Group #18079965 — subgroups

Subgroups — #18079965

Order 4864.

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

normal subgroups only

This group has 706 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	#14572676	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	#11926622	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597290	—	2	1	no	—
10	#11926508	—	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	4	no	—
29	C₁₉×#121	—	4	8	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×#64520	—	2	4	no	—
39	C₂×#64520	—	2	2	no	—
40	C₁₉×#95	C₂×C₄	1	2	yes	—
41	#10597290	—	4	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	complemented
47	C₄×C₁₉⋊C₈	—	2	2	no	—
48	C₂⁴×C₁₉	—	2	2	no	—
49	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂×D₄×C₁₉	—	2	4	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	2	1	no	—
54	C₂×D₄×C₁₉	—	2	1	no	—
55	C₂×D₄×C₁₉	—	4	4	no	—
56	C₂×D₄×C₁₉	—	4	8	no	—
57	C₂×D₄×C₁₉	—	4	8	no	—
58	C₂×D₄×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	1	no	—
61	C₂×D₄×C₁₉	—	4	2	no	—
62	C₂×D₄×C₁₉	—	4	1	no	—
63	C₂×D₄×C₁₉	—	4	1	no	—
64	C₂×D₄×C₁₉	—	8	4	no	—
65	C₂×D₄×C₁₉	—	8	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	4	4	no	—
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂²⋊C₄×C₁₉	—	2	4	no	—
77	C₂²⋊C₄×C₁₉	—	4	8	no	—
78	C₄²×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	C₂×D₄	1	2	yes	—
80	C₄²×C₁₉	#41	1	2	yes	—
81	#64520	—	4	2	no	—
82	#64520	—	4	2	no	—
83	#64520	—	8	4	no	—
84	C₂×C₁₉⋊C₈	—	2	4	no	—
85	C₂×C₁₉⋊C₈	—	4	2	no	—
86	#9405	—	19	1	no	maximal, Sylow
87	C₂³×C₁₉	—	2	2	no	—
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	—	2	2	no	—
90	C₂³×C₁₉	—	4	2	no	—
91	C₂³×C₁₉	—	4	2	no	—
92	C₂³×C₁₉	—	4	4	no	—
93	C₂³×C₁₉	—	4	4	no	—
94	C₂³×C₁₉	—	4	2	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	—	4	2	no	—
97	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	D₄×C₁₉	—	4	2	no	—
99	D₄×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	8	4	no	—
101	D₄×C₁₉	—	8	2	no	—
102	D₄×C₁₉	—	8	16	no	—
103	D₄×C₁₉	—	8	2	no	—
104	D₄×C₁₉	—	8	2	no	—
105	D₄×C₁₉	—	8	2	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	4	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	4	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	8	2	no	—
115	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
116	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
117	C₂×C₄×C₁₉	#121	1	2	yes	—
118	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
119	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
120	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
122	C₁₉⋊C₈	—	4	4	no	—
123	C₁₉⋊C₈	—	8	2	no	—
124	#2975	—	19	1	no	—
125	#2541	D₁₉	1	1	yes	characteristic
126	#1800	—	19	1	no	—
127	#1545	—	19	2	no	—
128	#1303	—	19	2	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	4	4	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	4	2	no	—
134	C₂²×C₁₉	—	4	2	no	—
135	C₂²×C₁₉	—	8	2	no	—
136	C₂²×C₁₉	—	8	4	no	—
137	C₂²×C₁₉	—	8	4	no	—
138	C₂²×C₁₉	—	8	2	no	—
139	C₂²×C₁₉	—	8	2	no	—
140	C₂²×C₁₉	—	8	2	no	—
141	C₂²×C₁₉	#386	1	1	yes	characteristic
142	C₂²×C₁₉	#417	1	1	yes	characteristic
143	C₂²×C₁₉	#418	1	1	yes	characteristic
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	2	2	no	—
146	C₄×C₁₉	—	4	4	no	—
147	C₄×C₁₉	—	4	2	no	—
148	C₄×C₁₉	#453	1	2	yes	—
149	C₄×C₁₉	#468	1	2	yes	—
150	C₄×C₁₉	#469	1	2	yes	—
151	C₂×#127	—	2	1	no	—
152	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
153	C₂×#121	—	2	2	no	—
154	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
155	#436	—	38	4	no	—
156	#431	—	19	2	no	—
157	#423	—	19	2	no	—
158	C₂×#100	—	38	1	no	—
159	#407	—	38	2	no	—
160	#392	Dic₁₉	1	4	yes	—
161	#390	—	2	1	no	—
162	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
163	#343	—	38	1	no	—
