Group #18081730 — subgroups

Subgroups — #18081730

Order 4864.

444 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄×#10597276	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562227	C₂	1	2	yes	maximal, complemented
3	#14562052	C₂	1	2	yes	maximal, complemented
4	C₈×#64520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3169	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	1	yes	characteristic
7	C₂×#10597276	—	2	1	no	—
8	C₄×#64520	C₂²	1	2	yes	—
9	C₄×#64520	C₂²	1	1	yes	characteristic
10	#11926309	—	2	1	no	—
11	#11926284	—	2	4	no	—
12	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
13	#11926266	—	2	1	no	—
14	C₈×C₁₉⋊C₈	—	2	1	no	—
15	C₁₉×#532	C₂²	1	2	yes	—
16	C₁₉×#500	C₄	1	1	yes	characteristic
17	C₁₉×#493	C₄	1	1	yes	characteristic
18	C₁₉×#486	C₄	1	2	yes	—
19	C₁₉×#466	—	2	1	no	—
20	C₁₉×#466	—	2	1	no	—
21	C₄×D₈×C₁₉	—	2	1	no	—
22	C₄×D₈×C₁₉	—	2	1	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×#41×C₁₉	—	2	2	no	—
25	C₂×D₈×C₁₉	—	2	1	no	—
26	C₂×D₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₉×#127	C₂×C₄	1	2	yes	—
31	C₁₉×#124	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₄×D₄×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64520	—	2	1	no	—
38	C₂×#64520	—	2	2	no	—
39	C₁₉×#107	—	2	1	no	—
40	C₁₉×#107	—	2	1	no	—
41	C₁₉×#102	—	2	2	no	—
42	C₁₉×#102	—	2	2	no	—
43	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
48	#10597276	—	2	4	no	—
49	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
50	#10597260	—	2	2	no	—
51	#10597260	D₄	1	2	yes	—
52	C₄×C₁₉⋊C₈	—	2	1	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	2	no	—
55	#41×C₁₉	—	8	4	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	2	2	no	—
58	C₂×D₄×C₁₉	—	2	2	no	—
59	C₂×D₄×C₁₉	—	2	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	4	2	no	—
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
65	D₈×C₁₉	—	4	2	no	—
66	D₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	2	2	no	—
68	C₂×C₈×C₁₉	—	4	1	no	—
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	4	2	no	—
76	C₂²⋊C₄×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
81	#64520	—	2	4	no	—
82	#64520	—	2	4	no	—
83	#64520	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	#9724	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	#124	1	1	yes	characteristic
90	Q₈×C₁₉	—	8	2	no	—
91	D₄×C₁₉	—	4	2	no	—
92	D₄×C₁₉	—	4	2	no	—
93	D₄×C₁₉	—	4	4	no	—
94	D₄×C₁₉	—	8	2	no	—
95	D₄×C₁₉	—	8	4	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	8	4	no	—
102	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	#104	1	2	yes	—
112	C₁₉⋊C₈	—	2	4	no	—
113	C₁₉⋊C₈	—	4	4	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	#3169	D₁₉	1	1	yes	characteristic
116	C₄×#108	—	19	1	no	—
117	#1525	—	19	2	no	—
118	#1484	—	19	2	no	—
119	C₈×M₁₆	—	19	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	—	8	2	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	#390	1	1	yes	characteristic
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	8	2	no	—
131	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
132	C₄×C₁₉	#421	1	1	yes	characteristic
133	C₄×C₁₉	#443	1	2	yes	—
134	C₄×C₁₉	#472	1	2	yes	—
135	#532	C₂×D₁₉	1	2	yes	—
136	#500	Dic₁₉	1	1	yes	characteristic
137	#493	Dic₁₉	1	1	yes	characteristic
138	#486	Dic₁₉	1	2	yes	—
139	#466	—	2	1	no	—
140	#466	—	2	1	no	—
141	C₄×D₈	—	2	1	no	—
142	C₄×D₈	—	2	1	no	—
143	#431	—	19	1	no	—
