Group #18075386 — subgroups

Subgroups — #18075386

Order 4864.

478 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂×#11926595	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	2	yes	maximal
3	C₂×#11926294	C₂	1	2	yes	maximal, complemented
4	#14561470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
7	#11926595	—	2	4	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×Dic₁₉⋊C₈	C₄	1	2	yes	—
10	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
11	C₂×(C₂×D₁₉)⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926298	—	2	2	no	—
14	#11926294	—	2	4	no	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
28	C₄²×D₁₉	—	2	2	no	—
29	C₄²×D₁₉	—	2	2	no	—
30	C₁₉×C₄⋊C₈	—	2	2	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₄×C₈×C₁₉	—	2	2	no	—
33	(C₂×D₁₉)⋊C₈	—	2	4	no	—
34	(C₂×D₁₉)⋊C₈	—	4	4	no	—
35	Dic₁₉⋊C₈	—	2	4	no	—
36	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
39	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
43	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₁₉	—	2	2	no	—
47	C₂×C₄×D₁₉	—	2	1	no	—
48	C₂×C₄×D₁₉	—	2	1	no	—
49	C₂×C₄×D₁₉	—	2	1	no	—
50	C₂×C₄×D₁₉	—	2	1	no	—
51	C₂×C₄×D₁₉	—	2	2	no	—
52	C₂×C₄×D₁₉	—	2	2	no	—
53	C₂×C₄×D₁₉	—	2	2	no	—
54	C₂×C₄×D₁₉	—	4	2	no	—
55	C₂×C₄×D₁₉	SD₁₆	1	4	yes	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	2	2	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₄×Dic₁₉	—	2	1	no	—
65	C₄×Dic₁₉	—	2	1	no	—
66	C₄×Dic₁₉	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	2	2	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
74	#8598	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×D₁₉	—	2	1	no	—
77	C₂²×D₁₉	—	2	2	no	—
78	C₂²×D₁₉	—	2	1	no	—
79	C₂²×D₁₉	—	2	2	no	—
80	C₂²×D₁₉	#106	1	2	yes	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₁₉	#131	1	2	yes	—
87	C₂×C₄×C₁₉	#131	1	2	yes	—
88	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
89	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
91	C₂×Dic₁₉	—	2	1	no	—
92	C₂×Dic₁₉	—	2	1	no	—
93	C₂×Dic₁₉	—	2	1	no	—
94	C₂×Dic₁₉	—	2	1	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	C₂×Dic₁₉	#106	1	2	yes	—
98	C₄×D₁₉	—	2	4	no	—
99	C₄×D₁₉	—	2	4	no	—
100	C₄×D₁₉	—	4	4	no	—
101	C₄×D₁₉	—	4	2	no	—
102	C₄×D₁₉	—	4	1	no	—
103	C₄×D₁₉	—	4	1	no	—
104	C₈×C₁₉	—	4	2	no	—
105	C₈×C₁₉	—	8	2	no	—
106	C₁₉⋊C₈	—	2	4	no	—
107	C₁₉⋊C₈	—	8	2	no	—
108	C₂×#431	—	19	1	no	—
109	#1797	—	19	2	no	—
110	C₂×#334	—	19	2	no	—
111	#1277	—	19	1	no	—
112	#1277	D₁₉	1	1	yes	characteristic, complemented
113	C₂²×C₁₉	#380	1	1	yes	characteristic
114	C₂²×C₁₉	#424	1	2	yes	—
115	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
116	C₂²×C₁₉	#427	1	1	yes	characteristic
117	C₂²×C₁₉	#430	1	2	yes	—
118	C₂×D₁₉	—	2	2	no	—
119	C₂×D₁₉	—	2	4	no	—
120	C₂×D₁₉	—	4	1	no	—
121	C₂×D₁₉	—	4	1	no	—
122	C₂×D₁₉	—	4	2	no	—
123	C₄×C₁₉	—	2	2	no	—
124	C₄×C₁₉	#408	1	2	yes	—
125	C₄×C₁₉	#433	1	1	yes	characteristic
126	C₄×C₁₉	#433	1	1	yes	characteristic
127	C₄×C₁₉	#465	1	2	yes	—
128	C₄×C₁₉	#465	1	2	yes	—
129	Dic₁₉	—	2	2	no	—
130	Dic₁₉	—	4	1	no	—
131	Dic₁₉	—	4	1	no	—
132	C₂²×C₄²	—	19	1	no	—
133	#431	—	38	4	no	—
134	C₂×C₄⋊C₈	—	19	2	no	—
135	C₂×C₄⋊C₈	—	19	2	no	—
136	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
137	C₂×C₂²⋊C₈	—	19	2	no	—
138	C₂×C₂²⋊C₈	—	38	2	no	—
139	C₂×C₄×C₈	—	19	1	no	—
