Group #18080479 — subgroups

Subgroups — #18080479

Order 4864.

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

normal subgroups only

This group has 880 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, complemented
2	#14563556	C₂	1	2	yes	maximal, complemented
3	#14561973	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561541	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2408	C₂	1	1	yes	maximal, characteristic
6	#11926616	—	2	4	no	—
7	#11926601	—	2	1	no	—
8	C₂×#10597290	—	2	4	no	—
9	#11926508	C₂²	1	2	yes	—
10	#11926508	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#120	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#394	—	2	1	no	—
19	C₁₉×#392	—	2	1	no	—
20	C₁₉×#390	—	2	1	no	—
21	C₁₉×#380	C₂²	1	1	yes	characteristic
22	C₁₉×#379	C₄	1	2	yes	—
23	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	4	4	no	—
30	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₁₉×#121	—	4	4	no	—
34	C₁₉×#120	—	4	4	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×#64520	—	2	2	no	—
47	C₂×#64520	D₄	1	4	yes	complemented
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₁₉×#95	—	2	1	no	—
50	#10597290	—	4	8	no	—
51	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	#10597260	—	2	2	no	—
58	C₂⁴×C₁₉	—	2	2	no	—
59	C₂⁴×C₁₉	—	2	4	no	—
60	C₂⁴×C₁₉	—	4	4	no	—
61	C₂⁴×C₁₉	—	4	2	no	—
62	C₂⁴×C₁₉	—	4	2	no	—
63	C₂⁴×C₁₉	—	8	2	no	—
64	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	4	no	—
67	C₂×D₄×C₁₉	—	2	8	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	4	1	no	—
71	C₂×D₄×C₁₉	—	4	4	no	—
72	C₂×D₄×C₁₉	—	4	2	no	—
73	C₂×D₄×C₁₉	—	4	4	no	—
74	C₂×D₄×C₁₉	—	4	8	no	—
75	C₂×D₄×C₁₉	—	4	4	no	—
76	C₂×D₄×C₁₉	—	4	4	no	—
77	C₂×D₄×C₁₉	—	4	1	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	8	2	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	2	no	—
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	2	yes	—
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₂²⋊C₄×C₁₉	—	2	2	no	—
96	C₂²⋊C₄×C₁₉	—	2	2	no	—
97	C₂²⋊C₄×C₁₉	—	4	4	no	—
98	C₂²⋊C₄×C₁₉	—	4	4	no	—
99	C₂²⋊C₄×C₁₉	—	4	2	no	—
100	C₂²⋊C₄×C₁₉	—	8	2	no	—
101	C₄²×C₁₉	—	2	1	no	—
102	C₄²×C₁₉	—	2	1	no	—
103	#64520	—	4	4	no	—
104	#64520	—	4	4	no	—
105	C₂×C₁₉⋊C₈	—	2	4	no	—
106	C₂×C₁₉⋊C₈	—	4	2	no	—
107	C₂×C₁₉⋊C₈	—	8	2	no	—
108	#9503	—	19	1	no	maximal, Sylow
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	4	no	—
114	C₂³×C₁₉	—	2	8	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	—	4	1	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	4	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	2	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	—	8	4	no	—
127	C₂³×C₁₉	—	8	4	no	—
128	C₂³×C₁₉	—	8	8	no	—
129	C₂³×C₁₉	—	8	8	no	—
130	C₂³×C₁₉	#100	1	2	yes	complemented
131	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₉	C₄×D₄	1	2	yes	—
133	D₄×C₁₉	—	4	8	no	—
134	D₄×C₁₉	—	4	4	no	—
135	D₄×C₁₉	—	4	4	no	—
136	D₄×C₁₉	—	4	4	no	—
137	D₄×C₁₉	—	8	8	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	2	yes	—
156	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
157	C₁₉⋊C₈	—	4	4	no	—
158	C₁₉⋊C₈	—	8	2	no	—
159	#2973	—	19	1	no	—
160	#2408	D₁₉	1	1	yes	characteristic
161	#1783	—	19	2	no	—
162	#1465	—	19	1	no	—
163	#1305	—	19	2	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	4	2	no	—
171	C₂²×C₁₉	—	4	2	no	—
172	C₂²×C₁₉	—	4	2	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	4	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	—	4	4	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	—	8	2	no	—