144	C₂×#108	—	38	1	no	—
145	C₄×M₁₆	—	19	1	no	—
146	C₄×M₁₆	—	19	2	no	—
147	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
148	#341	—	38	1	no	—
149	#329	—	38	4	no	—
150	D₄⋊C₈	—	38	4	no	—
151	#322	—	38	1	no	—
152	C₈²	—	38	1	no	—
153	C₂×C₁₉	—	4	1	no	—
154	C₂×C₁₉	—	16	2	no	—
155	C₂×C₁₉	#1974	1	1	yes	characteristic
156	C₂×C₁₉	#1978	1	1	yes	characteristic
157	C₂×C₁₉	#1980	1	1	yes	characteristic
158	C₂×#41	—	2	2	no	—
159	C₂×D₈	—	2	1	no	—
160	C₂×D₈	—	2	1	no	—
161	C₂×M₁₆	—	38	1	no	—
162	C₂×M₁₆	—	38	2	no	—
163	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
166	#127	C₂×Dic₁₉	1	2	yes	—
167	#124	—	2	2	no	—
168	#121	—	2	2	no	—
169	#121	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	#108	—	38	4	no	—
174	#107	—	2	1	no	—
175	#107	—	2	1	no	—
176	C₄⋊C₈	—	19	2	no	—
177	#102	—	2	2	no	—
178	#102	—	2	2	no	—
179	C₂²⋊C₈	—	38	1	no	—
180	#97	—	19	2	no	—
181	#97	—	38	2	no	—
182	C₄×C₈	—	38	2	no	—
183	C₄×C₈	—	38	1	no	—
184	C₄×C₈	—	38	1	no	—
185	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
186	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
187	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
188	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₁₉	#9724	1	1	yes	characteristic, complemented, Sylow
190	#41	—	8	4	no	—
191	C₂×Q₈	—	2	2	no	—
192	C₂×D₄	—	2	2	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	#64543	1	1	yes	characteristic
198	C₂²×C₄	#64543	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	D₈	—	4	2	no	—
201	D₈	—	4	2	no	—
202	M₁₆	—	38	4	no	—
203	M₁₆	—	38	4	no	—
204	M₁₆	—	76	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	38	2	no	—
208	C₂×C₈	—	38	2	no	—
209	C₂×C₈	—	76	2	no	—
210	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
211	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
212	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
213	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₂²⋊C₄	—	4	2	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₄²	D₄×D₁₉	1	1	yes	characteristic
219	C₄²	D₄×D₁₉	1	1	yes	characteristic
220	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
221	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
222	C₂³	—	4	2	no	—
223	C₂³	#10597382	1	1	yes	characteristic
224	Q₈	—	8	2	no	—
225	D₄	—	4	2	no	—
226	D₄	—	4	2	no	—
227	D₄	—	4	4	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	4	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	4	no	—
236	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
237	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
238	C₂×C₄	#10597384	1	1	yes	characteristic
239	C₂×C₄	#10597384	1	1	yes	characteristic
240	C₂×C₄	#10597386	1	1	yes	characteristic
241	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
242	C₈	—	2	1	no	—
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	38	4	no	—
246	C₈	—	76	4	no	—
247	C₈	—	76	2	no	—
248	C₈	#10597294	1	2	yes	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	8	2	no	—
253	C₂²	—	8	2	no	—
254	C₂²	—	8	2	no	—
255	C₂²	#11926447	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	8	2	no	—
260	C₄	C₂×#10597294	1	1	yes	characteristic
261	C₄	#11926561	1	1	yes	characteristic
262	C₄	#11926661	1	2	yes	—
263	C₄	#11926811	1	2	yes	—
264	C₂	—	4	1	no	—
265	C₂	—	16	2	no	—
266	C₂	#14564524	1	1	yes	characteristic
267	C₂	#14564546	1	1	yes	characteristic
268	C₂	#14564555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597276

