Group #18075454 — subgroups

Subgroups — #18075454

Order 4864.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563673	C₂	1	2	yes	maximal, complemented
2	#14561973	C₂	1	2	yes	maximal
3	#14561512	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597276	—	2	2	no	—
6	#11926508	C₂²	1	4	yes	—
7	#11926309	—	2	2	no	—
8	#11926270	—	2	2	no	—
9	#11926268	—	2	2	no	—
10	C₂²×M₁₆×C₁₉	C₄	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#435	—	2	2	no	—
14	C₁₉×#435	—	2	2	no	—
15	C₂×C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
17	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
19	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂×M₁₆×C₁₉	—	4	2	no	—
25	C₂²×C₈×C₁₉	—	4	2	no	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	D₄	1	2	yes	—
31	C₂²×C₈×C₁₉	D₄	1	2	yes	—
32	C₄×D₄×C₁₉	—	2	2	no	—
33	C₄×D₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×#64520	—	2	4	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	—	2	2	no	—
41	C₁₉×C₂²⋊C₈	—	2	2	no	—
42	C₁₉×#97	—	2	1	no	—
43	C₁₉×#97	—	2	1	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
46	#10597276	—	4	4	no	—
47	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
49	C₂×D₄×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	4	2	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂²×C₄×C₁₉	#41	1	2	yes	—
64	M₁₆×C₁₉	—	4	2	no	—
65	M₁₆×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	—	2	4	no	—
68	C₂×C₈×C₁₉	—	2	1	no	—
69	C₂×C₈×C₁₉	—	2	1	no	—
70	C₂×C₈×C₁₉	—	4	1	no	—
71	C₂×C₈×C₁₉	—	4	2	no	—
72	C₂×C₈×C₁₉	—	4	1	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	—	2	1	no	—
82	#64520	—	4	4	no	—
83	#64520	—	4	4	no	—
84	C₂×C₁₉⋊C₈	—	4	4	no	—
85	#8613	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	—	2	1	no	—
88	C₂³×C₁₉	—	2	2	no	—
89	C₂³×C₁₉	—	4	1	no	—
90	C₂³×C₁₉	—	4	1	no	—
91	C₂³×C₁₉	—	4	1	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
95	D₄×C₁₉	—	4	4	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	1	no	—
109	C₂×C₄×C₁₉	—	4	1	no	—
110	C₂×C₄×C₁₉	—	4	1	no	—
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	2	yes	—
114	C₈×C₁₉	—	2	2	no	—
115	C₈×C₁₉	—	2	1	no	—
116	C₈×C₁₉	—	4	1	no	—
117	C₈×C₁₉	—	4	1	no	—
118	C₈×C₁₉	#99	1	2	yes	—
119	C₁₉⋊C₈	—	8	4	no	—
120	C₂×#435	D₁₉	1	1	yes	characteristic
121	#1810	—	19	2	no	—
122	#1465	—	19	2	no	—
123	#1293	—	19	2	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	2	2	no	—
128	C₂²×C₁₉	—	2	2	no	—
129	C₂²×C₁₉	—	4	4	no	—
130	C₂²×C₁₉	—	4	1	no	—
131	C₂²×C₁₉	—	4	1	no	—
132	C₂²×C₁₉	—	4	1	no	—
133	C₂²×C₁₉	—	8	2	no	—
134	C₂²×C₁₉	#380	1	1	yes	characteristic
135	C₂²×C₁₉	#430	1	2	yes	—
136	C₄×C₁₉	—	2	2	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	4	1	no	—
139	C₄×C₁₉	—	4	1	no	—
140	C₄×C₁₉	—	4	1	no	—
141	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
142	C₄×C₁₉	#410	1	1	yes	characteristic
143	C₂²×M₁₆	Dic₁₉	1	1	yes	characteristic
144	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
146	#435	—	2	2	no	—
147	#435	—	2	2	no	—
148	C₂×#108	—	38	2	no	—
149	C₂×C₄⋊C₈	Dic₁₉	1	1	yes	characteristic
150	#407	—	19	4	no	—
151	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
152	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
153	C₂×#97	Dic₁₉	1	1	yes	characteristic
154	#341	—	38	2	no	—
155	#324	—	38	2	no	—
156	#323	—	38	2	no	—
157	C₂×C₁₉	—	2	2	no	—
158	C₂×C₁₉	—	4	2	no	—
159	C₂×C₁₉	—	8	1	no	—
160	C₂×C₁₉	#1799	1	1	yes	characteristic
