Group #18074898 — subgroups

Subgroups — #18074898

Order 4864.

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

normal subgroups only

This group has 692 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	#14564468	C₂	1	1	yes	maximal, characteristic
2	#14562365	C₂	1	2	yes	maximal, complemented
3	#14562270	C₂	1	1	yes	maximal, characteristic
4	#14562147	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	#11926568	C₂²	1	1	yes	characteristic
8	C₂×#10597294	—	2	2	no	—
9	#11926390	C₂²	1	1	yes	characteristic
10	#11926293	—	2	2	no	—
11	#11926290	—	2	2	no	—
12	#11926284	—	2	2	no	—
13	#11926281	—	2	4	no	—
14	C₁₉×#563	—	2	2	no	—
15	C₁₉×#559	C₄	1	2	yes	complemented
16	Q₈²×C₁₉	C₄	1	2	yes	complemented
17	C₁₉×#556	—	2	2	no	—
18	D₄×Q₈×C₁₉	—	2	2	no	—
19	C₁₉×#542	—	2	4	no	—
20	C₁₉×#536	—	2	2	no	—
21	C₁₉×#533	C₂²	1	2	yes	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×#41×C₁₉	D₄	1	2	yes	—
24	C₂²×Q₈×C₁₉	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	4	no	—
26	C₁₉×C₄⋊Q₈	—	2	4	no	—
27	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
28	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
31	C₁₉×#126	—	2	8	no	—
32	C₁₉×#125	—	2	2	no	—
33	C₁₉×#124	—	2	4	no	—
34	C₁₉×#124	—	2	4	no	—
35	C₁₉×#124	D₄	1	2	yes	—
36	C₁₉×#123	—	2	4	no	—
37	C₁₉×#123	—	2	4	no	—
38	C₁₉×C₂²⋊Q₈	—	2	4	no	—
39	C₁₉×C₂²⋊Q₈	—	2	8	no	—
40	C₁₉×C₂²⋊Q₈	—	2	2	no	—
41	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
42	C₁₉×#121	—	2	2	no	—
43	C₄×Q₈×C₁₉	—	2	4	no	—
44	C₄×Q₈×C₁₉	—	2	2	no	—
45	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
46	C₄×D₄×C₁₉	—	2	4	no	—
47	C₄×D₄×C₁₉	—	2	2	no	—
48	C₁₉×#117	—	2	2	no	—
49	C₁₉×#117	—	2	2	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂×#64520	—	2	1	no	—
53	#10597294	—	4	4	no	—
54	C₁₉⋊#95	—	2	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	#10597260	—	2	2	no	—
59	#41×C₁₉	—	4	2	no	—
60	#41×C₁₉	—	4	2	no	—
61	C₂×Q₈×C₁₉	—	2	4	no	—
62	C₂×Q₈×C₁₉	—	2	2	no	—
63	C₂×Q₈×C₁₉	—	8	2	no	—
64	C₂×Q₈×C₁₉	—	8	2	no	—
65	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
66	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
67	C₂×D₄×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
74	C₂²×Dic₁₉	—	4	1	no	—
75	C₄⋊C₄×C₁₉	—	2	8	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₄⋊C₄×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
83	C₂²⋊C₄×C₁₉	—	2	4	no	—
84	C₂²⋊C₄×C₁₉	—	2	8	no	—
85	C₂²⋊C₄×C₁₉	—	2	4	no	—
86	C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₄²×C₁₉	—	2	4	no	—
88	C₄²×C₁₉	—	2	4	no	—
