₂×Dic₁₉

yes

—

178

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

179

C₂³×C₄

C₂²⋊D₁₉

yes

—

180

C₂×M₁₆

—

181

C₂²×C₈

—

182

#127

—

183

#127

—

184

#127

—

185

#127

—

186

#121

—

187

C₄×D₄

—

188

C₄×D₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

191

C₂×C₂²⋊C₄

—

192

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

193

C₂×C₄²

—

194

C₂×C₄²

C₂²×D₁₉

yes

characteristic

195

C₄⋊C₈

—

196

C₄⋊C₈

—

197

C₄⋊C₈

—

198

#100

—

199

C₂²⋊C₈

—

200

C₂²⋊C₈

—

201

C₄×C₈

—

202

#95

C₂×Dic₁₉

yes

—

203

C₁₉

#9397

yes

characteristic, complemented, Sylow

204

C₂⁴

—

205

C₂⁴

C₂²⋊Dic₁₉

yes

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂×D₄

—

219

C₂×D₄

—

220

C₂×D₄

#64525

yes

—

221

C₂×D₄

#64526

yes

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

—

226

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

227

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

228

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

230

M₁₆

—

231

M₁₆

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

152

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₂²⋊C₄

—

238

C₂²⋊C₄

—

239

C₄²

—

240

C₄²

—

241

C₄²

D₄×D₁₉

yes

—

242

C₄²

#64543

yes

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

—

252

C₂³

#10597289

yes

—

253

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

258

D₄

—

259

D₄

—

260

D₄

—

261

D₄

—

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

C₂×#64525

yes

characteristic

272

C₂×C₄

C₂×#64526

yes

characteristic

273

C₂×C₄

D₄×Dic₁₉

yes

—

274

C₂×C₄

#10597381

yes

characteristic

275

C₂×C₄

#10597383

yes

characteristic

276

C₂×C₄

#10597385

yes

—

277

C₂×C₄

#10597396

yes

—

278

C₈

—

279

C₈

—

152

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

#11926424

yes

characteristic

293

C₂²

C₂×#10597289

yes

characteristic

294

C₂²

#11926540

yes

characteristic

295

C₄

—

296

C₄

—

297

C₄

—

298

C₄

—

299

C₄

#11926711

yes

—

300

C₄

#11926771

yes

—

301

C₄

#11926778

yes

—

302

C₂

—

303

C₂

—

304

C₂

—

305

C₂

—

306

C₂

#14564034

yes

characteristic

307

C₂

#14564064

yes

characteristic

308

C₂

#14564183

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2541	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2541	D₁₉
hypocenter	C₁₉	#9397
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2541

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2541

C₂

socle

C₂²×C₁₉

#386

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2541

N	H ≅ G/N	type
1. #14572659	C₂	semidirect
2. #14563627	C₂	semidirect
3. #14562303	C₂	semidirect
4. #14561538	C₂	semidirect
47. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
203. C₁₉	#9397	semidirect

H ≅ G/N

type

1. #14572659

C₂

semidirect

2. #14563627

C₂

semidirect

3. #14562303

C₂

semidirect

4. #14561538

C₂

semidirect

47. C₄⋊(C₁₉⋊C₈)

D₄

semidirect

203. C₁₉

#9397

semidirect

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

subgroup	index
#14572659	2
#14563627	2
#14562303	2
#14561538	2
C₁₉×#2541	2
#9397	19

subgroup

index

C₁₉×#2541

Subgroups — #18079925

Conjugacy classes of subgroups

Complements

Maximal subgroups