161	C₂×C₁₉	#1811	1	1	yes	characteristic
162	C₂×C₁₉	#1813	1	1	yes	characteristic
163	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
164	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
166	C₂×M₁₆	—	2	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	—	4	2	no	—
169	C₂×M₁₆	—	38	4	no	—
170	C₂²×C₈	—	4	2	no	—
171	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
172	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
173	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
174	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
175	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
176	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
177	C₄×D₄	—	2	2	no	—
178	C₄×D₄	—	2	2	no	—
179	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
180	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
181	C₂×C₂²⋊C₄	D₇₆	1	1	yes	characteristic
182	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
183	#108	—	76	4	no	—
184	C₄⋊C₈	—	2	2	no	—
185	C₂²⋊C₈	—	2	2	no	—
186	C₂²⋊C₈	—	2	2	no	—
187	C₂²⋊C₈	—	38	4	no	—
188	C₂²⋊C₈	—	38	4	no	—
189	#97	—	2	1	no	—
190	#97	—	2	1	no	—
191	C₁₉	#8613	1	1	yes	characteristic, complemented, Sylow
192	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
193	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	—	4	1	no	—
202	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
206	C₂²×C₄	#64541	1	2	yes	—
207	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
208	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
209	M₁₆	—	4	2	no	—
210	M₁₆	—	4	2	no	—
211	M₁₆	—	76	4	no	—
212	M₁₆	—	76	4	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	2	1	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	4	1	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	—	4	1	no	—
220	C₂×C₈	—	4	1	no	—
221	C₂×C₈	—	76	4	no	—
222	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
223	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
224	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
225	C₄⋊C₄	—	2	2	no	—
226	C₂²⋊C₄	—	2	2	no	—
227	C₂²⋊C₄	—	2	2	no	—
228	C₄²	—	2	1	no	—
229	C₄²	—	2	1	no	—
230	C₂³	—	2	2	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	2	2	no	—
233	C₂³	—	4	1	no	—
234	C₂³	—	4	1	no	—
235	C₂³	—	4	1	no	—
236	C₂³	—	4	1	no	—
237	C₂³	#10597370	1	2	yes	—
238	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
239	D₄	—	4	4	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	2	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	4	1	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	#10597372	1	1	yes	characteristic
256	C₂×C₄	#10597376	1	2	yes	—
257	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
258	C₈	—	2	1	no	—
259	C₈	—	2	2	no	—
260	C₈	—	4	1	no	—
261	C₈	—	4	1	no	—
262	C₈	—	152	4	no	—
263	C₈	#10597291	1	2	yes	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	4	4	no	—
270	C₂²	—	4	1	no	—
271	C₂²	—	4	1	no	—
272	C₂²	—	4	1	no	—
273	C₂²	—	8	2	no	—
274	C₂²	#11926404	1	1	yes	characteristic
275	C₂²	#11926593	1	2	yes	—
276	C₄	—	2	2	no	—
277	C₄	—	2	1	no	—
278	C₄	—	4	1	no	—
279	C₄	—	4	1	no	—
280	C₄	—	4	1	no	—
281	C₄	C₂×#10597291	1	1	yes	characteristic
282	C₄	#11926518	1	1	yes	characteristic
283	C₂	—	2	2	no	—
284	C₂	—	4	2	no	—
285	C₂	—	8	1	no	—
286	C₂	#14563623	1	1	yes	characteristic
287	C₂	#14563677	1	1	yes	characteristic
288	C₂	#14563685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563673

