Group #18069285 — subgroups

Subgroups — #18069285

Order 4864.

692 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14561478	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1438	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
5	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
6	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
7	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
8	C₂⁵×C₁₉	—	2	1	no	—
9	C₂²×D₄×C₁₉	—	2	1	no	—
10	C₂²×D₄×C₁₉	—	4	1	no	—
11	C₂²×D₄×C₁₉	—	4	1	no	—
12	C₂²×D₄×C₁₉	—	4	4	no	—
13	C₂²×D₄×C₁₉	C₈	1	2	yes	complemented
14	C₂³×C₄×C₁₉	—	2	1	no	—
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	D₄	1	2	yes	—
17	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
18	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
19	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
20	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
21	C₂²×C₁₉⋊C₈	—	4	2	no	—
22	C₁₉×#95	—	4	1	no	—
23	C₁₉×#95	—	4	1	no	—
24	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
26	C₂⁴×C₁₉	—	2	4	no	—
27	C₂⁴×C₁₉	—	2	2	no	—
28	C₂⁴×C₁₉	—	4	2	no	—
29	C₂⁴×C₁₉	—	4	2	no	—
30	C₂⁴×C₁₉	—	4	2	no	—
31	C₂⁴×C₁₉	—	4	1	no	—
32	C₂⁴×C₁₉	—	4	1	no	—
33	C₂⁴×C₁₉	—	4	2	no	—
34	C₂⁴×C₁₉	—	4	2	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×D₄×C₁₉	—	4	2	no	—
37	C₂×D₄×C₁₉	—	4	2	no	—
38	C₂×D₄×C₁₉	—	4	4	no	—
39	C₂×D₄×C₁₉	—	4	4	no	—
40	C₂×D₄×C₁₉	—	4	8	no	—
41	C₂×D₄×C₁₉	—	4	4	no	—
42	C₂×D₄×C₁₉	—	4	4	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	—	4	2	no	—
50	C₂²×C₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	D₈	1	2	yes	—
58	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
59	C₂²⋊C₄×C₁₉	—	4	8	no	—
60	C₂²⋊C₄×C₁₉	—	4	8	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	C₂×C₁₉⋊C₈	—	8	2	no	—
63	C₂×C₁₉⋊C₈	—	8	2	no	—
64	#7103	—	19	1	no	maximal, Sylow
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	1	no	—
67	C₂³×C₁₉	—	2	1	no	—
68	C₂³×C₁₉	—	2	4	no	—
69	C₂³×C₁₉	—	4	4	no	—
70	C₂³×C₁₉	—	4	4	no	—
71	C₂³×C₁₉	—	4	2	no	—
72	C₂³×C₁₉	—	4	4	no	—
73	C₂³×C₁₉	—	4	4	no	—
74	C₂³×C₁₉	—	4	4	no	—
75	C₂³×C₁₉	—	4	4	no	—
76	C₂³×C₁₉	—	4	2	no	—
77	C₂³×C₁₉	—	4	4	no	—
78	C₂³×C₁₉	—	4	4	no	—
79	C₂³×C₁₉	—	8	2	no	—
80	C₂³×C₁₉	—	8	2	no	—
81	C₂³×C₁₉	—	8	2	no	—
82	C₂³×C₁₉	—	8	2	no	—
83	C₂³×C₁₉	—	8	2	no	—
84	C₂³×C₁₉	—	8	2	no	—
85	C₂³×C₁₉	—	8	1	no	—
86	C₂³×C₁₉	—	8	1	no	—
87	C₂³×C₁₉	—	8	1	no	—
88	C₂³×C₁₉	—	8	1	no	—
89	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
90	C₂³×C₁₉	#99	1	1	yes	characteristic
91	C₂³×C₁₉	#100	1	1	yes	characteristic
92	C₂³×C₁₉	#102	1	2	yes	—
