Group #18070628 — subgroups

Subgroups — #18070628

Order 4864.

630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14563703	C₂	1	2	yes	maximal
2	#14561461	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂³×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#391	—	2	2	no	—
11	C₁₉×#391	C₄	1	2	yes	—
12	C₁₉×#391	C₂²	1	2	yes	—
13	C₂×C₁₉×#95	—	2	2	no	—
14	C₂²×Q₈×C₁₉	—	2	1	no	—
15	C₂²×Q₈×C₁₉	—	2	2	no	—
16	C₂²×Q₈×C₁₉	—	4	2	no	—
17	C₂²×Q₈×C₁₉	—	4	2	no	—
18	C₂²×Q₈×C₁₉	C₈	1	4	yes	complemented
19	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	—	2	1	no	—
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₉	—	4	2	no	—
28	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	4	no	—
32	C₁₉×#95	—	2	4	no	—
33	C₁₉×#95	—	2	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
35	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	2	2	no	—
38	C₂×Q₈×C₁₉	—	4	8	no	—
39	C₂×Q₈×C₁₉	—	4	2	no	—
40	C₂×Q₈×C₁₉	—	4	2	no	—
41	C₂×Q₈×C₁₉	—	4	8	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	—	4	2	no	—
44	C₂×Q₈×C₁₉	C₂×C₈	1	4	yes	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	—	2	4	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	4	2	no	—
53	C₂²×C₄×C₁₉	—	4	2	no	—
54	C₂²×C₄×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	4	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
60	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄²×C₁₉	—	4	1	no	—
66	C₄²×C₁₉	—	4	2	no	—
67	C₄²×C₁₉	—	4	1	no	—
68	C₂×C₁₉⋊C₈	—	4	4	no	—
69	C₂×C₁₉⋊C₈	—	4	4	no	—
70	C₂×C₁₉⋊C₈	—	4	4	no	—
71	#7595	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	—	2	2	no	—
74	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
75	C₂³×C₁₉	#99	1	2	yes	—
76	C₂³×C₁₉	#100	1	2	yes	—
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Q₈×C₁₉	—	4	4	no	—
79	Q₈×C₁₉	—	4	8	no	—
80	Q₈×C₁₉	—	4	4	no	—
81	C₂×C₄×C₁₉	—	2	4	no	—
82	C₂×C₄×C₁₉	—	2	4	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	2	no	—
89	C₂×C₄×C₁₉	—	2	4	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	8	no	—
94	C₂×C₄×C₁₉	—	4	8	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	4	no	—
99	C₂×C₄×C₁₉	—	8	4	no	—
100	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
101	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#137	1	4	yes	—
104	C₁₉⋊C₈	—	8	4	no	—
105	C₂×#391	D₁₉	1	1	yes	characteristic
106	#1817	—	19	2	no	—
107	#1272	—	19	4	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	4	no	—
110	C₂²×C₁₉	—	2	4	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	#323	1	4	yes	—
113	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
115	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
116	C₂²×C₁₉	#419	1	2	yes	—
117	C₂²×C₁₉	#421	1	2	yes	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	2	4	no	—
122	C₄×C₁₉	—	4	4	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	—	8	2	no	—
125	C₂³×Q₈	Dic₁₉	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
127	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
128	C₂×C₂²⋊C₈	—	38	2	no	—
129	#391	—	2	2	no	—
130	#391	Dic₁₉	1	2	yes	—
131	#391	C₂×D₁₉	1	2	yes	—
132	C₂×#95	—	2	2	no	—
133	#336	—	19	4	no	—
134	#336	—	38	2	no	—
135	C₂×C₁₉	—	2	4	no	—
136	C₂×C₁₉	C₂×#323	1	1	yes	characteristic
137	C₂×C₁₉	#1479	1	2	yes	—
138	C₂×C₁₉	#1511	1	2	yes	—
139	C₂×C₁₉	#1533	1	1	yes	characteristic
140	C₂×C₁₉	#1558	1	1	yes	characteristic
141	C₂²×Q₈	—	2	2	no	—
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×Q₈	—	4	2	no	—
144	C₂²×Q₈	—	4	2	no	—
145	C₂²×Q₈	C₁₉⋊C₈	1	4	yes	complemented
146	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
147	C₂³×C₄	—	2	1	no	—
148	C₂³×C₄	—	2	1	no	—
149	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
150	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
151	C₂²×C₈	—	38	4	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	—	4	2	no	—
154	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
155	C₂×C₄²	—	4	2	no	—
156	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
158	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
159	C₂²⋊C₈	—	76	4	no	—
160	#95	—	2	4	no	—
161	#95	—	2	4	no	—
162	C₁₉	#7595	1	1	yes	characteristic, complemented, Sylow
163	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
164	C₂×Q₈	—	2	4	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	2	no	—
168	C₂×Q₈	—	4	8	no	—
169	C₂×Q₈	—	4	8	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	C₂×C₁₉⋊C₈	1	4	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	4	no	—
177	C₂²×C₄	—	2	4	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	4	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
186	C₂²×C₄	#64520	1	2	yes	—
187	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
188	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₈	—	76	4	no	—
192	C₂×C₈	—	76	4	no	—
193	C₂×C₈	—	76	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄²	—	4	1	no	—
197	C₄²	—	4	2	no	—
198	C₄²	—	4	1	no	—
199	C₂³	—	2	2	no	—
200	C₂³	—	2	2	no	—
201	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
202	C₂³	#10597290	1	2	yes	—
203	C₂³	#10597291	1	2	yes	—
204	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
205	Q₈	—	4	4	no	—
206	Q₈	—	4	8	no	—
207	Q₈	—	4	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	8	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	8	no	—
224	C₂×C₄	—	4	4	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	8	4	no	—
227	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
228	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
229	C₂×C₄	C₂×#64520	1	1	yes	characteristic
230	C₂×C₄	#10597388	1	4	yes	—
231	C₈	—	152	4	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	4	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	4	no	—
236	C₂²	#11926268	1	4	yes	—
237	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
238	C₂²	C₂×#10597291	1	1	yes	characteristic
239	C₂²	C₂×#10597290	1	1	yes	characteristic
240	C₂²	#11926553	1	2	yes	—
241	C₂²	#11926561	1	2	yes	—
242	C₄	—	2	4	no	—
243	C₄	—	2	2	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	4	2	no	—
247	C₄	—	4	4	no	—
248	C₄	—	8	2	no	—
249	C₂	—	2	4	no	—
250	C₂	C₂×#11926268	1	1	yes	characteristic
251	C₂	#14562030	1	2	yes	—
252	C₂	#14562168	1	2	yes	—
253	C₂	#14562259	1	1	yes	characteristic
254	C₂	#14562361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal

#14561461

C₂

yes

maximal, complemented

C₂×C₁₉×#391

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926299

—

#11926299

C₂²

yes

—

C₂³×Q₈×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#391

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₂×C₁₉×#95

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₈

yes

complemented

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

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

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7595

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

—

C₂³×C₁₉

#99

yes

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

101

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

102

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

103

C₂×C₄×C₁₉

#137

yes

—

104

C₁₉⋊C₈

—

105

C₂×#391

D₁₉

yes

characteristic

106

#1817

—

107

#1272

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

#323

yes

—

113

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

114

C₂²×C₁₉

C₂×#99

yes

characteristic

115

C₂²×C₁₉

C₂×#100

yes

characteristic

116

C₂²×C₁₉

#419

yes

—

117

C₂²×C₁₉

#421

yes

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₂³×Q₈

Dic₁₉

yes

characteristic

126

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

127

C₂²×C₄²

C₂×D₁₉

yes

characteristic

128

C₂×C₂²⋊C₈

—

129

#391

—

130

#391

Dic₁₉

yes

—

131

#391

C₂×D₁₉

yes

—

132

C₂×#95

—

133

#336

—

134

#336

—

135

C₂×C₁₉

—

136

C₂×C₁₉

C₂×#323

yes

characteristic

137

C₂×C₁₉

#1479

yes

—

138

C₂×C₁₉

#1511

yes

—

139

C₂×C₁₉

#1533

yes

characteristic

140

C₂×C₁₉

#1558

yes

characteristic

141

C₂²×Q₈

—

142

C₂²×Q₈

—

143

C₂²×Q₈

—

144

C₂²×Q₈

—

145

C₂²×Q₈

C₁₉⋊C₈

yes

complemented

146

C₂²×Q₈

C₂×Dic₁₉

yes

—

147

C₂³×C₄

—

148

C₂³×C₄

—

149

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

150

C₂³×C₄

C₂²⋊D₁₉

yes

—

151

C₂²×C₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

157

C₂×C₄²

C₂²⋊D₁₉

yes

—

158

C₂×C₄²

C₂²×D₁₉

yes

characteristic

159

C₂²⋊C₈

—

160

#95

—

161

#95

—

162

C₁₉

#7595

yes

characteristic, complemented, Sylow

163

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

C₂×C₁₉⋊C₈

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂×C₁₉⋊C₈

yes

—

186

C₂²×C₄

#64520

yes

—

187

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

188

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

189

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

—

199

C₂³

—

200

C₂³

—

201

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

—

202

C₂³

#10597290

yes

—

203

C₂³

#10597291

yes

—

204

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

228

C₂×C₄

C₂²×C₁₉⋊C₈

yes

characteristic

229

C₂×C₄

C₂×#64520

yes

characteristic

230

C₂×C₄

#10597388

yes

—

231

C₈

—

152

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

#11926268

yes

—

237

C₂²

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

238

C₂²

C₂×#10597291

yes

characteristic

239

C₂²

C₂×#10597290

yes

characteristic

240

C₂²

#11926553

yes

—

241

C₂²

#11926561

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₂

—

250

C₂

C₂×#11926268

yes

characteristic

251

C₂

#14562030

yes

—

252

C₂

#14562168

yes

—

253

C₂

#14562259

yes

characteristic

254

C₂

#14562361

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#391	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#391	D₁₉
hypocenter	C₁₉	#7595
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#391

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

N	H ≅ G/N	type
2. #14561461	C₂	semidirect
18. C₂²×Q₈×C₁₉	C₈	semidirect
145. C₂²×Q₈	C₁₉⋊C₈	semidirect
162. C₁₉	#7595	semidirect

H ≅ G/N

type

2. #14561461

C₂

semidirect

18. C₂²×Q₈×C₁₉

C₈

semidirect

145. C₂²×Q₈

C₁₉⋊C₈

semidirect

162. C₁₉

#7595

semidirect

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

subgroup	index
#14563703	2
#14561461	2
C₂×C₁₉×#391	2
#7595	19

subgroup

index

#14563703

#14561461

C₂×C₁₉×#391

#7595

Subgroups — #18070628

Conjugacy classes of subgroups

Complements

Maximal subgroups