Group #18077220 — subgroups

Subgroups — #18077220

Order 4864.

542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14572720	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562026	C₂	1	2	yes	maximal
3	#14561959	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561468	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	4	no	—
7	#11926601	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926597	C₂²	1	2	yes	—
10	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
11	#11926270	—	2	2	no	—
12	C₂×C₁₉×#124	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#391	C₄	1	1	yes	characteristic
16	C₁₉×#390	C₄	1	1	yes	characteristic
17	C₁₉×#388	—	2	2	no	—
18	C₁₉×#382	C₄	1	1	yes	characteristic
19	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
20	C₄³×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	—	2	1	no	—
24	C₁₉×#124	—	2	2	no	—
25	C₁₉×#124	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₄×D₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	2	yes	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₁₉×#95	—	2	2	no	—
43	C₁₉×#95	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
49	#10597260	—	2	4	no	—
50	C₄×C₁₉⋊C₈	—	2	2	no	—
51	C₄×C₁₉⋊C₈	—	2	2	no	—
52	C₂⁴×C₁₉	—	2	1	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	1	no	—
55	C₂×Q₈×C₁₉	—	2	1	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	2	1	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	M₁₆	1	2	yes	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	4	4	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	2	8	no	—
76	C₂²⋊C₄×C₁₉	—	4	4	no	—
77	C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₄²×C₁₉	—	2	2	no	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	—	4	2	no	—
83	C₄²×C₁₉	—	4	2	no	—
84	C₄²×C₁₉	M₁₆	1	2	yes	—
85	C₄²×C₁₉	C₂×D₄	1	2	yes	—
86	C₄²×C₁₉	#41	1	2	yes	—
87	C₂×C₁₉⋊C₈	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#8964	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	—	2	2	no	—
91	C₂³×C₁₉	—	4	2	no	—
92	C₂³×C₁₉	—	4	2	no	—
93	C₂³×C₁₉	—	4	1	no	—
94	C₂³×C₁₉	—	4	1	no	—
95	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	Q₈×C₁₉	—	4	2	no	—
97	Q₈×C₁₉	—	4	2	no	—
98	D₄×C₁₉	—	2	4	no	—
99	D₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	1	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	1	no	—
115	C₂×C₄×C₁₉	—	8	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×M₁₆	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#131	1	2	yes	—
124	C₁₉⋊C₈	—	4	4	no	—
125	C₁₉⋊C₈	—	8	2	no	—
126	#2983	—	19	1	no	—
127	C₄×#124	D₁₉	1	1	yes	characteristic
128	#1478	—	19	2	no	—
129	#1461	—	19	1	no	—
130	#1276	—	19	2	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	4	4	no	—
134	C₂²×C₁₉	—	4	2	no	—
135	C₂²×C₁₉	—	8	2	no	—
136	C₂²×C₁₉	—	8	1	no	—
137	C₂²×C₁₉	—	8	1	no	—
138	C₂²×C₁₉	#386	1	1	yes	characteristic
139	C₂²×C₁₉	#407	1	1	yes	characteristic
140	C₂²×C₁₉	#408	1	1	yes	characteristic
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	4	2	no	—
144	C₄×C₁₉	—	4	2	no	—
145	C₄×C₁₉	—	4	2	no	—
146	C₄×C₁₉	—	4	2	no	—
147	C₄×C₁₉	—	8	1	no	—
148	C₄×C₁₉	#435	1	2	yes	—
149	C₄×C₁₉	#436	1	2	yes	—
150	C₄×C₁₉	#454	1	2	yes	—
151	C₂×#124	Dic₁₉	1	1	yes	characteristic
152	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
154	#446	—	38	4	no	—
155	#432	—	38	2	no	—
156	#431	—	19	2	no	—
157	#431	—	19	2	no	—
158	#391	Dic₁₉	1	1	yes	characteristic
159	#390	Dic₁₉	1	1	yes	characteristic
160	#388	—	2	2	no	—
161	#382	Dic₁₉	1	1	yes	characteristic
162	C₄×C₂²⋊C₄	—	2	2	no	—
163	C₄³	C₂×D₁₉	1	1	yes	characteristic
164	D₄⋊C₈	—	38	4	no	—
