Group #18076551 — subgroups

Subgroups — #18076551

Order 4864.

460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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	#14572664	C₂	1	1	yes	maximal, characteristic
2	#14563933	C₂	1	1	yes	maximal, characteristic
3	#14563842	C₂	1	2	yes	maximal, complemented
4	#14561523	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	1	yes	characteristic
7	#11926616	—	2	2	no	—
8	#11926616	—	2	2	no	—
9	#11926601	—	2	1	no	—
10	C₂×#10597276	—	2	2	no	—
11	#11926508	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#11926309	—	2	2	no	—
16	#11926299	—	2	1	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₁₉×#324	C₄	1	2	yes	—
20	C₁₉×#323	C₄	1	2	yes	—
21	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×#64520	—	2	2	no	—
32	C₂×#64520	—	4	2	no	—
33	C₂×#64520	D₄	1	2	yes	—
34	C₂×#64520	D₄	1	2	yes	—
35	C₂²×C₁₉⋊C₈	—	2	1	no	—
36	C₂²×C₁₉⋊C₈	—	2	1	no	—
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	1	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
46	#10597276	—	4	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	#10597260	—	2	2	no	—
50	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	—	4	1	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₉	#41	1	2	yes	—
68	C₂×C₈×C₁₉	—	2	4	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	1	no	—
75	C₄²×C₁₉	—	2	1	no	—
76	#64520	—	2	4	no	—
77	#64520	—	4	2	no	—
78	#64520	—	4	2	no	—
79	#64520	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	C₂×C₁₉⋊C₈	—	4	1	no	—
86	C₂×C₁₉⋊C₈	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	4	1	no	—
88	C₂×C₁₉⋊C₈	—	8	1	no	—
89	C₂×C₁₉⋊C₈	—	8	1	no	—
90	#8859	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	—	2	1	no	—
92	C₂³×C₁₉	—	2	1	no	—
93	C₂³×C₁₉	—	2	1	no	—
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	4	1	no	—
96	C₂³×C₁₉	—	4	1	no	—
97	C₂³×C₁₉	—	4	1	no	—
98	C₂³×C₁₉	—	4	1	no	—
99	C₂³×C₁₉	#108	1	2	yes	complemented
100	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
102	D₄×C₁₉	—	4	4	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	2	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	4	1	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	—	4	1	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	8	1	no	—
119	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
120	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
121	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
122	C₈×C₁₉	—	4	4	no	—
123	C₁₉⋊C₈	—	4	2	no	—
124	C₁₉⋊C₈	—	4	2	no	—
125	C₁₉⋊C₈	—	4	2	no	—
126	C₁₉⋊C₈	—	8	1	no	—
127	#2973	—	19	1	no	—
128	#1870	—	19	1	no	—
129	#1855	—	19	2	no	—
130	#1459	D₁₉	1	1	yes	characteristic
131	#1298	—	19	2	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	2	1	no	—
134	C₂²×C₁₉	—	2	2	no	—
135	C₂²×C₁₉	—	2	2	no	—
136	C₂²×C₁₉	—	2	2	no	—
137	C₂²×C₁₉	—	2	2	no	—
138	C₂²×C₁₉	—	4	2	no	—
139	C₂²×C₁₉	—	4	1	no	—
140	C₂²×C₁₉	—	4	1	no	—
141	C₂²×C₁₉	—	8	1	no	—
142	C₂²×C₁₉	—	8	1	no	—
143	C₂²×C₁₉	—	8	1	no	—
144	C₂²×C₁₉	#385	1	1	yes	characteristic
145	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
146	C₂²×C₁₉	#430	1	1	yes	characteristic
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	4	1	no	—
150	C₄×C₁₉	—	4	1	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
153	C₄×C₁₉	#458	1	1	yes	characteristic
154	C₂²×M₁₆	—	19	1	no	—
155	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
156	#435	—	38	2	no	—
157	#435	—	38	2	no	—
158	#432	—	38	1	no	—
159	C₂×#108	—	38	2	no	—
160	#407	—	19	2	no	—
161	C₂×C₂²⋊C₈	—	19	1	no	—
162	C₂×C₂²⋊C₈	—	38	1	no	—
163	C₂×C₂²⋊C₈	—	38	1	no	—
164	C₂×C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
165	#341	—	38	2	no	—
166	#336	—	38	1	no	—
167	#324	Dic₁₉	1	2	yes	—
