Group #18079930 — subgroups

Subgroups — #18079930

Order 4864.

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

normal subgroups only

This group has 574 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	#14572716	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563631	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562303	C₂	1	2	yes	maximal
4	#14561538	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2548	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	—	2	2	no	—
8	#11926597	C₂²	1	2	yes	—
9	#11926568	C₂²	1	2	yes	—
10	C₂×#10597293	—	2	1	no	—
11	#11926313	—	2	1	no	—
12	#11926288	—	2	4	no	—
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#394	C₄	1	4	yes	—
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#390	—	2	2	no	—
19	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₁₉×#127	—	2	2	no	—
25	C₁₉×#127	—	2	2	no	—
26	C₁₉×#124	—	4	2	no	—
27	C₁₉×#124	—	4	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₄×Q₈×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	D₄	1	2	yes	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×#64520	—	2	2	no	—
39	C₁₉×#95	C₂×C₄	1	2	yes	—
40	#10597293	—	4	2	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
46	C₄×C₁₉⋊C₈	—	2	4	no	—
47	C₄×C₁₉⋊C₈	—	2	2	no	—
48	C₂⁴×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	D₈	1	2	yes	—
52	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
53	C₂×D₄×C₁₉	—	2	4	no	—
54	C₂×D₄×C₁₉	—	4	4	no	—
55	C₂×D₄×C₁₉	—	4	1	no	—
56	C₂×D₄×C₁₉	—	4	2	no	—
57	C₂×D₄×C₁₉	—	4	1	no	—
58	C₂×D₄×C₁₉	—	4	1	no	—
59	C₂×D₄×C₁₉	—	4	1	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂×D₄×C₁₉	—	8	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₄⋊C₄×C₁₉	—	2	4	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₂²⋊C₄×C₁₉	—	4	8	no	—
72	C₂²⋊C₄×C₁₉	—	8	4	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	C₄²×C₁₉	#41	1	2	yes	—
79	#64520	—	4	2	no	—
80	#64520	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	4	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#9398	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	4	4	no	—
85	C₂³×C₁₉	—	4	4	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	Q₈×C₁₉	—	2	4	no	—
91	Q₈×C₁₉	—	2	4	no	—
92	D₄×C₁₉	—	8	4	no	—
93	D₄×C₁₉	—	8	2	no	—
94	D₄×C₁₉	—	8	2	no	—
95	D₄×C₁₉	—	8	2	no	—
96	D₄×C₁₉	—	8	2	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	4	1	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	#102	1	4	yes	—
107	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
108	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#121	1	2	yes	—
110	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#135	1	2	yes	—
114	C₁₉⋊C₈	—	4	4	no	—
115	C₁₉⋊C₈	—	8	2	no	—
116	#2982	—	19	1	no	—
117	#2548	D₁₉	1	1	yes	characteristic
118	#1801	—	19	1	no	—
119	#1545	—	19	2	no	—
120	#1303	—	19	2	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	8	4	no	—
124	C₂²×C₁₉	—	8	4	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	—	8	2	no	—
127	C₂²×C₁₉	—	8	2	no	—
128	C₂²×C₁₉	#386	1	1	yes	characteristic
129	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
130	C₂²×C₁₉	#416	1	1	yes	characteristic
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	4	no	—
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	4	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₄×C₁₉	#454	1	2	yes	—
137	C₄×C₁₉	#465	1	2	yes	—
138	C₄×C₁₉	#466	1	2	yes	—
139	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
140	C₂×#124	—	2	1	no	—
141	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
142	C₈×Q₈	—	38	4	no	—