164	#331	—	38	4	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	8	2	no	—
168	C₂×C₁₉	—	16	2	no	—
169	C₂×C₁₉	#1887	1	1	yes	characteristic
170	C₂×C₁₉	#1895	1	1	yes	characteristic
171	C₂×C₁₉	#1914	1	1	yes	characteristic
172	C₂²×D₄	—	2	4	no	—
173	C₂²×D₄	—	2	1	no	—
174	C₂²×D₄	—	2	1	no	—
175	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
176	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
177	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
178	C₂×M₁₆	—	38	4	no	—
179	C₂×M₁₆	—	38	2	no	—
180	#127	—	2	2	no	—
181	#127	—	2	2	no	—
182	#127	—	4	4	no	—
183	#121	—	4	8	no	—
184	C₄×D₄	—	2	2	no	—
185	C₄×D₄	—	2	2	no	—
186	C₂×C₄⋊C₄	—	2	1	no	—
187	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	—	2	4	no	—
189	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
190	C₂×C₄²	—	2	1	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	C₄⋊C₈	—	19	4	no	—
193	C₄⋊C₈	—	38	2	no	—
194	C₄⋊C₈	—	38	2	no	—
195	#100	—	76	2	no	—
196	C₂²⋊C₈	—	38	4	no	—
197	C₂²⋊C₈	—	38	2	no	—
198	C₄×C₈	—	38	2	no	—
199	#95	C₂×Dic₁₉	1	2	yes	—
200	C₁₉	#9405	1	1	yes	characteristic, complemented, Sylow
201	C₂⁴	—	2	2	no	—
202	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
203	C₂×D₄	—	2	2	no	—
204	C₂×D₄	—	2	4	no	—
205	C₂×D₄	—	2	2	no	—
206	C₂×D₄	—	2	1	no	—
207	C₂×D₄	—	2	1	no	—
208	C₂×D₄	—	4	4	no	—
209	C₂×D₄	—	4	8	no	—
210	C₂×D₄	—	4	8	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	1	no	—
213	C₂×D₄	—	4	1	no	—
214	C₂×D₄	—	4	2	no	—
215	C₂×D₄	—	4	1	no	—
216	C₂×D₄	—	4	1	no	—
217	C₂×D₄	—	8	4	no	—
218	C₂×D₄	—	8	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	4	4	no	—
223	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
224	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
226	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
227	M₁₆	—	76	2	no	—
228	M₁₆	—	76	2	no	—
229	M₁₆	—	152	4	no	—
230	C₂×C₈	—	38	4	no	—
231	C₂×C₈	—	76	2	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	2	no	—
234	C₂²⋊C₄	—	2	4	no	—
235	C₂²⋊C₄	—	4	8	no	—
236	C₄²	—	4	2	no	—
237	C₄²	D₄×D₁₉	1	2	yes	—
238	C₄²	#64543	1	2	yes	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	2	no	—
241	C₂³	—	2	2	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	4	4	no	—
245	C₂³	—	4	4	no	—
246	C₂³	—	4	2	no	—
247	C₂³	—	4	2	no	—
248	C₂³	—	4	2	no	—
249	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
250	D₄	—	4	2	no	—
251	D₄	—	4	2	no	—
252	D₄	—	8	4	no	—
253	D₄	—	8	2	no	—
254	D₄	—	8	16	no	—
255	D₄	—	8	2	no	—
256	D₄	—	8	2	no	—
257	D₄	—	8	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	4	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	4	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	8	2	no	—
267	C₂×C₄	#10597378	1	2	yes	—
268	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
269	C₂×C₄	#10597381	1	1	yes	characteristic
270	C₂×C₄	#10597383	1	1	yes	characteristic
271	C₂×C₄	#10597385	1	2	yes	—
272	C₂×C₄	#10597395	1	1	yes	characteristic
273	C₂×C₄	#10597397	1	1	yes	characteristic
274	C₈	—	76	4	no	—
275	C₈	—	152	2	no	—
276	C₂²	—	2	1	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	4	4	no	—
279	C₂²	—	4	2	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	4	2	no	—
282	C₂²	—	8	2	no	—
283	C₂²	—	8	4	no	—
284	C₂²	—	8	4	no	—
285	C₂²	—	8	2	no	—
286	C₂²	—	8	2	no	—
287	C₂²	—	8	2	no	—
288	C₂²	#11926424	1	1	yes	characteristic
289	C₂²	#11926545	1	1	yes	characteristic
290	C₂²	#11926549	1	1	yes	characteristic
291	C₄	—	2	2	no	—
292	C₄	—	2	1	no	—
293	C₄	—	4	4	no	—
294	C₄	—	4	2	no	—
295	C₄	#11926711	1	2	yes	—
296	C₄	#11926788	1	2	yes	—
297	C₄	#11926795	1	2	yes	—
298	C₂	—	2	1	no	—
299	C₂	—	2	1	no	—
300	C₂	—	8	2	no	—
301	C₂	—	16	2	no	—
302	C₂	#14564034	1	1	yes	characteristic
303	C₂	#14564074	1	1	yes	characteristic
304	C₂	#14564183	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572676

