Group #18077858 — subgroups

Subgroups — #18077858

Order 4864.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14574061	C₂	1	1	yes	maximal, characteristic
2	#14572702	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562053	C₂	1	2	yes	maximal, complemented
4	#14561473	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1525	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597396	—	2	2	no	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926926	—	2	2	no	—
9	#11926923	C₄	1	1	yes	characteristic
10	#11926920	C₄	1	1	yes	characteristic
11	#11926918	C₄	1	1	yes	characteristic
12	#11926916	C₄	1	1	yes	characteristic
13	#11926622	—	2	2	no	—
14	D₄×C₁₉⋊C₈	—	2	2	no	—
15	#11926597	C₂²	1	2	yes	—
16	#11926511	—	2	2	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926273	—	2	2	no	—
19	#11926273	—	2	2	no	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#329	—	2	2	no	—
23	C₂×#41×C₁₉	D₄	1	2	yes	—
24	C₂×#64541	—	2	1	no	—
25	C₂×M₁₆×C₁₉	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
27	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
28	C₁₉×#124	D₄	1	2	yes	—
29	C₁₉×#121	—	2	2	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	#10597396	—	4	4	no	—
33	#10597396	—	4	4	no	—
34	C₂×#64528	—	2	2	no	—
35	C₂×#64527	—	2	2	no	—
36	C₂×#64526	—	2	2	no	—
37	C₂×#64525	—	2	2	no	—
38	#10597376	—	2	2	no	—
39	C₂×#64520	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	1	no	—
41	C₂²×C₁₉⋊C₈	—	2	2	no	—
42	#10597321	—	2	1	no	—
43	#10597320	C₂×C₄	1	1	yes	characteristic
44	C₄×D₇₆	—	2	2	no	—
45	#10597315	C₂×C₄	1	1	yes	characteristic
46	C₁₉×#97	—	2	2	no	—
47	C₄×C₈×C₁₉	—	2	2	no	—
48	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
51	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
52	C₄×C₁₉⋊C₈	—	2	2	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	#41×C₁₉	—	4	2	no	—
57	#41×C₁₉	—	4	2	no	—
58	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	—	2	2	no	—
61	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	2	yes	—
65	C₂×C₂²⋊D₁₉	—	4	1	no	—
66	#64541	—	4	2	no	—
67	#64541	—	4	2	no	—
68	C₂×D₇₆	—	2	1	no	—
69	C₂×D₇₆	—	2	2	no	—
70	C₂×C₄×D₁₉	—	4	1	no	—
71	C₂×Dic₃₈	—	2	1	no	—
72	M₁₆×C₁₉	—	2	4	no	—
73	M₁₆×C₁₉	—	4	2	no	—
74	C₂×C₈×C₁₉	—	4	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₂²⋊C₄×C₁₉	—	2	4	no	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	2	yes	—
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	#64528	—	4	4	no	—
81	#64527	—	4	4	no	—
82	#64526	—	4	4	no	—
83	#64525	—	4	4	no	—