168	#323	Dic₁₉	1	2	yes	—
169	C₂×C₁₉	—	2	1	no	—
170	C₂×C₁₉	—	2	1	no	—
171	C₂×C₁₉	—	4	2	no	—
172	C₂×C₁₉	—	4	2	no	—
173	C₂×C₁₉	#1855	1	1	yes	characteristic
174	C₂×C₁₉	#1858	1	1	yes	characteristic
175	C₂×C₁₉	#1867	1	1	yes	characteristic
176	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
177	C₂³×C₄	D₇₆	1	1	yes	characteristic
178	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
179	C₂×M₁₆	—	19	2	no	—
180	C₂×M₁₆	—	19	2	no	—
181	C₂×M₁₆	—	38	2	no	—
182	C₂×M₁₆	—	76	2	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	—	38	1	no	—
185	C₂²×C₈	—	38	1	no	—
186	C₂²×C₈	—	38	1	no	—
187	C₂²×C₈	—	38	1	no	—
188	C₄×D₄	—	2	2	no	—
189	C₄×D₄	—	2	2	no	—
190	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
192	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
193	C₂×C₄²	D₇₆	1	1	yes	characteristic
194	#108	—	76	4	no	—
195	C₄⋊C₈	—	38	1	no	—
196	C₄⋊C₈	—	38	1	no	—
197	C₂²⋊C₈	—	2	2	no	—
198	C₂²⋊C₈	—	38	2	no	—
199	C₂²⋊C₈	—	38	2	no	—
200	C₂²⋊C₈	—	38	2	no	—
201	C₂²⋊C₈	—	38	2	no	—
202	C₂²⋊C₈	—	76	2	no	—
203	C₂²⋊C₈	C₂×Dic₁₉	1	4	yes	—
204	#97	—	38	2	no	—
205	C₁₉	#8859	1	1	yes	characteristic, complemented, Sylow
206	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
207	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
208	C₂×D₄	—	2	2	no	—
209	C₂×D₄	—	2	2	no	—
210	C₂×D₄	—	4	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	—	4	1	no	—
215	C₂²×C₄	—	4	1	no	—
216	C₂²×C₄	—	4	1	no	—
217	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
218	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
219	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
221	C₂²×C₄	D₄×D₁₉	1	2	yes	—
222	C₂²×C₄	#64543	1	2	yes	—
223	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
224	M₁₆	—	38	4	no	—
225	M₁₆	—	76	2	no	—
226	M₁₆	—	76	2	no	—
227	M₁₆	—	76	2	no	—
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	4	2	no	—
230	C₂×C₈	—	4	2	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	38	2	no	—
234	C₂×C₈	—	76	1	no	—
235	C₂×C₈	—	76	1	no	—
236	C₂×C₈	—	76	1	no	—
237	C₂×C₈	—	76	1	no	—
238	C₂×C₈	—	76	1	no	—
239	C₂×C₈	—	152	1	no	—
240	C₂×C₈	—	152	1	no	—
241	C₄⋊C₄	—	2	2	no	—
242	C₂²⋊C₄	—	2	2	no	—
243	C₂²⋊C₄	—	2	2	no	—
244	C₄²	—	2	1	no	—
245	C₄²	—	2	1	no	—
246	C₂³	—	2	1	no	—
247	C₂³	—	2	1	no	—
248	C₂³	—	2	1	no	—
249	C₂³	—	2	1	no	—
250	C₂³	—	4	1	no	—
251	C₂³	—	4	1	no	—
252	C₂³	—	4	1	no	—
253	C₂³	—	4	1	no	—
254	C₂³	#10597276	1	2	yes	complemented
255	C₂³	#10597324	1	2	yes	—
256	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
257	D₄	—	4	4	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	—	4	1	no	—
269	C₂×C₄	—	4	1	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	8	1	no	—
274	C₂×C₄	#10597328	1	1	yes	characteristic
275	C₂×C₄	#10597332	1	1	yes	characteristic
276	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
277	C₈	—	4	4	no	—
278	C₈	—	76	2	no	—
279	C₈	—	76	2	no	—
280	C₈	—	76	2	no	—
281	C₈	—	152	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	—	2	2	no	—
285	C₂²	—	2	2	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	4	2	no	—
289	C₂²	—	4	1	no	—
290	C₂²	—	4	1	no	—
291	C₂²	—	8	1	no	—
292	C₂²	—	8	1	no	—
293	C₂²	—	8	1	no	—
294	C₂²	#11926419	1	1	yes	characteristic
295	C₂²	C₂×#10597276	1	1	yes	characteristic
296	C₂²	#11926593	1	1	yes	characteristic
297	C₄	—	2	2	no	—
298	C₄	—	2	1	no	—
299	C₄	—	4	1	no	—
300	C₄	—	4	1	no	—
301	C₄	—	4	1	no	—
302	C₄	#11926732	1	1	yes	characteristic
303	C₄	#11926735	1	1	yes	characteristic
304	C₂	—	2	1	no	—
305	C₂	—	2	1	no	—
306	C₂	—	4	2	no	—
307	C₂	—	4	2	no	—
308	C₂	#14563842	1	1	yes	characteristic
309	C₂	#14563857	1	1	yes	characteristic
310	C₂	#14563918	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572664

