Group #18075452 — subgroups

Subgroups — #18075452

Order 4864.

460 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11926616	C₂	1	1	yes	maximal, characteristic
2	#14563671	C₂	1	2	yes	maximal, complemented
3	#14561973	C₂	1	1	yes	maximal, characteristic
4	#14561511	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1465	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₄	1	1	yes	characteristic
7	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	#11926616	—	2	2	no	—
9	#11926616	—	2	2	no	—
10	C₂×#10597279	—	2	2	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
12	#11926508	C₂²	1	2	yes	—
13	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
14	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597260	C₄	1	1	yes	characteristic
16	#11926308	—	2	2	no	—
17	#11926270	—	2	1	no	—
18	#11926268	—	2	1	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#407	C₂²	1	2	yes	—
21	C₁₉×#324	—	2	1	no	—
22	C₁₉×#323	—	2	1	no	—
23	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₄×D₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×#64520	—	2	1	no	—
34	C₂×#64520	—	2	1	no	—
35	C₂×#64520	—	2	2	no	—
36	C₂×#64520	—	4	2	no	—
37	C₂²×C₁₉⋊C₈	—	4	2	no	—
38	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
44	C₁₉×C₂²⋊C₈	—	2	2	no	—
45	C₁₉×C₂²⋊C₈	—	2	2	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
50	#10597279	—	4	4	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	#10597260	—	2	1	no	—
53	#10597260	—	2	1	no	—
54	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	4	1	no	—
61	C₂²×C₄×C₁₉	—	4	1	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	#41	1	2	yes	—
71	M₁₆×C₁₉	—	4	2	no	—
72	M₁₆×C₁₉	—	4	2	no	—
73	C₂×C₈×C₁₉	—	4	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₄²×C₁₉	—	2	1	no	—
78	C₄²×C₁₉	—	2	1	no	—
79	#64520	—	4	2	no	—
80	#64520	—	4	2	no	—
81	#64520	—	4	2	no	—
82	#64520	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	2	4	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	1	no	—
86	C₂×C₁₉⋊C₈	—	2	1	no	—
87	C₂×C₁₉⋊C₈	—	4	1	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	1	no	—
90	C₂×C₁₉⋊C₈	—	4	1	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
94	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
95	#8613	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	—	2	2	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	2	2	no	—
99	C₂³×C₁₉	—	4	1	no	—
100	C₂³×C₁₉	—	4	1	no	—
101	C₂³×C₁₉	—	4	1	no	—
102	C₂³×C₁₉	—	4	1	no	—
103	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