143	#431	—	19	2	no	—
144	#431	—	38	2	no	—
145	#423	—	19	2	no	—
146	C₂×#101	—	38	1	no	—
147	#394	Dic₁₉	1	4	yes	—
148	#390	—	2	1	no	—
149	#390	—	2	2	no	—
150	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
151	#343	—	38	1	no	—
152	#331	—	38	4	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	—	16	2	no	—
156	C₂×C₁₉	#1888	1	1	yes	characteristic
157	C₂×C₁₉	#1893	1	1	yes	characteristic
158	C₂×C₁₉	#1914	1	1	yes	characteristic
159	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
160	C₂²×D₄	—	2	1	no	—
161	C₂²×D₄	—	2	1	no	—
162	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
163	C₂×M₁₆	—	38	2	no	—
164	#127	—	2	2	no	—
165	#127	—	2	2	no	—
166	#124	—	4	2	no	—
167	#124	—	4	2	no	—
168	C₄×Q₈	—	2	2	no	—
169	C₄×Q₈	—	2	2	no	—
170	C₂×C₄⋊C₄	—	2	1	no	—
171	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
172	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	—	2	4	no	—
174	C₂×C₂²⋊C₄	—	2	4	no	—
175	C₂×C₄²	—	2	1	no	—
176	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
177	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
178	C₄⋊C₈	—	19	4	no	—
179	C₄⋊C₈	—	38	4	no	—
180	C₄⋊C₈	—	38	2	no	—
181	C₄⋊C₈	—	38	2	no	—
182	#101	—	76	2	no	—
183	C₂²⋊C₈	—	38	2	no	—
184	C₄×C₈	—	38	4	no	—
185	C₄×C₈	—	38	2	no	—
186	#95	C₂×Dic₁₉	1	2	yes	—
187	C₁₉	#9398	1	1	yes	characteristic, complemented, Sylow
188	C₂⁴	—	2	2	no	—
189	C₂×Q₈	—	2	2	no	—
190	C₂×Q₈	—	2	2	no	—
191	C₂×Q₈	#64525	1	2	yes	—
192	C₂×Q₈	#64526	1	2	yes	—
193	C₂×D₄	—	2	4	no	—
194	C₂×D₄	—	4	4	no	—
195	C₂×D₄	—	4	1	no	—
196	C₂×D₄	—	4	1	no	—
197	C₂×D₄	—	4	1	no	—
198	C₂×D₄	—	4	1	no	—
199	C₂×D₄	—	4	2	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂×D₄	—	8	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
204	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
205	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
208	M₁₆	—	76	2	no	—
209	M₁₆	—	76	2	no	—
210	C₂×C₈	—	38	4	no	—
211	C₂×C₈	—	76	2	no	—
212	C₄⋊C₄	—	2	4	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₂²⋊C₄	—	4	8	no	—
216	C₂²⋊C₄	—	8	4	no	—
217	C₄²	—	2	2	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	4	1	no	—
220	C₄²	—	4	1	no	—
221	C₄²	D₄×D₁₉	1	2	yes	—
222	C₄²	#64543	1	2	yes	—
223	C₂³	—	4	4	no	—
224	C₂³	—	4	4	no	—
225	C₂³	—	4	2	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	2	no	—
228	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
229	Q₈	—	2	4	no	—
230	Q₈	—	2	4	no	—
231	D₄	—	8	4	no	—
232	D₄	—	8	2	no	—
233	D₄	—	8	2	no	—
234	D₄	—	8	2	no	—
235	D₄	—	8	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	2	no	—
245	C₂×C₄	#10597289	1	4	yes	—
246	C₂×C₄	C₂×#64525	1	1	yes	characteristic
247	C₂×C₄	C₂×#64526	1	1	yes	characteristic
248	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
249	C₂×C₄	#10597381	1	1	yes	characteristic
250	C₂×C₄	#10597383	1	1	yes	characteristic
251	C₂×C₄	#10597385	1	2	yes	—
252	C₂×C₄	#10597396	1	2	yes	—
253	C₈	—	76	4	no	—
254	C₈	—	152	2	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	8	4	no	—
258	C₂²	—	8	4	no	—
259	C₂²	—	8	2	no	—
260	C₂²	—	8	2	no	—
261	C₂²	—	8	2	no	—
262	C₂²	#11926424	1	1	yes	characteristic
263	C₂²	C₂×#10597289	1	1	yes	characteristic
264	C₂²	#11926540	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	4	no	—
268	C₄	—	4	2	no	—
269	C₄	—	8	2	no	—
270	C₄	#11926716	1	2	yes	—
271	C₄	#11926771	1	2	yes	—
272	C₄	#11926778	1	2	yes	—
273	C₂	—	2	1	no	—
274	C₂	—	2	1	no	—
275	C₂	—	16	2	no	—
276	C₂	#14564039	1	1	yes	characteristic
277	C₂	#14564064	1	1	yes	characteristic
278	C₂	#14564183	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572716