181	C₂²×C₁₉	—	8	8	no	—
182	C₂²×C₁₉	—	8	8	no	—
183	C₂²×C₁₉	—	8	2	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	#386	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
187	C₂²×C₁₉	#413	1	1	yes	characteristic
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	4	1	no	—
191	C₄×C₁₉	—	4	1	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	8	2	no	—
194	C₄×C₁₉	B(4,𝔽₂)	1	2	yes	—
195	C₂³×D₄	C₂×D₁₉	1	1	yes	characteristic
196	C₂×#121	—	2	1	no	—
197	C₂×#120	Dic₁₉	1	2	yes	—
198	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
199	#435	—	38	4	no	—
200	#432	—	38	1	no	—
201	C₂×#100	—	38	4	no	—
202	#407	—	19	2	no	—
203	#407	—	19	2	no	—
204	C₂×C₂²⋊C₈	—	38	1	no	—
205	#394	—	2	1	no	—
206	#392	—	2	1	no	—
207	#390	—	2	1	no	—
208	#380	C₂×D₁₉	1	1	yes	characteristic
209	#379	Dic₁₉	1	2	yes	—
210	#324	—	38	1	no	—
211	#323	—	38	1	no	—
212	C₂×C₁₉	—	2	1	no	—
213	C₂×C₁₉	—	2	1	no	—
214	C₂×C₁₉	—	4	2	no	—
215	C₂×C₁₉	—	4	2	no	—
216	C₂×C₁₉	—	8	4	no	—
217	C₂×C₁₉	#1889	1	1	yes	characteristic
218	C₂×C₁₉	#1900	1	1	yes	characteristic
219	C₂×C₁₉	#1914	1	1	yes	characteristic
220	C₂⁵	C₂×Dic₁₉	1	2	yes	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	4	4	no	—
227	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
228	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
230	C₂×M₁₆	—	19	4	no	—
231	C₂×M₁₆	—	38	2	no	—
232	C₂²×C₈	—	38	2	no	—
233	#121	—	4	4	no	—
234	#120	—	4	4	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₄⋊C₈	—	38	2	no	—
247	#100	—	76	8	no	—
248	C₂²⋊C₈	—	38	2	no	—
249	C₂²⋊C₈	—	38	2	no	—
250	C₂²⋊C₈	—	38	2	no	—
251	C₂²⋊C₈	—	38	2	no	—
252	C₂²⋊C₈	—	38	2	no	—
253	#97	—	38	2	no	—
254	#95	—	2	1	no	—
255	C₁₉	#9503	1	1	yes	characteristic, complemented, Sylow
256	C₂⁴	—	2	2	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	4	4	no	—
259	C₂⁴	—	4	2	no	—
260	C₂⁴	—	4	2	no	—
261	C₂⁴	—	8	2	no	—
262	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
263	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	—	4	8	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	8	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
287	C₂²×C₄	D₄×D₁₉	1	2	yes	—
288	C₂²×C₄	#64543	1	2	yes	—
289	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
291	M₁₆	—	76	4	no	—
292	M₁₆	—	76	4	no	—
293	C₂×C₈	—	38	4	no	—
294	C₂×C₈	—	76	2	no	—
295	C₂×C₈	—	152	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	8	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	8	4	no	—
324	C₂³	—	8	4	no	—
325	C₂³	—	8	8	no	—
326	C₂³	—	8	8	no	—
327	C₂³	#10597290	1	2	yes	complemented
328	C₂³	D₄×Dic₁₉	1	2	yes	—
329	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
330	D₄	—	4	8	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	8	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	#10597381	1	1	yes	characteristic
352	C₂×C₄	#10597383	1	1	yes	characteristic
353	C₂×C₄	#10597385	1	2	yes	—
354	C₈	—	76	4	no	—
355	C₈	—	152	2	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	8	no	—
374	C₂²	—	8	8	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	#11926424	1	1	yes	characteristic
378	C₂²	C₂×#10597290	1	1	yes	characteristic
379	C₂²	#11926528	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	8	2	no	—
386	C₄	#11926730	1	2	yes	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	4	2	no	—
390	C₂	—	4	2	no	—
391	C₂	—	8	4	no	—
392	C₂	#14564044	1	1	yes	characteristic
393	C₂	#14564099	1	1	yes	characteristic
394	C₂	#14564183	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572664