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

#11926622

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

—

—

—

—

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×#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

—

C₂×#64520

—

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

—

C₂×D₄×C₁₉

—

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

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9405

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×C₁₉

—

103

D₄×C₁₉

—

104

D₄×C₁₉

—

105

D₄×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

C₄×D₄

yes

—

116

C₂×C₄×C₁₉

#120

yes

characteristic

117

C₂×C₄×C₁₉

#121

yes

—

118

C₂×C₄×C₁₉

#123

yes

characteristic

119

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

120

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

121

C₂×C₄×C₁₉

#137

yes

characteristic

122

C₁₉⋊C₈

—

123

C₁₉⋊C₈

—

124

#2975

—

125

#2541

D₁₉

yes

characteristic

126

#1800

—

127

#1545

—

128

#1303

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

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

#386

yes

characteristic

142

C₂²×C₁₉

#417

yes

characteristic

143

C₂²×C₁₉

#418

yes

characteristic

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

#453

yes

—

149

C₄×C₁₉

#468

yes

—

150

C₄×C₁₉

#469

yes

—

151

C₂×#127

—

152

C₂×#127

C₂×D₁₉

yes

characteristic

153

C₂×#121

—

154

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

155

#436

—

156

#431

—

157

#423

—

158

C₂×#100

—

159

#407

—

160

#392

Dic₁₉

yes

—

161

#390

—

162

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

163

#343

—

164

#331

—

165

C₂×C₁₉

—

166

C₂×C₁₉

—

167

C₂×C₁₉

—

168

C₂×C₁₉

—

169

C₂×C₁₉

#1887

yes

characteristic

170

C₂×C₁₉

#1895

yes

characteristic

171

C₂×C₁₉

#1914

yes

characteristic

172

C₂²×D₄

—

173

C₂²×D₄

—

174

C₂²×D₄

—

175

C₂²×D₄

C₂×Dic₁₉

yes

—

176

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

177

C₂³×C₄

C₂²⋊D₁₉

yes

—

178

C₂×M₁₆

—

179

C₂×M₁₆

—

180

#127

—

181

#127

—

182

#127

—

183

#121

—

184

C₄×D₄

—

185

C₄×D₄

—

186

C₂×C₄⋊C₄

—

187

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

188

C₂×C₂²⋊C₄

—

189

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

190

C₂×C₄²

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

C₄⋊C₈

—

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

#100

—

196

C₂²⋊C₈

—

197

C₂²⋊C₈

—

198

C₄×C₈

—

199

#95

C₂×Dic₁₉

yes

—

200

C₁₉

#9405

yes

characteristic, complemented, Sylow

201

C₂⁴

—

202

C₂⁴

C₂²⋊Dic₁₉

yes

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

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

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

—

223

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

224

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

225

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

226

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

227

M₁₆

—

228

M₁₆

—

229

M₁₆

—

152

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₄²

—

237

C₄²

D₄×D₁₉

yes

—

238

C₄²

#64543

yes

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

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

#10597378

yes

—

268

C₂×C₄

D₄×Dic₁₉

yes

—

269

C₂×C₄

#10597381

yes

characteristic

270

C₂×C₄

#10597383

yes

characteristic

271

C₂×C₄

#10597385

yes

—

272

C₂×C₄

#10597395

yes

characteristic

273

C₂×C₄

#10597397

yes

characteristic

274

C₈

—

275

C₈

—

152

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

288

C₂²

#11926424

yes

characteristic

289

C₂²

#11926545

yes

characteristic

290

C₂²

#11926549

yes

characteristic

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

295

C₄

#11926711

yes

—

296

C₄

#11926788

yes

—

297

C₄

#11926795

yes

—

298

C₂

—

299

C₂

—

300

C₂

—

301

C₂

—

302

C₂

#14564034

yes

characteristic

303

C₂

#14564074

yes

characteristic

304

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	#9405
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. #14572676	C₂	semidirect
2. #14563627	C₂	semidirect
3. #14562303	C₂	semidirect
4. #14561538	C₂	semidirect
46. C₄⋊(C₁₉⋊C₈)	D₄	semidirect
200. C₁₉	#9405	semidirect

H ≅ G/N

type

1. #14572676

C₂

semidirect

2. #14563627

C₂

semidirect

3. #14562303

C₂

semidirect

4. #14561538

C₂

semidirect

46. C₄⋊(C₁₉⋊C₈)

D₄

semidirect

200. C₁₉

#9405

semidirect

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

subgroup	index
#14572676	2
#14563627	2
#14562303	2
#14561538	2
C₁₉×#2541	2
#9405	19

subgroup

index

C₁₉×#2541

Subgroups — #18079965

Conjugacy classes of subgroups

Complements

Maximal subgroups