84	(C₂×D₁₉)⋊C₄	—	4	2	no	—
85	C₄⋊Dic₁₉	—	2	2	no	—
86	#64520	—	8	2	no	—
87	C₂×C₁₉⋊C₈	—	2	2	no	—
88	C₂×C₁₉⋊C₈	—	2	2	no	—
89	C₂×C₁₉⋊C₈	—	2	1	no	—
90	C₂×C₁₉⋊C₈	—	2	1	no	—
91	C₂×C₁₉⋊C₈	—	2	2	no	—
92	C₂×C₁₉⋊C₈	—	2	2	no	—
93	C₂×C₁₉⋊C₈	—	8	2	no	—
94	#9069	—	19	1	no	maximal, Sylow
95	C₂³×C₁₉	—	2	2	no	—
96	C₂³×C₁₉	#123	1	1	yes	characteristic
97	C₂²×D₁₉	—	4	1	no	—
98	Q₈×C₁₉	—	4	2	no	—
99	D₄×C₁₉	—	4	2	no	—
100	D₄×C₁₉	—	4	2	no	—
101	D₄×C₁₉	—	4	2	no	—
102	D₄×C₁₉	—	8	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₂²⋊D₁₉	—	8	2	no	—
115	C₂×Dic₁₉	—	4	1	no	—
116	D₇₆	—	4	2	no	—
117	D₇₆	—	4	2	no	—
118	D₇₆	—	4	2	no	—
119	C₄×D₁₉	—	8	1	no	—
120	C₄×D₁₉	—	8	1	no	—
121	Dic₃₈	—	4	2	no	—
122	C₈×C₁₉	—	4	4	no	—
123	C₁₉⋊C₈	—	2	2	no	—
124	C₁₉⋊C₈	—	2	2	no	—
125	C₁₉⋊C₈	—	4	2	no	—
126	C₁₉⋊C₈	—	4	2	no	—
127	#3147	—	19	1	no	—
128	#2979	—	19	1	no	—
129	#1525	D₁₉	1	1	yes	characteristic, complemented
130	#1484	—	19	2	no	—
131	#1278	—	19	2	no	—
132	C₂²×C₁₉	—	2	2	no	—
133	C₂²×C₁₉	—	2	1	no	—
134	C₂²×C₁₉	—	4	4	no	—
135	C₂²×C₁₉	—	4	2	no	—
136	C₂²×C₁₉	#386	1	1	yes	characteristic
137	C₂×D₁₉	—	8	2	no	—
138	C₂×D₁₉	—	8	1	no	—
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	2	1	no	—
141	C₄×C₁₉	—	4	2	no	—
142	C₄×C₁₉	#443	1	2	yes	—
143	C₄×C₁₉	#444	1	2	yes	—
144	C₄×C₁₉	#453	1	1	yes	characteristic
145	C₄×C₁₉	#453	1	1	yes	characteristic
146	Dic₁₉	—	8	1	no	—
147	C₂×#135	—	38	2	no	—
148	#532	—	19	1	no	—
149	#532	C₂×D₁₉	1	1	yes	characteristic
150	#495	—	38	2	no	—
151	#494	—	19	1	no	—
152	#493	—	19	1	no	—
153	#492	—	19	1	no	—
154	#492	—	19	1	no	—
155	#436	—	38	2	no	—
156	C₈×D₄	—	38	2	no	—
157	#431	—	19	2	no	—
158	#408	—	38	2	no	—
159	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
160	C₂×C₄×C₈	—	19	1	no	—
161	#329	—	2	2	no	—
162	D₄⋊C₈	—	38	2	no	—
163	D₄⋊C₈	—	38	2	no	—
164	C₂×C₁₉	—	4	1	no	—
165	C₂×C₁₉	—	8	2	no	—
166	C₂×C₁₉	#1876	1	2	yes	—
167	C₂×C₁₉	#1887	1	1	yes	characteristic
168	D₁₉	—	16	1	no	—
169	C₂×#41	—	38	1	no	—
170	C₂×#41	D₇₆	1	2	yes	—
171	#135	—	76	4	no	—
172	#135	—	76	4	no	—
173	C₂×Q₁₆	—	38	2	no	—
174	C₂×SD₁₆	—	38	2	no	—
175	C₂×SD₁₆	—	38	2	no	—
176	C₂×D₈	—	38	2	no	—
177	C₂×M₁₆	—	2	2	no	—
178	C₂×M₁₆	—	38	2	no	—
179	C₂²×C₈	—	38	1	no	—
180	C₂²×C₈	—	38	2	no	—
181	C₄⋊Q₈	—	19	1	no	—
182	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
183	#127	—	19	1	no	—
184	#127	C₄×D₁₉	1	1	yes	characteristic
185	#124	—	38	1	no	—
186	#124	C₂²⋊D₁₉	1	2	yes	—
187	#121	—	2	2	no	—
188	#121	—	38	2	no	—
189	C₄×D₄	—	2	2	no	—