C₂

yes

maximal, characteristic

#14563933

C₂

yes

maximal, characteristic

#14563842

C₂

yes

maximal, complemented

#14561523

C₂

yes

maximal, complemented

C₁₉×#1459

C₂

yes

maximal, characteristic

C₂²×#64520

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926309

—

#11926299

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#324

C₄

yes

—

C₁₉×#323

C₄

yes

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

—

D₄

yes

—

C₂×#64520

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂×Q₈

yes

characteristic

C₂×D₄×C₁₉

—

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

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8859

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#108

yes

complemented

100

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

101

C₂³×C₁₉

C₂²⋊Q₈

yes

—

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

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

—

113

C₂×C₄×C₁₉

—

114

C₂×C₄×C₁₉

—

115

C₂×C₄×C₁₉

—

116

C₂×C₄×C₁₉

—

117

C₂×C₄×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

C₄×D₄

yes

—

120

C₂×C₄×C₁₉

#120

yes

characteristic

121

C₂×C₄×C₁₉

#123

yes

characteristic

122

C₈×C₁₉

—

123

C₁₉⋊C₈

—

124

C₁₉⋊C₈

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

#2973

—

128

#1870

—

129

#1855

—

130

#1459

D₁₉

yes

characteristic

131

#1298

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

—

142

C₂²×C₁₉

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

#385

yes

characteristic

145

C₂²×C₁₉

C₂×#108

yes

characteristic

146

C₂²×C₁₉

#430

yes

characteristic

147

C₄×C₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

B(4,𝔽₂)