105	D₄×C₁₉	—	4	4	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	2	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	2	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	1	no	—
118	C₂×C₄×C₁₉	—	4	1	no	—
119	C₂×C₄×C₁₉	—	4	1	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#121	1	2	yes	—
124	C₈×C₁₉	—	8	2	no	—
125	C₁₉⋊C₈	—	2	2	no	—
126	C₁₉⋊C₈	—	2	1	no	—
127	C₁₉⋊C₈	—	4	1	no	—
128	C₁₉⋊C₈	—	4	1	no	—
129	C₁₉⋊C₈	—	8	2	no	—
130	C₁₉⋊C₈	#99	1	2	yes	—
131	C₂×#435	—	19	1	no	—
132	#1810	—	19	2	no	—
133	#1465	—	19	1	no	—
134	#1465	D₁₉	1	1	yes	characteristic
135	#1293	—	19	2	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	—	2	2	no	—
139	C₂²×C₁₉	—	2	2	no	—
140	C₂²×C₁₉	—	2	2	no	—
141	C₂²×C₁₉	—	4	4	no	—
142	C₂²×C₁₉	—	4	1	no	—
143	C₂²×C₁₉	—	4	1	no	—
144	C₂²×C₁₉	—	4	1	no	—
145	C₂²×C₁₉	—	8	2	no	—
146	C₂²×C₁₉	#380	1	1	yes	characteristic
147	C₂²×C₁₉	#430	1	2	yes	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	4	1	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	C₂×#99	1	1	yes	characteristic
154	C₄×C₁₉	#410	1	1	yes	characteristic
155	C₂²×M₁₆	—	19	1	no	—
156	C₂³×C₈	—	19	1	no	—
157	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
158	#435	—	38	2	no	—
159	#435	—	38	2	no	—
160	C₂×#108	—	38	2	no	—
161	C₂×C₄⋊C₈	—	19	1	no	—
162	#407	—	19	2	no	—
163	#407	C₂×D₁₉	1	2	yes	—
164	C₂×C₂²⋊C₈	—	19	1	no	—
165	C₂×C₂²⋊C₈	—	19	1	no	—
166	C₂×#97	—	19	1	no	—
167	#341	—	38	2	no	—
168	#324	—	2	1	no	—
169	#324	—	38	1	no	—
170	#323	—	2	1	no	—
171	#323	—	38	1	no	—
172	C₂×C₁₉	—	2	2	no	—
173	C₂×C₁₉	—	4	2	no	—
174	C₂×C₁₉	—	8	1	no	—
175	C₂×C₁₉	#1799	1	1	yes	characteristic
176	C₂×C₁₉	#1811	1	1	yes	characteristic
177	C₂×C₁₉	#1813	1	1	yes	characteristic
178	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
179	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
180	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
181	C₂×M₁₆	—	2	2	no	—
182	C₂×M₁₆	—	38	1	no	—
183	C₂×M₁₆	—	38	1	no	—
184	C₂×M₁₆	—	38	2	no	—
185	C₂×M₁₆	—	76	2	no	—
186	C₂²×C₈	—	19	1	no	—
187	C₂²×C₈	—	19	2	no	—
188	C₂²×C₈	—	19	1	no	—
189	C₂²×C₈	—	19	2	no	—
190	C₂²×C₈	—	19	1	no	—
191	C₂²×C₈	—	19	1	no	—
192	C₂²×C₈	—	76	2	no	—
193	C₄×D₄	—	2	2	no	—
194	C₄×D₄	—	2	2	no	—
195	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
199	#108	—	76	4	no	—
200	C₄⋊C₈	—	38	2	no	—
201	C₂²⋊C₈	—	2	2	no	—
202	C₂²⋊C₈	—	2	2	no	—
203	C₂²⋊C₈	—	38	2	no	—
204	C₂²⋊C₈	—	38	2	no	—
205	C₂²⋊C₈	—	38	2	no	—
206	C₂²⋊C₈	—	38	2	no	—
207	#97	—	38	1	no	—
208	#97	—	38	1	no	—