89	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₄²×C₁₉	C₂×D₄	1	2	yes	—
91	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄×Dic₁₉	—	2	2	no	—
93	C₄×Dic₁₉	—	4	1	no	—
94	#64520	—	4	2	no	—
95	C₂×C₁₉⋊C₈	—	4	2	no	—
96	C₂×C₁₉⋊C₈	—	4	1	no	—
97	#8492	—	19	1	no	maximal, Sylow
98	C₂³×C₁₉	—	2	2	no	—
99	C₂³×C₁₉	#120	1	1	yes	characteristic
100	Q₈×C₁₉	—	4	4	no	—
101	Q₈×C₁₉	—	4	2	no	—
102	Q₈×C₁₉	—	4	2	no	—
103	Q₈×C₁₉	—	4	2	no	—
104	Q₈×C₁₉	—	8	4	no	—
105	D₄×C₁₉	—	4	2	no	—
106	D₄×C₁₉	—	4	4	no	—
107	D₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	4	no	—
111	C₂×C₄×C₁₉	—	2	2	no	—
112	C₂×C₄×C₁₉	—	2	4	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	2	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	8	4	no	—
117	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
118	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#120	1	2	yes	—
120	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	8	2	no	—
123	C₁₉⋊C₈	—	8	2	no	—
124	C₁₉⋊C₈	—	8	1	no	—
125	#3550	D₁₉	1	1	yes	characteristic
126	#1963	—	19	1	no	—
127	#1559	—	19	2	no	—
128	#1536	—	19	1	no	—
129	#1506	—	19	2	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	2	2	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	4	4	no	—
134	C₂²×C₁₉	#379	1	1	yes	characteristic
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	2	2	no	—
138	C₄×C₁₉	—	4	2	no	—
139	C₄×C₁₉	—	4	4	no	—
140	C₄×C₁₉	—	4	4	no	—
141	C₄×C₁₉	#453	1	1	yes	characteristic
142	C₄×C₁₉	#455	1	1	yes	characteristic
143	Dic₁₉	—	8	2	no	—
144	#563	—	2	2	no	—
145	#559	Dic₁₉	1	2	yes	complemented
146	Q₈²	Dic₁₉	1	2	yes	complemented
147	#556	—	2	2	no	—
148	D₄×Q₈	—	2	2	no	—
149	#542	—	2	4	no	—
150	#536	—	2	2	no	—
151	#533	C₂×D₁₉	1	2	yes	—
152	#532	C₂×D₁₉	1	1	yes	characteristic
153	#432	—	19	2	no	—
154	#423	—	19	1	no	—
155	C₂×#104	—	38	2	no	—
156	#376	—	19	1	no	—
157	#333	—	38	2	no	—
158	#332	—	38	2	no	—
159	#329	—	38	2	no	—
160	#328	—	38	4	no	—
161	C₂×C₁₉	—	4	1	no	—
162	C₂×C₁₉	—	8	2	no	—
163	C₂×C₁₉	#1792	1	1	yes	characteristic
164	C₂×C₁₉	#1796	1	2	yes	—
165	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
166	C₂²×Q₈	—	2	2	no	—
167	C₂×M₁₆	—	38	1	no	—
168	C₄⋊Q₈	—	2	4	no	—
169	C₄⋊Q₈	—	2	4	no	—
170	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
171	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
172	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
173	#127	C₂×Dic₁₉	1	1	yes	characteristic
174	#126	—	2	8	no	—
175	#125	—	2	2	no	—
176	#124	—	2	4	no	—
177	#124	—	2	4	no	—
178	#124	C₂²⋊D₁₉	1	2	yes	—
179	#123	—	2	4	no	—
180	#123	—	2	4	no	—
181	C₂²⋊Q₈	—	2	4	no	—