C₂

yes

maximal, characteristic, complemented

#14563631

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal

#14561538

C₂

yes

maximal, complemented

C₁₉×#2548

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

—

#11926597

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597293

—

#11926313

—

#11926288

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#124

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#394

C₄

yes

—

C₁₉×#390

—

C₁₉×#390

—

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#124

—

C₁₉×#124

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×#95

C₂×C₄

yes

—

#10597293

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₈

yes

—

C₂×Q₈×C₁₉

SD₁₆

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

—

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

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9398

—

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

—

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

#102

yes

—

107

C₂×C₄×C₁₉

C₄×D₄

yes

—

108

C₂×C₄×C₁₉

#120

yes

characteristic

109

C₂×C₄×C₁₉

#121

yes

—

110

C₂×C₄×C₁₉

#123

yes

characteristic

111

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

112

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

113

C₂×C₄×C₁₉

#135

yes

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

#2982

—

117

#2548

D₁₉

yes

characteristic

118

#1801

—

119

#1545

—

120

#1303

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#386

yes

characteristic

129

C₂²×C₁₉

C₂×#102

yes

characteristic

130

C₂²×C₁₉

#416

yes

characteristic

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

#454

yes

—

137

C₄×C₁₉

#465

yes

—

138

C₄×C₁₉

#466

yes

—

139

C₂×#127

C₂×D₁₉

yes

characteristic

140

C₂×#124

—

141

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

142

C₈×Q₈

—

143

#431

—

144

#431

—

145

#423

—

146

C₂×#101

—

147

#394

Dic₁₉

yes

—

148

#390

—

149

#390

—

150

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

151

#343

—

152

#331

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

#1888

yes

characteristic

157

C₂×C₁₉

#1893

yes

characteristic

158

C₂×C₁₉

#1914

yes

characteristic

159

C₂²×Q₈

C₂²⋊D₁₉

yes

characteristic

160

C₂²×D₄

—

161

C₂²×D₄

—

162

C₂²×D₄

C₂×Dic₁₉

yes

—

163

C₂×M₁₆

—

164

#127

—

165

#127

—

166

#124

—

167

#124

—

168

C₄×Q₈

—

169

C₄×Q₈

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

172

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

173

C₂×C₂²⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₄²

—

176

C₂×C₄²

C₂²⋊D₁₉

yes

—

177

C₂×C₄²

C₂²×D₁₉

yes

characteristic

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

#101

—

183

C₂²⋊C₈

—

184

C₄×C₈

—

185

C₄×C₈

—

186

#95

C₂×Dic₁₉

yes

—

187

C₁₉

#9398

yes

characteristic, complemented, Sylow

188

C₂⁴

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

#64525

yes

—

192

C₂×Q₈

#64526

yes

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂²×C₄

—

203

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

204

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

205

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

206

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

207

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

208

M₁₆

—

209

M₁₆

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

D₄×D₁₉

yes

—

222

C₄²

#64543

yes

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

229

Q₈

—

230

Q₈

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

D₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

#10597289

yes

—

246

C₂×C₄

C₂×#64525

yes

characteristic

247

C₂×C₄

C₂×#64526

yes

characteristic

248

C₂×C₄

D₄×Dic₁₉

yes

—

249

C₂×C₄

#10597381

yes

characteristic

250

C₂×C₄

#10597383

yes

characteristic

251

C₂×C₄

#10597385

yes

—

252

C₂×C₄

#10597396

yes

—

253

C₈

—

254

C₈

—

152

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

#11926424

yes

characteristic

263

C₂²

C₂×#10597289

yes

characteristic

264

C₂²

#11926540

yes

characteristic

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

#11926716

yes

—

271

C₄

#11926771

yes

—

272

C₄

#11926778

yes

—

273

C₂

—

274

C₂

—

275

C₂

—

276

C₂

#14564039

yes

characteristic

277

C₂

#14564064

yes

characteristic

278

C₂

#14564183

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2548	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2548	D₁₉
hypocenter	C₁₉	#9398
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2548

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2548

N	H ≅ G/N	type
1. #14572716	C₂	semidirect
2. #14563631	C₂	semidirect
4. #14561538	C₂	semidirect
187. C₁₉	#9398	semidirect

H ≅ G/N

type

1. #14572716

C₂

semidirect

2. #14563631

C₂

semidirect

4. #14561538

C₂

semidirect

187. C₁₉

#9398

semidirect

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

subgroup	index
#14572716	2
#14563631	2
#14562303	2
#14561538	2
C₁₉×#2548	2
#9398	19

subgroup

index

C₁₉×#2548

Subgroups — #18079930

Conjugacy classes of subgroups

Complements

Maximal subgroups