C₂

yes

maximal, characteristic, complemented

#14562227

C₂

yes

maximal, complemented

#14562052

C₂

yes

maximal, complemented

C₈×#64520

C₂

yes

maximal, characteristic, complemented

C₁₉×#3169

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

C₂×#10597276

—

C₄×#64520

C₂²

yes

—

C₄×#64520

C₂²

yes

characteristic

#11926309

—

#11926284

—

D₄⋊(C₁₉⋊C₈)

—

#11926266

—

C₈×C₁₉⋊C₈

—

C₁₉×#532

C₂²

yes

—

C₁₉×#500

C₄

yes

characteristic

C₁₉×#493

C₄

yes

characteristic

C₁₉×#486

C₄

yes

—

C₁₉×#466

—

C₁₉×#466

—

C₄×D₈×C₁₉

—

C₄×D₈×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#127

C₂×C₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂×#64520

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#102

—

C₁₉×#102

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9724

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#124

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

104

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

105

C₂×C₄×C₁₉

#121

yes

characteristic

106

C₂×C₄×C₁₉

#121

yes

characteristic

107

C₂×C₄×C₁₉

#127

yes

characteristic

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

#104

yes

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#3169

D₁₉

yes

characteristic

116

C₄×#108

—

117

#1525

—

118

#1484

—

119

C₈×M₁₆

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#390

yes

characteristic

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

C₂×#104

yes

characteristic

132

C₄×C₁₉

#421

yes

characteristic

133

C₄×C₁₉

#443

yes

—

134

C₄×C₁₉

#472

yes

—

135

#532

C₂×D₁₉

yes

—

136

#500

Dic₁₉

yes

characteristic

137

#493

Dic₁₉

yes

characteristic

138

#486

Dic₁₉

yes

—

139

#466

—

140

#466

—

141

C₄×D₈

—

142

C₄×D₈

—

143

#431

—

144

C₂×#108

—

145

C₄×M₁₆

—

146

C₄×M₁₆

—

147

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

148

#341

—

149

#329

—

150

D₄⋊C₈

—

151

#322

—

152

C₈²

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#1974

yes

characteristic

156

C₂×C₁₉

#1978

yes

characteristic

157

C₂×C₁₉

#1980

yes

characteristic

158

C₂×#41

—

159

C₂×D₈

—

160

C₂×D₈

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

164

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

165

C₄⋊Q₈

C₂×Dic₁₉

yes

—

166

#127

C₂×Dic₁₉

yes

—

167

#124

—

168

#121

—

169

#121

—

170

C₄×D₄

—

171

C₄×D₄

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

#108

—

174

#107

—

175

#107

—

176

C₄⋊C₈

—

177

#102

—

178

#102

—

179

C₂²⋊C₈

—

180

#97

—

181

#97

—

182

C₄×C₈

—

183

C₄×C₈

—

184

C₄×C₈

—

185

C₄×C₈

C₂×Dic₁₉

yes

characteristic

186

C₄×C₈

C₂×Dic₁₉

yes

characteristic

187

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

188

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

189

C₁₉

#9724

yes

characteristic, complemented, Sylow

190

#41

—

191

C₂×Q₈

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

#64543

yes

characteristic

198

C₂²×C₄

#64543

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

200

D₈

—

201

D₈

—

202

M₁₆

—

203

M₁₆

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

211

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

212

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

213

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₂²⋊C₄

—

217

C₂²⋊C₄

—

218

C₄²

D₄×D₁₉

yes

characteristic

219

C₄²

D₄×D₁₉

yes

characteristic

220

C₄²

C₂²×Dic₁₉

yes

characteristic

221

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

222

C₂³

—

223

C₂³

#10597382

yes

characteristic

224

Q₈

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

D₄×Dic₁₉

yes

characteristic

237

C₂×C₄

D₄×Dic₁₉

yes

characteristic

238

C₂×C₄

#10597384

yes

characteristic

239

C₂×C₄

#10597384

yes

characteristic

240

C₂×C₄

#10597386

yes

characteristic

241

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

#10597294

yes

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

#11926447

yes

characteristic

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

C₂×#10597294

yes

characteristic

261

C₄

#11926561

yes

characteristic

262

C₄

#11926661

yes

—

263

C₄

#11926811

yes

—

264

C₂

—

265

C₂

—

266

C₂

#14564524

yes

characteristic

267

C₂

#14564546

yes

characteristic

268

C₂

#14564555

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3169	C₂
socle	C₂²×C₁₉	#390
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3169	D₁₉
hypocenter	C₁₉	#9724
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

subgroup

G/H

center

C₂×C₄

#10597384

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#3169

C₂

socle

C₂²×C₁₉

#390

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

N	H ≅ G/N	type
1. C₄×#10597276	C₂	semidirect
2. #14562227	C₂	semidirect
3. #14562052	C₂	semidirect
4. C₈×#64520	C₂	semidirect
189. C₁₉	#9724	semidirect

H ≅ G/N

type

1. C₄×#10597276

C₂

semidirect

2. #14562227

C₂

semidirect

3. #14562052

C₂

semidirect

4. C₈×#64520

C₂

semidirect

189. C₁₉

#9724

semidirect

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

subgroup	index
C₄×#10597276	2
#14562227	2
#14562052	2
C₈×#64520	2
C₁₉×#3169	2
#9724	19

subgroup

index

C₁₉×#3169

Subgroups — #18081730

Conjugacy classes of subgroups

Complements

Maximal subgroups