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#336	—	38	2	no	—
142	#334	—	38	4	no	—
143	C₂×C₁₉	#1570	1	2	yes	—
144	C₂×C₁₉	#1572	1	2	yes	—
145	C₂×C₁₉	#1798	1	1	yes	characteristic
146	C₂×C₁₉	#1807	1	1	yes	characteristic
147	C₂×C₁₉	#1811	1	1	yes	characteristic
148	D₁₉	—	4	2	no	—
149	C₂³×C₄	—	19	1	no	—
150	C₂³×C₄	—	19	1	no	—
151	C₂³×C₄	—	19	1	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	—	19	2	no	—
154	C₂²×C₈	—	38	2	no	—
155	C₂²×C₈	C₄×D₁₉	1	2	yes	—
156	C₂×C₄²	—	19	1	no	—
157	C₂×C₄²	—	19	1	no	—
158	C₂×C₄²	—	19	1	no	—
159	C₂×C₄²	—	38	2	no	—
160	C₂×C₄²	—	38	2	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	38	4	no	—
165	C₄⋊C₈	—	38	2	no	—
166	C₄⋊C₈	—	38	2	no	—
167	C₂²⋊C₈	—	38	4	no	—
168	C₂²⋊C₈	—	76	4	no	—
169	C₄×C₈	—	2	2	no	—
170	C₄×C₈	—	19	4	no	—
171	C₁₉	#8598	1	1	yes	characteristic, complemented, Sylow
172	C₂⁴	—	19	1	no	—
173	C₂²×C₄	—	19	1	no	—
174	C₂²×C₄	—	19	4	no	—
175	C₂²×C₄	—	19	1	no	—
176	C₂²×C₄	—	19	1	no	—
177	C₂²×C₄	—	38	2	no	—
178	C₂²×C₄	—	38	1	no	—
179	C₂²×C₄	—	38	1	no	—
180	C₂²×C₄	—	38	1	no	—
181	C₂²×C₄	—	38	1	no	—
182	C₂²×C₄	—	38	2	no	—
183	C₂²×C₄	—	38	2	no	—
184	C₂²×C₄	—	38	2	no	—
185	C₂²×C₄	—	76	2	no	—
186	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
187	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
188	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	19	4	no	—
196	C₂×C₈	—	38	2	no	—
197	C₂×C₈	—	38	2	no	—
198	C₂×C₈	—	76	2	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	—	76	2	no	—
201	C₄²	—	38	1	no	—
202	C₄²	—	38	1	no	—
203	C₄²	—	38	2	no	—
204	C₄²	—	38	2	no	—
205	C₄²	#64541	1	2	yes	—
206	C₄²	D₄×D₁₉	1	2	yes	—
207	C₂³	—	19	2	no	—
208	C₂³	—	38	2	no	—
209	C₂³	—	38	1	no	—
210	C₂³	—	38	2	no	—
211	C₂³	—	38	1	no	—
212	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	19	2	no	—
215	C₂×C₄	—	38	1	no	—
216	C₂×C₄	—	38	1	no	—
217	C₂×C₄	—	38	4	no	—
218	C₂×C₄	—	38	4	no	—
219	C₂×C₄	—	38	2	no	—
220	C₂×C₄	—	38	2	no	—
221	C₂×C₄	—	38	1	no	—
222	C₂×C₄	—	38	1	no	—
223	C₂×C₄	—	76	4	no	—
224	C₂×C₄	—	76	1	no	—
225	C₂×C₄	—	76	1	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	#10597318	1	1	yes	characteristic
228	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
229	C₂×C₄	#10597330	1	2	yes	—
230	C₂×C₄	#10597342	1	2	yes	—
231	C₂×C₄	#10597347	1	2	yes	—
232	C₂×C₄	#10597353	1	2	yes	—
233	C₂×C₄	#10597358	1	1	yes	characteristic
234	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
235	C₂×C₄	#10597365	1	1	yes	characteristic
236	C₈	—	4	2	no	—
237	C₈	—	8	2	no	—
238	C₈	—	38	4	no	—
239	C₈	—	152	2	no	—
240	C₂²	—	38	2	no	—
241	C₂²	—	38	4	no	—
242	C₂²	—	76	1	no	—
243	C₂²	—	76	1	no	—
244	C₂²	—	76	2	no	—
245	C₂²	#11926403	1	1	yes	characteristic
246	C₂²	#11926569	1	2	yes	—
247	C₂²	#106×D₁₉	1	1	yes	characteristic
248	C₂²	#11926581	1	1	yes	characteristic
249	C₂²	#11926591	1	2	yes	—
250	C₄	—	2	2	no	—
251	C₄	—	38	2	no	—
252	C₄	—	76	1	no	—
253	C₄	—	76	1	no	—
254	C₄	#11926509	1	2	yes	—
255	C₄	#11926603	1	1	yes	characteristic
256	C₄	#11926606	1	1	yes	characteristic
257	C₄	#11926772	1	2	yes	—
258	C₄	#11926776	1	2	yes	—
259	C₂	—	76	2	no	—
260	C₂	#14562404	1	2	yes	—
261	C₂	#14562414	1	2	yes	—
262	C₂	#14563618	1	1	yes	characteristic
263	C₂	#14563659	1	1	yes	characteristic
264	C₂	#14563676	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926595