yes

characteristic

153

C₄×C₁₉

#458

yes

characteristic

154

C₂²×M₁₆

—

155

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

156

#435

—

157

#435

—

158

#432

—

159

C₂×#108

—

160

#407

—

161

C₂×C₂²⋊C₈

—

162

C₂×C₂²⋊C₈

—

163

C₂×C₂²⋊C₈

—

164

C₂×C₂²⋊C₈

C₂×D₁₉

yes

—

165

#341

—

166

#336

—

167

#324

Dic₁₉

yes

—

168

#323

Dic₁₉

yes

—

169

C₂×C₁₉

—

170

C₂×C₁₉

—

171

C₂×C₁₉

—

172

C₂×C₁₉

—

173

C₂×C₁₉

#1855

yes

characteristic

174

C₂×C₁₉

#1858

yes

characteristic

175

C₂×C₁₉

#1867

yes

characteristic

176

C₂²×D₄

Dic₃₈

yes

characteristic

177

C₂³×C₄

D₇₆

yes

characteristic

178

C₂³×C₄

C₂²×D₁₉

yes

characteristic

179

C₂×M₁₆

—

180

C₂×M₁₆

—

181

C₂×M₁₆

—

182

C₂×M₁₆

—

183

C₂²×C₈

—

184

C₂²×C₈

—

185

C₂²×C₈

—

186

C₂²×C₈

—

187

C₂²×C₈

—

188

C₄×D₄

—

189

C₄×D₄

—

190

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

191

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

192

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

characteristic

193

C₂×C₄²

D₇₆

yes

characteristic

194

#108

—

195

C₄⋊C₈

—

196

C₄⋊C₈

—

197

C₂²⋊C₈

—

198

C₂²⋊C₈

—

199

C₂²⋊C₈

—

200

C₂²⋊C₈

—

201

C₂²⋊C₈

—

202

C₂²⋊C₈

—

203

C₂²⋊C₈

C₂×Dic₁₉

yes

—

204

#97

—

205

C₁₉

#8859

yes

characteristic, complemented, Sylow

206

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

207

C₂⁴

C₂×Dic₃₈

yes

characteristic

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

218

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

219

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

220

C₂²×C₄

C₂×D₇₆

yes

characteristic

221

C₂²×C₄

D₄×D₁₉

yes

—

222

C₂²×C₄

#64543

yes

—

223

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

224

M₁₆

—

225

M₁₆

—

226

M₁₆

—

227

M₁₆

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₂×C₈

—

239

C₂×C₈

—

152

—

240

C₂×C₈

—

152

—

241

C₄⋊C₄

—

242

C₂²⋊C₄

—

243

C₂²⋊C₄

—

244

C₄²

—

245

C₄²

—

246

C₂³

—

247

C₂³

—

248

C₂³

—

249

C₂³

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

#10597276

yes

complemented

255

C₂³

#10597324

yes

—

256

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

257

D₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

#10597328

yes

characteristic

275

C₂×C₄

#10597332

yes

characteristic

276

C₂×C₄

D₄×Dic₁₉

yes

—

277

C₈

—

278

C₈

—

279

C₈

—

280

C₈

—

281

C₈

—

152

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

#11926419

yes

characteristic

295

C₂²

C₂×#10597276

yes

characteristic

296

C₂²

#11926593

yes

characteristic

297

C₄

—

298

C₄

—

299

C₄

—

300

C₄

—

301

C₄

—

302

C₄

#11926732

yes

characteristic

303

C₄

#11926735

yes

characteristic

304

C₂

—

305

C₂

—

306

C₂

—

307

C₂

—

308

C₂

#14563842

yes

characteristic

309

C₂

#14563857

yes

characteristic

310

C₂

#14563918

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1459	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂²×D₄×C₁₉	Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1459	D₁₉
hypocenter	C₁₉	#8859
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1459

subgroup

G/H

center

C₂×C₄

#10597328

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#1459

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂²×D₄×C₁₉

Q₈

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1459

N	H ≅ G/N	type
3. #14563842	C₂	semidirect
4. #14561523	C₂	semidirect
99. C₂³×C₁₉	#108	semidirect
205. C₁₉	#8859	semidirect
254. C₂³	#10597276	semidirect

H ≅ G/N

type

3. #14563842

C₂

semidirect

4. #14561523

C₂

semidirect

99. C₂³×C₁₉

#108

semidirect

205. C₁₉

#8859

semidirect

254. C₂³

#10597276

semidirect

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

subgroup	index
#14572664	2
#14563933	2
#14563842	2
#14561523	2
C₁₉×#1459	2
#8859	19

subgroup

index

C₁₉×#1459

Subgroups — #18076551

Conjugacy classes of subgroups

Complements

Maximal subgroups