190	C₄×D₄	—	38	2	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	C₄⋊C₈	—	19	2	no	—
193	C₄⋊C₈	—	19	2	no	—
194	C₂²⋊C₈	—	38	4	no	—
195	C₂²⋊C₈	—	38	2	no	—
196	#97	—	2	2	no	—
197	C₄×C₈	—	2	2	no	—
198	C₄×C₈	—	19	1	no	—
199	C₄×C₈	—	19	1	no	—
200	C₄×C₈	—	38	2	no	—
201	C₄×C₈	—	38	1	no	—
202	C₁₉	#9069	1	1	yes	characteristic, complemented, Sylow
203	#41	—	4	2	no	—
204	#41	—	4	2	no	—
205	#41	—	76	2	no	—
206	#41	—	76	2	no	—
207	C₂×Q₈	—	38	1	no	—
208	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	2	2	no	—
211	C₂×D₄	—	38	2	no	—
212	C₂×D₄	—	38	1	no	—
213	C₂×D₄	—	76	1	no	—
214	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	76	1	no	—
217	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
218	C₂²×C₄	#64543	1	2	yes	—
219	Q₁₆	—	76	4	no	—
220	SD₁₆	—	76	4	no	—
221	SD₁₆	—	76	4	no	—
222	D₈	—	76	4	no	—
223	M₁₆	—	2	4	no	—
224	M₁₆	—	4	2	no	—
225	M₁₆	—	152	2	no	—
226	C₂×C₈	—	4	2	no	—
227	C₂×C₈	—	38	2	no	—
228	C₂×C₈	—	38	2	no	—
229	C₂×C₈	—	38	1	no	—
230	C₂×C₈	—	38	1	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	152	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	38	2	no	—
236	C₂²⋊C₄	—	2	4	no	—
237	C₂²⋊C₄	—	76	2	no	—
238	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
239	C₄²	D₄×D₁₉	1	2	yes	—
240	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂³	—	2	2	no	—
242	C₂³	—	76	1	no	—
243	C₂³	#10597332	1	1	yes	characteristic
244	Q₈	—	4	2	no	—
245	Q₈	—	76	2	no	—
246	D₄	—	4	2	no	—
247	D₄	—	4	2	no	—
248	D₄	—	4	2	no	—
249	D₄	—	8	2	no	—
250	D₄	—	76	2	no	—
251	D₄	—	76	2	no	—
252	D₄	—	76	2	no	—
253	D₄	—	152	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	76	1	no	—
262	C₂×C₄	—	152	1	no	—
263	C₂×C₄	—	152	1	no	—
264	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
265	C₂×C₄	#10597328	1	1	yes	characteristic
266	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
267	C₂×C₄	#10597385	1	2	yes	—
268	C₈	—	4	4	no	—
269	C₈	—	38	2	no	—
270	C₈	—	38	2	no	—
271	C₈	—	76	2	no	—
272	C₈	—	76	2	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	1	no	—
275	C₂²	—	4	4	no	—
276	C₂²	—	4	2	no	—
277	C₂²	—	152	2	no	—
278	C₂²	—	152	1	no	—
279	C₂²	#11926421	1	1	yes	characteristic
280	C₄	—	2	2	no	—
281	C₄	—	2	1	no	—
282	C₄	—	4	2	no	—
283	C₄	—	152	1	no	—
284	C₄	#11926658	1	2	yes	—
285	C₄	#11926663	1	2	yes	—
286	C₄	#11926714	1	1	yes	characteristic
287	C₄	#11926714	1	1	yes	characteristic
288	C₂	—	4	1	no	—
289	C₂	—	8	2	no	—
290	C₂	—	304	1	no	—
291	C₂	#14563960	1	2	yes	—
292	C₂	#14564031	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574061