C₂

yes

maximal, characteristic

#14563612

C₂

yes

maximal

C₂×#11926294

C₂

yes

maximal, complemented

#14561470

C₂

yes

maximal, characteristic, complemented

C₁₉×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₁₉

C₂²

yes

characteristic

#11926595

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Dic₁₉⋊C₈

C₄

yes

—

C₂×(C₂×D₁₉)⋊C₈

—

C₂×(C₂×D₁₉)⋊C₈

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926298

—

#11926294

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×D₁₉

D₄

yes

characteristic

C₂²×C₄×D₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₄²×D₁₉

—

C₄²×D₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂³×D₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

#8598

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

#106

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#106

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

100

C₄×D₁₉

—

101

C₄×D₁₉

—

102

C₄×D₁₉

—

103

C₄×D₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₁₉⋊C₈

—

107

C₁₉⋊C₈

—

108

C₂×#431

—

109

#1797

—

110

C₂×#334

—

111

#1277

—

112

#1277

D₁₉

yes

characteristic, complemented

113

C₂²×C₁₉

#380

yes

characteristic

114

C₂²×C₁₉

#424

yes

—

115

C₂²×C₁₉

C₂×#106

yes

characteristic

116

C₂²×C₁₉

#427

yes

characteristic

117

C₂²×C₁₉

#430

yes

—

118

C₂×D₁₉

—

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

#408

yes

—

125

C₄×C₁₉

#433

yes

characteristic

126

C₄×C₁₉

#433

yes

characteristic

127

C₄×C₁₉

#465

yes

—

128

C₄×C₁₉

#465

yes

—

129

Dic₁₉

—

130

Dic₁₉

—

131

Dic₁₉

—

132

C₂²×C₄²

—

133

#431

—

134

C₂×C₄⋊C₈

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

137

C₂×C₂²⋊C₈

—

138

C₂×C₂²⋊C₈

—

139

C₂×C₄×C₈

—

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#336

—

142

#334

—

143

C₂×C₁₉

#1570

yes

—

144

C₂×C₁₉

#1572

yes

—

145

C₂×C₁₉

#1798

yes

characteristic

146

C₂×C₁₉

#1807

yes

characteristic

147

C₂×C₁₉

#1811

yes

characteristic

148

D₁₉

—

149

C₂³×C₄

—

150

C₂³×C₄

—

151

C₂³×C₄

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

C₄×D₁₉

yes

—

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₁₉

#8598

yes

characteristic, complemented, Sylow

172

C₂⁴

—

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

—

186

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

187

C₂²×C₄

D₄×D₁₉

yes

characteristic

188

C₂²×C₄

Q₈×D₁₉

yes

characteristic

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

#64541

yes

—

206

C₄²

D₄×D₁₉

yes

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₄⋊C₄×D₁₉

yes

characteristic

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

#10597318

yes

characteristic

228

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

229

C₂×C₄

#10597330

yes

—

230

C₂×C₄

#10597342

yes

—

231

C₂×C₄

#10597347

yes

—

232

C₂×C₄

#10597353

yes

—

233

C₂×C₄

#10597358

yes

characteristic

234

C₂×C₄

SD₁₆×D₁₉

yes

—

235

C₂×C₄

#10597365

yes

characteristic

236

C₈

—

237

C₈

—

238

C₈

—

239

C₈

—

152

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926403

yes

characteristic

246

C₂²

#11926569

yes

—

247

C₂²

#106×D₁₉

yes

characteristic

248

C₂²

#11926581

yes

characteristic

249

C₂²

#11926591

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

#11926509

yes

—

255

C₄

#11926603

yes

characteristic

256

C₄

#11926606

yes

characteristic

257

C₄

#11926772

yes

—

258

C₄

#11926776

yes

—

259

C₂

—

260

C₂

#14562404

yes

—

261

C₂

#14562414

yes

—

262

C₂

#14563618

yes

characteristic

263

C₂

#14563659

yes

characteristic

264

C₂

#14563676

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1277	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1277	D₁₉
hypocenter	C₁₉	#8598
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1277

C₂

socle

C₂³×C₁₉

C₂×C₄⋊C₄

prime radical

C₂³×D₁₉

C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
3. C₂×#11926294	C₂	semidirect
4. #14561470	C₂	semidirect
5. C₁₉×#1277	C₂	semidirect
112. #1277	D₁₉	semidirect
171. C₁₉	#8598	semidirect

H ≅ G/N

type

3. C₂×#11926294

C₂

semidirect

4. #14561470

C₂

semidirect

5. C₁₉×#1277

C₂

semidirect

112. #1277

D₁₉

semidirect

171. C₁₉

#8598

semidirect

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

subgroup	index
C₂×#11926595	2
#14563612	2
C₂×#11926294	2
#14561470	2
C₁₉×#1277	2
#8598	19

subgroup

index

C₁₉×#1277

Subgroups — #18075386

Conjugacy classes of subgroups

Complements

Maximal subgroups