93	C₂³×C₁₉	#104	1	2	yes	—
94	D₄×C₁₉	—	4	4	no	—
95	D₄×C₁₉	—	4	4	no	—
96	D₄×C₁₉	—	4	8	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	4	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	8	2	no	—
112	C₂×C₄×C₁₉	—	8	1	no	—
113	C₂×C₄×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	—	8	1	no	—
115	C₁₉⋊C₈	—	8	4	no	—
116	#1438	D₁₉	1	1	yes	characteristic
117	#1280	—	19	2	no	—
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	2	no	—
123	C₂²×C₁₉	—	2	2	no	—
124	C₂²×C₁₉	—	2	2	no	—
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	—	4	8	no	—
127	C₂²×C₁₉	—	4	4	no	—
128	C₂²×C₁₉	—	8	4	no	—
129	C₂²×C₁₉	—	8	4	no	—
130	C₂²×C₁₉	—	8	4	no	—
131	C₂²×C₁₉	—	8	2	no	—
132	C₂²×C₁₉	—	8	4	no	—
133	C₂²×C₁₉	—	8	4	no	—
134	C₂²×C₁₉	—	8	2	no	—
135	C₂²×C₁₉	#323	1	1	yes	characteristic
136	C₂²×C₁₉	D₄⋊C₈	1	2	yes	—
137	C₂²×C₁₉	#327	1	2	yes	—
138	C₂²×C₁₉	#329	1	1	yes	characteristic
139	C₂²×C₁₉	#331	1	1	yes	characteristic
140	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	2	yes	—
141	C₂²×C₁₉	#353	1	1	yes	characteristic
142	C₂²×C₁₉	#355	1	1	yes	characteristic
143	C₄×C₁₉	—	4	1	no	—
144	C₄×C₁₉	—	4	1	no	—
145	C₄×C₁₉	—	4	2	no	—
146	C₄×C₁₉	—	4	2	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₂³×D₄	Dic₁₉	1	1	yes	characteristic
149	C₂²×C₂²⋊C₄	—	2	2	no	—
150	C₂×C₂²⋊C₈	—	38	2	no	—
151	C₂×#95	Dic₁₉	1	1	yes	characteristic
152	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	2	2	no	—
155	C₂×C₁₉	—	2	1	no	—
156	C₂×C₁₉	—	8	4	no	—
157	C₂×C₁₉	#1270	1	1	yes	characteristic
158	C₂×C₁₉	#1316	1	1	yes	characteristic
159	C₂×C₁₉	#1318	1	1	yes	characteristic
160	C₂×C₁₉	#1343	1	2	yes	—
161	C₂×C₁₉	#1345	1	2	yes	—
162	C₂⁵	—	2	1	no	—
163	C₂²×D₄	—	2	1	no	—
164	C₂²×D₄	—	4	1	no	—
165	C₂²×D₄	—	4	1	no	—
166	C₂²×D₄	—	4	4	no	—
167	C₂²×D₄	C₁₉⋊C₈	1	2	yes	complemented
168	C₂³×C₄	—	2	1	no	—
169	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
170	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
171	C₂²×C₈	—	76	2	no	—
172	C₂×C₂²⋊C₄	—	4	4	no	—
173	C₂×C₂²⋊C₄	—	4	4	no	—
174	C₂×C₂²⋊C₄	—	4	2	no	—
175	C₂×C₂²⋊C₄	—	4	2	no	—
176	C₂²⋊C₈	—	38	4	no	—
177	C₂²⋊C₈	—	76	2	no	—
178	#95	—	4	1	no	—
179	#95	—	4	1	no	—
180	C₁₉	#7103	1	1	yes	characteristic, complemented, Sylow
181	C₂⁴	—	2	4	no	—
182	C₂⁴	—	2	2	no	—
183	C₂⁴	—	4	2	no	—
184	C₂⁴	—	4	2	no	—
185	C₂⁴	—	4	2	no	—
186	C₂⁴	—	4	2	no	—
187	C₂⁴	—	4	1	no	—
188	C₂⁴	—	4	1	no	—
189	C₂⁴	—	4	2	no	—
190	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
191	C₂×D₄	—	4	2	no	—
192	C₂×D₄	—	4	2	no	—
193	C₂×D₄	—	4	4	no	—
194	C₂×D₄	—	4	4	no	—
195	C₂×D₄	—	4	8	no	—