182	C₂²⋊Q₈	—	2	8	no	—
183	C₂²⋊Q₈	—	2	2	no	—
184	C₂²⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
185	#121	—	2	2	no	—
186	C₄×Q₈	—	2	4	no	—
187	C₄×Q₈	—	2	2	no	—
188	C₄×Q₈	C₂×Dic₁₉	1	4	yes	—
189	C₄×D₄	—	2	4	no	—
190	C₄×D₄	—	2	2	no	—
191	#117	—	2	2	no	—
192	#117	—	2	2	no	—
193	C₂×C₄²	—	38	1	no	—
194	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
195	C₄⋊C₈	—	38	2	no	—
196	C₄⋊C₈	—	38	2	no	—
197	#104	—	76	4	no	—
198	C₂²⋊C₈	—	38	2	no	—
199	#97	—	38	2	no	—
200	#95	—	38	2	no	—
201	C₁₉	#8492	1	1	yes	characteristic, complemented, Sylow
202	#41	—	4	2	no	—
203	#41	—	4	2	no	—
204	C₂×Q₈	—	2	4	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	—	8	2	no	—
207	C₂×Q₈	—	8	2	no	—
208	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
209	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	—	2	2	no	—
212	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	76	1	no	—
216	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
218	M₁₆	—	76	2	no	—
219	C₂×C₈	—	76	2	no	—
220	C₂×C₈	—	76	1	no	—
221	C₄⋊C₄	—	2	8	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	2	4	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
229	C₂²⋊C₄	—	2	4	no	—
230	C₂²⋊C₄	—	2	8	no	—
231	C₂²⋊C₄	—	2	4	no	—
232	C₂²⋊C₄	—	2	4	no	—
233	C₄²	—	2	4	no	—
234	C₄²	—	2	4	no	—
235	C₄²	—	38	2	no	—
236	C₄²	—	76	1	no	—
237	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
238	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
239	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
240	C₂³	—	2	2	no	—
241	C₂³	#10597399	1	1	yes	characteristic
242	Q₈	—	4	2	no	—
243	Q₈	—	4	4	no	—
244	Q₈	—	4	2	no	—
245	Q₈	—	4	2	no	—
246	Q₈	—	8	4	no	—
247	D₄	—	4	2	no	—
248	D₄	—	4	4	no	—
249	D₄	—	8	2	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	8	4	no	—
259	C₂×C₄	—	76	2	no	—
260	C₂×C₄	—	152	2	no	—
261	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
262	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
263	C₂×C₄	#10597399	1	2	yes	—
264	C₂×C₄	#10597399	1	1	yes	characteristic
265	C₈	—	152	2	no	—
266	C₈	—	152	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	4	2	no	—
270	C₂²	—	4	4	no	—
271	C₂²	#11926400	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	2	no	—
274	C₄	—	2	2	no	—
275	C₄	—	4	2	no	—
276	C₄	—	4	4	no	—
277	C₄	—	4	4	no	—
278	C₄	—	152	2	no	—
279	C₄	#11926712	1	1	yes	characteristic
280	C₄	#11926722	1	1	yes	characteristic
281	C₂	—	4	1	no	—
282	C₂	—	8	2	no	—
283	C₂	#14563589	1	1	yes	characteristic
284	C₂	#14563610	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564468