C₂

yes

maximal, complemented

#14561973

C₂

yes

maximal

#14561512

C₂

yes

maximal, complemented

C₂×C₁₉×#435

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926508

C₂²

yes

—

#11926309

—

#11926270

—

#11926268

—

C₂²×M₁₆×C₁₉

C₄

yes

characteristic

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#435

—

C₁₉×#435

—

C₂×C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₄

yes

characteristic

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂×Q₈

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#8613

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂³×C₁₉

C₂²⋊Q₈

yes

—

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

—

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

—

111

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

112

C₂×C₄×C₁₉

#117

yes

characteristic

113

C₂×C₄×C₁₉

#121

yes

—

114

C₈×C₁₉

—

115

C₈×C₁₉

—

116

C₈×C₁₉

—

117

C₈×C₁₉

—

118

C₈×C₁₉

#99

yes

—

119

C₁₉⋊C₈

—

120

C₂×#435

D₁₉

yes

characteristic

121

#1810

—

122

#1465

—

123

#1293

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

#380

yes

characteristic

135

C₂²×C₁₉

#430

yes

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

C₂×#99

yes

characteristic

142

C₄×C₁₉

#410

yes

characteristic

143

C₂²×M₁₆

Dic₁₉

yes

characteristic

144

C₂³×C₈

C₂×D₁₉

yes

characteristic

145

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

146

#435

—

147

#435

—

148

C₂×#108

—

149

C₂×C₄⋊C₈

Dic₁₉

yes

characteristic

150

#407

—

151

C₂×C₂²⋊C₈

Dic₁₉

yes

characteristic

152

C₂×C₂²⋊C₈

C₂×D₁₉

yes

characteristic

153

C₂×#97

Dic₁₉

yes

characteristic

154

#341

—

155

#324

—

156

#323

—

157

C₂×C₁₉

—

158

C₂×C₁₉

—

159

C₂×C₁₉

—

160

C₂×C₁₉

#1799

yes

characteristic

161

C₂×C₁₉

#1811

yes

characteristic

162

C₂×C₁₉

#1813

yes

characteristic

163

C₂²×D₄

Dic₃₈

yes

characteristic

164

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

165

C₂³×C₄

C₂²×D₁₉

yes

characteristic

166

C₂×M₁₆

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

170

C₂²×C₈

—

171

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

172

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

173

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

174

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

175

C₂²×C₈

C₂²⋊D₁₉

yes

—

176

C₂²×C₈

C₂²⋊D₁₉

yes

—

177

C₄×D₄

—

178

C₄×D₄

—

179

C₂×C₄⋊C₄

D₇₆

yes

characteristic

180

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

181

C₂×C₂²⋊C₄

D₇₆

yes

characteristic

182

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

183

#108

—

184

C₄⋊C₈

—

185

C₂²⋊C₈

—

186

C₂²⋊C₈

—

187

C₂²⋊C₈

—

188

C₂²⋊C₈

—

189

#97

—

190

#97

—

191

C₁₉

#8613

yes

characteristic, complemented, Sylow

192

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

193

C₂⁴

C₂×Dic₃₈

yes

characteristic

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

203

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

204

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

205

C₂²×C₄

C₂×D₇₆

yes

characteristic

206

C₂²×C₄

#64541

yes

—

207

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

208

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

209

M₁₆

—

210

M₁₆

—

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

223

C₂×C₈

C₂²⋊Dic₁₉

yes

—

224

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

225

C₄⋊C₄

—

226

C₂²⋊C₄

—

227

C₂²⋊C₄

—

228

C₄²

—

229

C₄²

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

#10597370

yes

—

238

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

239

D₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

#10597372

yes

characteristic

256

C₂×C₄

#10597376

yes

—

257

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

258

C₈

—

259

C₈

—

260

C₈

—

261

C₈

—

262

C₈

—

152

—

263

C₈

#10597291

yes

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

#11926404

yes

characteristic

275

C₂²

#11926593

yes

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

C₂×#10597291

yes

characteristic

282

C₄

#11926518

yes

characteristic

283

C₂

—

284

C₂

—

285

C₂

—

286

C₂

#14563623

yes

characteristic

287

C₂

#14563677

yes

characteristic

288

C₂

#14563685

yes

characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#435	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#435	D₁₉
hypocenter	C₁₉	#8613
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#435

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#435

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₄×C₁₉

Q₈

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#435

N	H ≅ G/N	type
1. #14563673	C₂	semidirect
3. #14561512	C₂	semidirect
191. C₁₉	#8613	semidirect

H ≅ G/N

type

1. #14563673

C₂

semidirect

3. #14561512

C₂

semidirect

191. C₁₉

#8613

semidirect

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

subgroup	index
#14563673	2
#14561973	2
#14561512	2
C₂×C₁₉×#435	2
#8613	19

subgroup

index

C₂×C₁₉×#435

Subgroups — #18075454

Conjugacy classes of subgroups

Complements

Maximal subgroups