C₂

yes

maximal, characteristic

#14572702

C₂

yes

maximal, characteristic, complemented

#14562053

C₂

yes

maximal, complemented

#14561473

C₂

yes

maximal, complemented

C₁₉×#1525

C₂

yes

maximal, characteristic, complemented

C₂×#10597396

—

#11927094

C₂²

yes

characteristic

#11926926

—

#11926923

C₄

yes

characteristic

#11926920

C₄

yes

characteristic

#11926918

C₄

yes

characteristic

#11926916

C₄

yes

characteristic

#11926622

—

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926511

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926273

—

#11926273

—

C₁₉×#532

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#329

—

C₂×#41×C₁₉

D₄

yes

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

D₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597321

—

#10597320

C₂×C₄

yes

characteristic

C₄×D₇₆

—

#10597315

C₂×C₄

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

—

—

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9069

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

100

D₄×C₁₉

—

101

D₄×C₁₉

—

102

D₄×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

C₂×C₂²⋊C₄

yes

characteristic

111

C₂×C₄×C₁₉

C₄×D₄

yes

—

112

C₂×C₄×C₁₉

#120

yes

characteristic

113

C₂×C₄×C₁₉

#121

yes

—

114

C₂²⋊D₁₉

—

115

C₂×Dic₁₉

—

116

D₇₆

—

117

D₇₆

—

118

D₇₆

—

119

C₄×D₁₉

—

120

C₄×D₁₉

—

121

Dic₃₈

—

122

C₈×C₁₉

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

#3147

—

128

#2979

—

129

#1525

D₁₉

yes

characteristic, complemented

130

#1484

—

131

#1278

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

#386

yes

characteristic

137

C₂×D₁₉

—

138

C₂×D₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

#443

yes

—

143

C₄×C₁₉

#444

yes

—

144

C₄×C₁₉

#453

yes

characteristic

145

C₄×C₁₉

#453

yes

characteristic

146

Dic₁₉

—

147

C₂×#135

—

148

#532

—

149

#532

C₂×D₁₉

yes

characteristic

150

#495

—

151

#494

—

152

#493

—

153

#492

—

154

#492

—

155

#436

—

156

C₈×D₄

—

157

#431

—

158

#408

—

159

C₄×M₁₆

C₂×D₁₉

yes

—

160

C₂×C₄×C₈

—

161

#329

—

162

D₄⋊C₈

—

163

D₄⋊C₈

—

164

C₂×C₁₉

—

165

C₂×C₁₉

—

166

C₂×C₁₉

#1876

yes

—

167

C₂×C₁₉

#1887

yes

characteristic

168

D₁₉

—

169

C₂×#41

—

170

C₂×#41

D₇₆

yes

—

171

#135

—

172

#135

—

173

C₂×Q₁₆

—

174

C₂×SD₁₆

—

175

C₂×SD₁₆

—

176

C₂×D₈

—

177

C₂×M₁₆

—

178

C₂×M₁₆

—

179

C₂²×C₈

—

180

C₂²×C₈

—

181

C₄⋊Q₈

—

182

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

183

#127

—

184

#127

C₄×D₁₉

yes

characteristic

185

#124

—

186

#124

C₂²⋊D₁₉

yes

—

187

#121

—

188

#121

—

189

C₄×D₄

—

190

C₄×D₄

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

C₄⋊C₈

—

193

C₄⋊C₈

—

194

C₂²⋊C₈

—

195

C₂²⋊C₈

—

196

#97

—

197

C₄×C₈

—

198

C₄×C₈

—

199

C₄×C₈

—

200

C₄×C₈

—

201

C₄×C₈

—

202

C₁₉

#9069

yes

characteristic, complemented, Sylow

203

#41

—

204

#41

—

205

#41

—

206

#41

—

207

C₂×Q₈

—

208

C₂×Q₈

(C₂×D₁₉)⋊C₄

yes

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

(C₂×D₁₉)⋊C₄

yes

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

C₂×D₇₆

yes

characteristic

218

C₂²×C₄

#64543

yes

—

219

Q₁₆

—

220

SD₁₆

—

221

SD₁₆

—

222

D₈

—

223

M₁₆

—

224

M₁₆

—

225

M₁₆

—

152

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

152

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₂²⋊C₄

—

237

C₂²⋊C₄

—

238

C₄²

C₂×C₄×D₁₉

yes

characteristic

239

C₄²

D₄×D₁₉

yes

—

240

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

241

C₂³

—

242

C₂³

—

243

C₂³

#10597332

yes

characteristic

244

Q₈

—

245

Q₈

—

246

D₄

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

152

—

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

—

152

—

263

C₂×C₄

—

152

—

264

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

265

C₂×C₄

#10597328

yes

characteristic

266

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

267

C₂×C₄

#10597385

yes

—

268

C₈

—

269

C₈

—

270

C₈

—

271

C₈

—

272

C₈

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

152

—

278

C₂²

—

152

—

279

C₂²

#11926421

yes

characteristic

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

152

—

284

C₄

#11926658

yes

—

285

C₄

#11926663

yes

—

286

C₄

#11926714

yes

characteristic

287

C₄

#11926714

yes

characteristic

288

C₂

—

289

C₂

—

290

C₂

—

304

—

291

C₂

#14563960

yes

—

292

C₂

#14564031

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1525	C₂
socle	C₂²×C₁₉	#386
prime radical	#14574061	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1525	D₁₉
hypocenter	C₁₉	#9069
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1525

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

N	H ≅ G/N	type
2. #14572702	C₂	semidirect
3. #14562053	C₂	semidirect
4. #14561473	C₂	semidirect
5. C₁₉×#1525	C₂	semidirect
129. #1525	D₁₉	semidirect
202. C₁₉	#9069	semidirect

H ≅ G/N

type

2. #14572702

C₂

semidirect

3. #14562053

C₂

semidirect

4. #14561473

C₂

semidirect

5. C₁₉×#1525

C₂

semidirect

129. #1525

D₁₉

semidirect

202. C₁₉

#9069

semidirect

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

subgroup	index
#14574061	2
#14572702	2
#14562053	2
#14561473	2
C₁₉×#1525	2
#9069	19

subgroup

index

C₁₉×#1525

Subgroups — #18077858

Conjugacy classes of subgroups

Complements

Maximal subgroups