209	C₁₉	#8613	1	1	yes	characteristic, complemented, Sylow
210	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
211	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
212	C₂×D₄	—	2	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂²×C₄	—	2	1	no	—
215	C₂²×C₄	—	2	1	no	—
216	C₂²×C₄	—	4	1	no	—
217	C₂²×C₄	—	4	1	no	—
218	C₂²×C₄	—	4	1	no	—
219	C₂²×C₄	—	4	1	no	—
220	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
221	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
222	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
223	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
224	C₂²×C₄	D₄×D₁₉	1	2	yes	—
225	C₂²×C₄	#64543	1	2	yes	—
226	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
227	M₁₆	—	4	2	no	—
228	M₁₆	—	4	2	no	—
229	M₁₆	—	76	2	no	—
230	M₁₆	—	76	2	no	—
231	M₁₆	—	76	2	no	—
232	M₁₆	—	76	2	no	—
233	C₂×C₈	—	4	2	no	—
234	C₂×C₈	—	19	1	no	—
235	C₂×C₈	—	19	1	no	—
236	C₂×C₈	—	19	2	no	—
237	C₂×C₈	—	38	4	no	—
238	C₂×C₈	—	38	2	no	—
239	C₂×C₈	—	38	1	no	—
240	C₂×C₈	—	38	1	no	—
241	C₂×C₈	—	76	2	no	—
242	C₂×C₈	—	76	1	no	—
243	C₂×C₈	—	76	1	no	—
244	C₂×C₈	—	76	1	no	—
245	C₂×C₈	—	76	2	no	—
246	C₄⋊C₄	—	2	2	no	—
247	C₂²⋊C₄	—	2	2	no	—
248	C₂²⋊C₄	—	2	2	no	—
249	C₄²	—	2	1	no	—
250	C₄²	—	2	1	no	—
251	C₂³	—	2	2	no	—
252	C₂³	—	2	1	no	—
253	C₂³	—	2	2	no	—
254	C₂³	—	4	1	no	—
255	C₂³	—	4	1	no	—
256	C₂³	—	4	1	no	—
257	C₂³	—	4	1	no	—
258	C₂³	#10597324	1	2	yes	—
259	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
260	D₄	—	4	4	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	4	1	no	—
274	C₂×C₄	—	4	1	no	—
275	C₂×C₄	—	4	1	no	—
276	C₂×C₄	#10597323	1	1	yes	characteristic
277	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
278	C₂×C₄	#10597385	1	2	yes	—
279	C₈	—	8	2	no	—
280	C₈	—	19	2	no	—
281	C₈	—	38	1	no	—
282	C₈	—	38	2	no	—
283	C₈	—	76	1	no	—
284	C₈	—	76	1	no	—
285	C₈	—	152	2	no	—
286	C₂²	—	2	1	no	—
287	C₂²	—	2	1	no	—
288	C₂²	—	2	2	no	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	4	4	no	—
292	C₂²	—	4	1	no	—
293	C₂²	—	4	1	no	—
294	C₂²	—	4	1	no	—
295	C₂²	—	8	2	no	—
296	C₂²	#11926402	1	1	yes	characteristic
297	C₂²	#11926592	1	2	yes	—
298	C₄	—	2	2	no	—
299	C₄	—	2	1	no	—
300	C₄	—	4	1	no	—
301	C₄	—	4	1	no	—
302	C₄	—	4	1	no	—
303	C₄	#99×D₁₉	1	1	yes	characteristic
304	C₄	#11926516	1	1	yes	characteristic
305	C₂	—	2	2	no	—
306	C₂	—	4	2	no	—
307	C₂	—	8	1	no	—
308	C₂	#14563621	1	1	yes	characteristic
309	C₂	#14563675	1	1	yes	characteristic
310	C₂	#14563683	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926616