196	C₂×D₄	—	4	4	no	—
197	C₂×D₄	—	4	4	no	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	4	2	no	—
204	C₂²×C₄	—	4	2	no	—
205	C₂²×C₄	—	4	2	no	—
206	C₂²×C₄	—	4	2	no	—
207	C₂²×C₄	—	4	1	no	—
208	C₂²×C₄	—	4	2	no	—
209	C₂²×C₄	—	4	1	no	—
210	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
211	C₂²×C₄	#64520	1	1	yes	characteristic
212	C₂²×C₄	#64525	1	2	yes	—
213	C₂²×C₄	#64526	1	2	yes	—
214	C₂×C₈	—	76	4	no	—
215	C₂×C₈	—	152	2	no	—
216	C₂×C₈	—	152	2	no	—
217	C₂²⋊C₄	—	4	8	no	—
218	C₂²⋊C₄	—	4	8	no	—
219	C₂³	—	2	2	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	2	1	no	—
222	C₂³	—	2	4	no	—
223	C₂³	—	4	4	no	—
224	C₂³	—	4	4	no	—
225	C₂³	—	4	2	no	—
226	C₂³	—	4	4	no	—
227	C₂³	—	4	4	no	—
228	C₂³	—	4	4	no	—
229	C₂³	—	4	4	no	—
230	C₂³	—	4	4	no	—
231	C₂³	—	4	4	no	—
232	C₂³	—	4	2	no	—
233	C₂³	—	8	2	no	—
234	C₂³	—	8	2	no	—
235	C₂³	—	8	2	no	—
236	C₂³	—	8	2	no	—
237	C₂³	—	8	2	no	—
238	C₂³	—	8	2	no	—
239	C₂³	—	8	1	no	—
240	C₂³	—	8	1	no	—
241	C₂³	—	8	1	no	—
242	C₂³	—	8	1	no	—
243	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
244	C₂³	#10597289	1	2	yes	—
245	C₂³	#10597290	1	1	yes	characteristic
246	C₂³	#10597291	1	1	yes	characteristic
247	C₂³	#10597294	1	2	yes	—
248	D₄	—	4	4	no	—
249	D₄	—	4	4	no	—
250	D₄	—	4	8	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	1	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	2	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	4	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	8	2	no	—
266	C₂×C₄	—	8	1	no	—
267	C₂×C₄	—	8	2	no	—
268	C₂×C₄	—	8	1	no	—
269	C₈	—	152	4	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	2	1	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	2	2	no	—
278	C₂²	—	4	8	no	—
279	C₂²	—	4	4	no	—
280	C₂²	—	8	4	no	—
281	C₂²	—	8	4	no	—
282	C₂²	—	8	4	no	—
283	C₂²	—	8	2	no	—
284	C₂²	—	8	4	no	—
285	C₂²	—	8	4	no	—
286	C₂²	—	8	2	no	—
287	C₂²	#11926268	1	1	yes	characteristic
288	C₂²	D₄⋊(C₁₉⋊C₈)	1	2	yes	—
289	C₂²	#11926278	1	2	yes	—
290	C₂²	#11926284	1	1	yes	characteristic
291	C₂²	#11926288	1	1	yes	characteristic
292	C₂²	#11926331	1	2	yes	—
293	C₂²	#11926337	1	1	yes	characteristic
294	C₂²	#11926341	1	1	yes	characteristic
295	C₄	—	4	1	no	—
296	C₄	—	4	1	no	—
297	C₄	—	4	2	no	—
298	C₄	—	4	2	no	—
299	C₄	—	8	2	no	—
300	C₂	—	2	1	no	—
301	C₂	—	2	2	no	—
302	C₂	—	2	1	no	—
303	C₂	—	8	4	no	—
304	C₂	#14561456	1	1	yes	characteristic
305	C₂	#14561563	1	1	yes	characteristic
306	C₂	#14561567	1	1	yes	characteristic
307	C₂	#14561632	1	2	yes	—
308	C₂	#14561638	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14561478