165	#324	—	38	2	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	2	1	no	—
168	C₂×C₁₉	—	8	2	no	—
169	C₂×C₁₉	#1870	1	1	yes	characteristic
170	C₂×C₁₉	#1884	1	1	yes	characteristic
171	C₂×C₁₉	#1888	1	1	yes	characteristic
172	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
173	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂³×C₄	—	2	1	no	—
175	#124	—	2	2	no	—
176	#124	—	2	2	no	—
177	C₄×Q₈	—	2	2	no	—
178	C₄×Q₈	—	2	2	no	—
179	C₄×D₄	—	2	2	no	—
180	C₄×D₄	—	2	2	no	—
181	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
184	C₂×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²	—	2	1	no	—
188	C₂×C₄²	—	2	1	no	—
189	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
190	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
191	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
192	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
193	C₄⋊C₈	—	19	4	no	—
194	C₄⋊C₈	—	38	4	no	—
195	C₄⋊C₈	—	38	2	no	—
196	C₂²⋊C₈	—	38	2	no	—
197	C₂²⋊C₈	—	38	2	no	—
198	#97	—	38	4	no	—
199	C₄×C₈	—	38	2	no	—
200	C₄×C₈	—	38	2	no	—
201	#95	—	2	2	no	—
202	#95	—	2	2	no	—
203	C₁₉	#8964	1	1	yes	characteristic, complemented, Sylow
204	C₂⁴	—	2	1	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	—	2	1	no	—
208	C₂×Q₈	—	2	1	no	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	—	2	1	no	—
212	C₂×D₄	#64520	1	2	yes	—
213	C₂²×C₄	—	2	1	no	—
214	C₂²×C₄	—	2	1	no	—
215	C₂²×C₄	—	2	1	no	—
216	C₂²×C₄	—	4	4	no	—
217	C₂²×C₄	—	4	1	no	—
218	C₂²×C₄	—	4	1	no	—
219	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
220	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
221	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
222	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
224	C₂×C₈	—	38	4	no	—
225	C₂×C₈	—	76	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	2	2	no	—
229	C₂²⋊C₄	—	2	8	no	—
230	C₂²⋊C₄	—	4	4	no	—
231	C₂²⋊C₄	—	4	2	no	—
232	C₄²	—	2	2	no	—
233	C₄²	—	2	2	no	—
234	C₄²	—	2	1	no	—
235	C₄²	—	2	2	no	—
236	C₄²	—	4	2	no	—
237	C₄²	—	4	2	no	—
238	C₄²	#64520	1	2	yes	—
239	C₄²	D₄×D₁₉	1	2	yes	—
240	C₄²	#64543	1	2	yes	—
241	C₂³	—	2	2	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	4	1	no	—
245	C₂³	—	4	1	no	—
246	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
247	Q₈	—	4	2	no	—
248	Q₈	—	4	2	no	—
249	D₄	—	2	4	no	—
250	D₄	—	4	2	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	1	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	1	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	—	8	2	no	—
267	C₂×C₄	—	8	2	no	—
268	C₂×C₄	C₂×#64520	1	1	yes	characteristic
269	C₂×C₄	C₂×#64520	1	1	yes	characteristic
270	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
271	C₂×C₄	#10597381	1	1	yes	characteristic
272	C₂×C₄	#10597383	1	1	yes	characteristic
273	C₂×C₄	#10597385	1	2	yes	—
274	C₂×C₄	#10597394	1	2	yes	—
275	C₈	—	76	4	no	—
276	C₈	—	152	2	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	4	4	no	—
280	C₂²	—	4	2	no	—
281	C₂²	—	8	2	no	—
282	C₂²	—	8	1	no	—
283	C₂²	—	8	1	no	—
284	C₂²	#11926424	1	1	yes	characteristic
285	C₂²	#11926508	1	1	yes	characteristic
286	C₂²	#11926511	1	1	yes	characteristic
287	C₄	—	2	2	no	—
288	C₄	—	2	1	no	—
289	C₄	—	4	2	no	—
290	C₄	—	4	2	no	—
291	C₄	—	4	2	no	—
292	C₄	—	4	2	no	—
293	C₄	—	8	1	no	—
294	C₄	#11926616	1	2	yes	—
295	C₄	#11926622	1	2	yes	—
296	C₄	#11926716	1	2	yes	—
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	8	2	no	—
300	C₂	#14563933	1	1	yes	characteristic
301	C₂	#14564019	1	1	yes	characteristic
302	C₂	#14564039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic, complemented