C₂

yes

maximal, characteristic

#14562365

C₂

yes

maximal, complemented

#14562270

C₂

yes

maximal, characteristic

#14562147

C₂

yes

maximal, complemented

C₁₉×#3550

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597294

—

#11926390

C₂²

yes

—

—

—

—

C₁₉×#563

—

C₁₉×#559

C₄

yes

complemented

Q₈²×C₁₉

C₄

yes

complemented

C₁₉×#556

—

D₄×Q₈×C₁₉

—

C₁₉×#542

—

C₁₉×#536

—

C₁₉×#533

C₂²

yes

—

C₁₉×#532

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#126

—

C₁₉×#125

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

D₄

yes

—

C₁₉×#123

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

D₄

yes

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₂×C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×#64520

—

#10597294

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8492

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

100

Q₈×C₁₉

—

101

Q₈×C₁₉

—

102

Q₈×C₁₉

—

103

Q₈×C₁₉

—

104

Q₈×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

C₂×C₂²⋊C₄

yes

—

118

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

119

C₂×C₄×C₁₉

#120

yes

—

120

C₂×C₄×C₁₉

#120

yes

characteristic

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

#3550

D₁₉

yes

characteristic

126

#1963

—

127

#1559

—

128

#1536

—

129

#1506

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

#379

yes

characteristic

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

#453

yes

characteristic

142

C₄×C₁₉

#455

yes

characteristic

143

Dic₁₉

—

144

#563

—

145

#559

Dic₁₉

yes

complemented

146

Q₈²

Dic₁₉

yes

complemented

147

#556

—

148

D₄×Q₈

—

149

#542

—

150

#536

—

151

#533

C₂×D₁₉

yes

—

152

#532

C₂×D₁₉

yes

characteristic

153

#432

—

154

#423

—

155

C₂×#104

—

156

#376

—

157

#333

—

158

#332

—

159

#329

—

160

#328

—

161

C₂×C₁₉

—

162

C₂×C₁₉

—

163

C₂×C₁₉

#1792

yes

characteristic

164

C₂×C₁₉

#1796

yes

—

165

C₂×#41

C₂²⋊D₁₉

yes

—

166

C₂²×Q₈

—

167

C₂×M₁₆

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

171

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

172

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

173

#127

C₂×Dic₁₉

yes

characteristic

174

#126

—

175

#125

—

176

#124

—

177

#124

—

178

#124

C₂²⋊D₁₉

yes

—

179

#123

—

180

#123

—

181

C₂²⋊Q₈

—

182

C₂²⋊Q₈

—

183

C₂²⋊Q₈

—

184

C₂²⋊Q₈

C₂²⋊D₁₉

yes

—

185

#121

—

186

C₄×Q₈

—

187

C₄×Q₈

—

188

C₄×Q₈

C₂×Dic₁₉

yes

—

189

C₄×D₄

—

190

C₄×D₄

—

191

#117

—

192

#117

—

193

C₂×C₄²

—

194

C₂×C₄²

C₂²×D₁₉

yes

characteristic

195

C₄⋊C₈

—

196

C₄⋊C₈

—

197

#104

—

198

C₂²⋊C₈

—

199

#97

—

200

#95

—

201

C₁₉

#8492

yes

characteristic, complemented, Sylow

202

#41

—

203

#41

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

209

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

C₂²⋊Dic₁₉

yes

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

217

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

218

M₁₆

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₂²⋊C₄

—

232

C₂²⋊C₄

—

233

C₄²

—

234

C₄²

—

235

C₄²

—

236

C₄²

—

237

C₄²

C₂²×Dic₁₉

yes

characteristic

238

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

239

C₄²

C₂×C₂²⋊D₁₉

yes

—

240

C₂³

—

241

C₂³

#10597399

yes

characteristic

242

Q₈

—

243

Q₈

—

244

Q₈

—

245

Q₈

—

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

C₂×C₄

—

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

—

152

—

261

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

262

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

263

C₂×C₄

#10597399

yes

—

264

C₂×C₄

#10597399

yes

characteristic

265

C₈

—

152

—

266

C₈

—

152

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

#11926400

yes

characteristic

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

152

—

279

C₄

#11926712

yes

characteristic

280

C₄

#11926722

yes

characteristic

281

C₂

—

282

C₂

—

283

C₂

#14563589

yes

characteristic

284

C₂

#14563610

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3550	C₂
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3550	D₁₉
hypocenter	C₁₉	#8492
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3550

subgroup

G/H

center

C₂²

#11926400

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3550

C₂

socle

C₂²×C₁₉

#379

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3550

N	H ≅ G/N	type
2. #14562365	C₂	semidirect
4. #14562147	C₂	semidirect
15. C₁₉×#559	C₄	semidirect
16. Q₈²×C₁₉	C₄	semidirect
145. #559	Dic₁₉	semidirect
146. Q₈²	Dic₁₉	semidirect
201. C₁₉	#8492	semidirect

H ≅ G/N

type

2. #14562365

C₂

semidirect

4. #14562147

C₂

semidirect

15. C₁₉×#559

C₄

semidirect

16. Q₈²×C₁₉

C₄

semidirect

145. #559

Dic₁₉

semidirect

146. Q₈²

Dic₁₉

semidirect

201. C₁₉

#8492

semidirect

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

subgroup	index
#14564468	2
#14562365	2
#14562270	2
#14562147	2
C₁₉×#3550	2
#8492	19

subgroup

index

C₁₉×#3550

Subgroups — #18074898

Conjugacy classes of subgroups

Complements

Maximal subgroups