C₂

yes

maximal, complemented

C₁₉×#1438

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂³×D₄×C₁₉

C₄

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

—

C₂×C₁₉×#95

C₄

yes

characteristic

C₂×C₁₉×#95

C₂²

yes

characteristic

C₂⁵×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₈

yes

complemented

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

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×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

SD₁₆

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7103

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

—

C₂³×C₁₉

#104

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

C₁₉⋊C₈

—

116

#1438

D₁₉

yes

characteristic

117

#1280

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

#323

yes

characteristic

136

C₂²×C₁₉

D₄⋊C₈

yes

—

137

C₂²×C₁₉

#327

yes

—

138

C₂²×C₁₉

#329

yes

characteristic

139

C₂²×C₁₉

#331

yes

characteristic

140

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

—

141

C₂²×C₁₉

#353

yes

characteristic

142

C₂²×C₁₉

#355

yes

characteristic

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₂³×D₄

Dic₁₉

yes

characteristic

149

C₂²×C₂²⋊C₄

—

150

C₂×C₂²⋊C₈

—

151

C₂×#95

Dic₁₉

yes

characteristic

152

C₂×#95

C₂×D₁₉

yes

characteristic

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

—

157

C₂×C₁₉

#1270

yes

characteristic

158

C₂×C₁₉

#1316

yes

characteristic

159

C₂×C₁₉

#1318

yes

characteristic

160

C₂×C₁₉

#1343

yes

—

161

C₂×C₁₉

#1345

yes

—

162

C₂⁵

—

163

C₂²×D₄

—

164

C₂²×D₄

—

165

C₂²×D₄

—

166

C₂²×D₄

—

167

C₂²×D₄

C₁₉⋊C₈

yes

complemented

168

C₂³×C₄

—

169

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

170

C₂³×C₄

C₂²⋊D₁₉

yes

—

171

C₂²×C₈

—

172

C₂×C₂²⋊C₄

—

173

C₂×C₂²⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

#95

—

179

#95

—

180

C₁₉

#7103

yes

characteristic, complemented, Sylow

181

C₂⁴

—

182

C₂⁴

—

183

C₂⁴

—

184

C₂⁴

—

185

C₂⁴

—

186

C₂⁴

—

187

C₂⁴

—

188

C₂⁴

—

189

C₂⁴

—

190

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

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

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

211

C₂²×C₄

#64520

yes

characteristic

212

C₂²×C₄

#64525

yes

—

213

C₂²×C₄

#64526

yes

—

214

C₂×C₈

—

215

C₂×C₈

—

152

—

216

C₂×C₈

—

152

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

244

C₂³

#10597289

yes

—

245

C₂³

#10597290

yes

characteristic

246

C₂³

#10597291

yes

characteristic

247

C₂³

#10597294

yes

—

248

D₄

—

249

D₄

—

250

D₄

—

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

C₈

—

152

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

#11926268

yes

characteristic

288

C₂²

D₄⋊(C₁₉⋊C₈)

yes

—

289

C₂²

#11926278

yes

—

290

C₂²

#11926284

yes

characteristic

291

C₂²

#11926288

yes

characteristic

292

C₂²

#11926331

yes

—

293

C₂²

#11926337

yes

characteristic

294

C₂²

#11926341

yes

characteristic

295

C₄

—

296

C₄

—

297

C₄

—

298

C₄

—

299

C₄

—

300

C₂

—

301

C₂

—

302

C₂

—

303

C₂

—

304

C₂

#14561456

yes

characteristic

305

C₂

#14561563

yes

characteristic

306

C₂

#14561567

yes

characteristic

307

C₂

#14561632

yes

—

308

C₂

#14561638

yes

—

	subgroup	G/H
center	C₂³	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×#95	C₂×D₁₉
Fitting	C₁₉×#1438	C₂
socle	C₂³×C₁₉	#99
prime radical	C₂³×D₄×C₁₉	C₄
cosocle	C₂×C₁₉×#95	C₂²
hypercenter	#1438	D₁₉
hypocenter	C₁₉	#7103
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂×#95 ◁ #1438

subgroup

G/H

center

C₂³

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×#95

C₂×D₁₉

Fitting

C₁₉×#1438

C₂

socle

C₂³×C₁₉

#99

prime radical

C₂³×D₄×C₁₉

C₄

cosocle

C₂×C₁₉×#95

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂×#95 ◁ #1438

N	H ≅ G/N	type
1. #14561478	C₂	semidirect
13. C₂²×D₄×C₁₉	C₈	semidirect
167. C₂²×D₄	C₁₉⋊C₈	semidirect
180. C₁₉	#7103	semidirect

H ≅ G/N

type

1. #14561478

C₂

semidirect

13. C₂²×D₄×C₁₉

C₈

semidirect

167. C₂²×D₄

C₁₉⋊C₈

semidirect

180. C₁₉

#7103

semidirect

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

subgroup	index
#14561478	2
C₁₉×#1438	2
#7103	19

subgroup

index

#14561478

C₁₉×#1438

#7103

Subgroups — #18069285

Conjugacy classes of subgroups

Complements

Maximal subgroups