#14562026

C₂

yes

maximal

#14561959

C₂

yes

maximal, characteristic, complemented

#14561468

C₂

yes

maximal, complemented

C₄×C₁₉×#124

C₂

yes

maximal, characteristic

#11926675

—

#11926601

—

#11926597

C₂²

yes

—

#11926597

C₂²

yes

—

D₄⋊(C₁₉⋊C₈)

—

#11926270

—

C₂×C₁₉×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#391

C₄

yes

characteristic

C₁₉×#390

C₄

yes

characteristic

C₁₉×#388

—

C₁₉×#382

C₄

yes

characteristic

C₄×C₂²⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₁₉×#124

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×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

—

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

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8964

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×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

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×M₁₆

yes

characteristic

122

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

123

C₂×C₄×C₁₉

#131

yes

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

#2983

—

127

C₄×#124

D₁₉

yes

characteristic

128

#1478

—

129

#1461

—

130

#1276

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

#386

yes

characteristic

139

C₂²×C₁₉

#407

yes

characteristic

140

C₂²×C₁₉

#408

yes

characteristic

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

#435

yes

—

149

C₄×C₁₉

#436

yes

—

150

C₄×C₁₉

#454

yes

—

151

C₂×#124

Dic₁₉

yes

characteristic

152

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

153

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

154

#446

—

155

#432

—

156

#431

—

157

#431

—

158

#391

Dic₁₉

yes

characteristic

159

#390

Dic₁₉

yes

characteristic

160

#388

—

161

#382

Dic₁₉

yes

characteristic

162

C₄×C₂²⋊C₄

—

163

C₄³

C₂×D₁₉

yes

characteristic

164

D₄⋊C₈

—

165

#324

—

166

C₂×C₁₉

—

167

C₂×C₁₉

—

168

C₂×C₁₉

—

169

C₂×C₁₉

#1870

yes

characteristic

170

C₂×C₁₉

#1884

yes

characteristic

171

C₂×C₁₉

#1888

yes

characteristic

172

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

173

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

174

C₂³×C₄

—

175

#124

—

176

#124

—

177

C₄×Q₈

—

178

C₄×Q₈

—

179

C₄×D₄

—

180

C₄×D₄

—

181

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

182

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

183

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

184

C₂×C₂²⋊C₄

—

185

C₂×C₂²⋊C₄

—

186

C₂×C₂²⋊C₄

—

187

C₂×C₄²

—

188

C₂×C₄²

—

189

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

190

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

191

C₂×C₄²

C₂²⋊D₁₉

yes

—

192

C₂×C₄²

C₂²×D₁₉

yes

characteristic

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

C₄⋊C₈

—

196

C₂²⋊C₈

—

197

C₂²⋊C₈

—

198

#97

—

199

C₄×C₈

—

200

C₄×C₈

—

201

#95

—

202

#95

—

203

C₁₉

#8964

yes

characteristic, complemented, Sylow

204

C₂⁴

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

#64520

yes

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

220

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

221

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

222

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

224

C₂×C₈

—

225

C₂×C₈

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₂²⋊C₄

—

232

C₄²

—

233

C₄²

—

234

C₄²

—

235

C₄²

—

236

C₄²

—

237

C₄²

—

238

C₄²

#64520

yes

—

239

C₄²

D₄×D₁₉

yes

—

240

C₄²

#64543

yes

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

247

Q₈

—

248

Q₈

—

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

C₂×#64520

yes

characteristic

269

C₂×C₄

C₂×#64520

yes

characteristic

270

C₂×C₄

D₄×Dic₁₉

yes

—

271

C₂×C₄

#10597381

yes

characteristic

272

C₂×C₄

#10597383

yes

characteristic

273

C₂×C₄

#10597385

yes

—

274

C₂×C₄

#10597394

yes

—

275

C₈

—

276

C₈

—

152

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

—

283

C₂²

—

284

C₂²

#11926424

yes

characteristic

285

C₂²

#11926508

yes

characteristic

286

C₂²

#11926511

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

#11926616

yes

—

295

C₄

#11926622

yes

—

296

C₄

#11926716

yes

—

297

C₂

—

298

C₂

—

299

C₂

—

300

C₂

#14563933

yes

characteristic

301

C₂

#14564019

yes

characteristic

302

C₂

#14564039

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#124	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#124	D₁₉
hypocenter	C₁₉	#8964
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#124

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#124

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

C₂×C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#124

N	H ≅ G/N	type
1. #14572720	C₂	semidirect
3. #14561959	C₂	semidirect
4. #14561468	C₂	semidirect
203. C₁₉	#8964	semidirect

H ≅ G/N

type

1. #14572720

C₂

semidirect

3. #14561959

C₂

semidirect

4. #14561468

C₂

semidirect

203. C₁₉

#8964

semidirect

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

subgroup	index
#14572720	2
#14562026	2
#14561959	2
#14561468	2
C₄×C₁₉×#124	2
#8964	19

subgroup

index

C₄×C₁₉×#124

Subgroups — #18077220

Conjugacy classes of subgroups

Complements

Maximal subgroups