C₂

yes

maximal, characteristic

#14563671

C₂

yes

maximal, complemented

#14561973

C₂

yes

maximal, characteristic

#14561511

C₂

yes

maximal, complemented

C₁₉×#1465

C₂

yes

maximal, characteristic

C₂²×#64520

C₄

yes

characteristic

C₂³×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

characteristic

#11926508

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597260

C₄

yes

—

—

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#407

C₂²

yes

—

C₁₉×#324

—

C₁₉×#323

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

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

—

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

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

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×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

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8613

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

104

C₂³×C₁₉

C₂²⋊Q₈

yes

—

105

D₄×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

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

122

C₂×C₄×C₁₉

#117

yes

characteristic

123

C₂×C₄×C₁₉

#121

yes

—

124

C₈×C₁₉

—

125

C₁₉⋊C₈

—

126

C₁₉⋊C₈

—

127

C₁₉⋊C₈

—

128

C₁₉⋊C₈

—

129

C₁₉⋊C₈

—

130

C₁₉⋊C₈

#99

yes

—

131

C₂×#435

—

132

#1810

—

133

#1465

—

134

#1465

D₁₉

yes

characteristic

135

#1293

—

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

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

#380

yes

characteristic

147

C₂²×C₁₉

#430

yes

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

C₂×#99

yes

characteristic

154

C₄×C₁₉

#410

yes

characteristic

155

C₂²×M₁₆

—

156

C₂³×C₈

—

157

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

158

#435

—

159

#435

—

160

C₂×#108

—

161

C₂×C₄⋊C₈

—

162

#407

—

163

#407

C₂×D₁₉

yes

—

164

C₂×C₂²⋊C₈

—

165

C₂×C₂²⋊C₈

—

166

C₂×#97

—

167

#341

—

168

#324

—

169

#324

—

170

#323

—

171

#323

—

172

C₂×C₁₉

—

173

C₂×C₁₉

—

174

C₂×C₁₉

—

175

C₂×C₁₉

#1799

yes

characteristic

176

C₂×C₁₉

#1811

yes

characteristic

177

C₂×C₁₉

#1813

yes

characteristic

178

C₂²×D₄

Dic₃₈

yes

characteristic

179

C₂³×C₄

C₄×D₁₉

yes

characteristic

180

C₂³×C₄

C₂²×D₁₉

yes

characteristic

181

C₂×M₁₆

—

182

C₂×M₁₆

—

183

C₂×M₁₆

—

184

C₂×M₁₆

—

185

C₂×M₁₆

—

186

C₂²×C₈

—

187

C₂²×C₈

—

188

C₂²×C₈

—

189

C₂²×C₈

—

190

C₂²×C₈

—

191

C₂²×C₈

—

192

C₂²×C₈

—

193

C₄×D₄

—

194

C₄×D₄

—

195

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

196

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

197

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

characteristic

198

C₂×C₄²

C₄×D₁₉

yes

characteristic

199

#108

—

200

C₄⋊C₈

—

201

C₂²⋊C₈

—

202

C₂²⋊C₈

—

203

C₂²⋊C₈

—

204

C₂²⋊C₈

—

205

C₂²⋊C₈

—

206

C₂²⋊C₈

—

207

#97

—

208

#97

—

209

C₁₉

#8613

yes

characteristic, complemented, Sylow

210

C₂⁴

Dic₁₉⋊C₄

yes

characteristic

211

C₂⁴

C₂×Dic₃₈

yes

characteristic

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

221

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

222

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

223

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

224

C₂²×C₄

D₄×D₁₉

yes

—

225

C₂²×C₄

#64543

yes

—

226

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

227

M₁₆

—

228

M₁₆

—

229

M₁₆

—

230

M₁₆

—

231

M₁₆

—

232

M₁₆

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

236

C₂×C₈

—

237

C₂×C₈

—

238

C₂×C₈

—

239

C₂×C₈

—

240

C₂×C₈

—

241

C₂×C₈

—

242

C₂×C₈

—

243

C₂×C₈

—

244

C₂×C₈

—

245

C₂×C₈

—

246

C₄⋊C₄

—

247

C₂²⋊C₄

—

248

C₂²⋊C₄

—

249

C₄²

—

250

C₄²

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

—

258

C₂³

#10597324

yes

—

259

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

260

D₄

—

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

—

275

C₂×C₄

—

276

C₂×C₄

#10597323

yes

characteristic

277

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

278

C₂×C₄

#10597385

yes

—

279

C₈

—

280

C₈

—

281

C₈

—

282

C₈

—

283

C₈

—

284

C₈

—

285

C₈

—

152

—

286

C₂²

—

287

C₂²

—

288

C₂²

—

289

C₂²

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

294

C₂²

—

295

C₂²

—

296

C₂²

#11926402

yes

characteristic

297

C₂²

#11926592

yes

—

298

C₄

—

299

C₄

—

300

C₄

—

301

C₄

—

302

C₄

—

303

C₄

#99×D₁₉

yes

characteristic

304

C₄

#11926516

yes

characteristic

305

C₂

—

306

C₂

—

307

C₂

—

308

C₂

#14563621

yes

characteristic

309

C₂

#14563675

yes

characteristic

310

C₂

#14563683

yes

characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1465	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1465	D₁₉
hypocenter	C₁₉	#8613
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1465

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting

C₁₉×#1465

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 ◁ #1465

N	H ≅ G/N	type
2. #14563671	C₂	semidirect
4. #14561511	C₂	semidirect
209. C₁₉	#8613	semidirect

H ≅ G/N

type

2. #14563671

C₂

semidirect

4. #14561511

C₂

semidirect

209. C₁₉

#8613

semidirect

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

subgroup	index
C₂×#11926616	2
#14563671	2
#14561973	2
#14561511	2
C₁₉×#1465	2
#8613	19

subgroup

index

C₁₉×#1465

Subgroups — #18075452

Conjugacy classes of subgroups

Complements

Maximal subgroups