C₂

yes

maximal, characteristic, complemented

#14563556

C₂

yes

maximal, complemented

#14561973

C₂

yes

maximal, characteristic, complemented

#14561541

C₂

yes

maximal, complemented

C₁₉×#2408

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#11926508

C₂²

yes

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926270

—

#11926268

—

C₂³×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#121

—

C₂×C₁₉×#120

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#394

—

C₁₉×#392

—

C₁₉×#390

—

C₁₉×#380

C₂²

yes

characteristic

C₁₉×#379

C₄

yes

—

C₂⁵×C₁₉

C₂×C₄

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#121

—

C₁₉×#120

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×#64520

—

C₂×#64520

D₄

yes

complemented

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

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

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊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

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

100

C₂²⋊C₄×C₁₉

—

101

C₄²×C₁₉

—

102

C₄²×C₁₉

—

103

#64520

—

104

#64520

—

105

C₂×C₁₉⋊C₈

—

106

C₂×C₁₉⋊C₈

—

107

C₂×C₁₉⋊C₈

—

108

#9503

—

maximal, Sylow

109

C₂³×C₁₉

—

110

C₂³×C₁₉

—

111

C₂³×C₁₉

—

112

C₂³×C₁₉

—

113

C₂³×C₁₉

—

114

C₂³×C₁₉

—

115

C₂³×C₁₉

—

116

C₂³×C₁₉

—

117

C₂³×C₁₉

—

118

C₂³×C₁₉

—

119

C₂³×C₁₉

—

120

C₂³×C₁₉

—

121

C₂³×C₁₉

—

122

C₂³×C₁₉

—

123

C₂³×C₁₉

—

124

C₂³×C₁₉

—

125

C₂³×C₁₉

—

126

C₂³×C₁₉

—

127

C₂³×C₁₉

—

128

C₂³×C₁₉

—

129

C₂³×C₁₉

—

130

C₂³×C₁₉

#100

yes

complemented

131

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

132

C₂³×C₁₉

C₄×D₄

yes

—

133

D₄×C₁₉

—

134

D₄×C₁₉

—

135

D₄×C₁₉

—

136

D₄×C₁₉

—

137

D₄×C₁₉

—

138

C₂×C₄×C₁₉

—

139

C₂×C₄×C₁₉

—

140

C₂×C₄×C₁₉

—

141

C₂×C₄×C₁₉

—

142

C₂×C₄×C₁₉

—

143

C₂×C₄×C₁₉

—

144

C₂×C₄×C₁₉

—

145

C₂×C₄×C₁₉

—

146

C₂×C₄×C₁₉

—

147

C₂×C₄×C₁₉

—

148

C₂×C₄×C₁₉

—

149

C₂×C₄×C₁₉

—

150

C₂×C₄×C₁₉

—

151

C₂×C₄×C₁₉

—

152

C₂×C₄×C₁₉

—

153

C₂×C₄×C₁₉

—

154

C₂×C₄×C₁₉

#120

yes

characteristic

155

C₂×C₄×C₁₉

#121

yes

—

156

C₂×C₄×C₁₉

#123

yes

characteristic

157

C₁₉⋊C₈

—

158

C₁₉⋊C₈

—

159

#2973

—

160

#2408

D₁₉

yes

characteristic

161

#1783

—

162

#1465

—

163

#1305

—

164

C₂²×C₁₉

—

165

C₂²×C₁₉

—

166

C₂²×C₁₉

—

167

C₂²×C₁₉

—

168

C₂²×C₁₉

—

169

C₂²×C₁₉

—

170

C₂²×C₁₉

—

171

C₂²×C₁₉

—

172

C₂²×C₁₉

—

173

C₂²×C₁₉

—

174

C₂²×C₁₉

—

175

C₂²×C₁₉

—

176

C₂²×C₁₉

—

177

C₂²×C₁₉

—

178

C₂²×C₁₉

—

179

C₂²×C₁₉

—

180

C₂²×C₁₉

—

181

C₂²×C₁₉

—

182

C₂²×C₁₉

—

183

C₂²×C₁₉

—

184

C₂²×C₁₉

—

185

C₂²×C₁₉

#386

yes

characteristic

186

C₂²×C₁₉

C₂×#100

yes

characteristic

187

C₂²×C₁₉

#413

yes

characteristic

188

C₄×C₁₉

—

189

C₄×C₁₉

—

190

C₄×C₁₉

—

191

C₄×C₁₉

—

192

C₄×C₁₉

—

193

C₄×C₁₉

—

194

C₄×C₁₉

B(4,𝔽₂)

yes

—

195

C₂³×D₄

C₂×D₁₉

yes

characteristic

196

C₂×#121

—

197

C₂×#120

Dic₁₉

yes

—

198

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

199

#435

—

200

#432

—

201

C₂×#100

—

202

#407

—

203

#407

—

204

C₂×C₂²⋊C₈

—

205

#394

—

206

#392

—

207

#390

—

208

#380

C₂×D₁₉

yes

characteristic

209

#379

Dic₁₉

yes

—

210

#324

—

211

#323

—

212

C₂×C₁₉

—

213

C₂×C₁₉

—

214

C₂×C₁₉

—

215

C₂×C₁₉

—

216

C₂×C₁₉

—

217

C₂×C₁₉

#1889

yes

characteristic

218

C₂×C₁₉

#1900

yes

characteristic

219

C₂×C₁₉

#1914

yes

characteristic

220

C₂⁵

C₂×Dic₁₉

yes

—

221

C₂²×D₄

—

222

C₂²×D₄

—

223

C₂²×D₄

—

224

C₂²×D₄

—

225

C₂²×D₄

—

226

C₂²×D₄

—

227

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

228

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

229

C₂³×C₄

C₂²×D₁₉

yes

characteristic

230

C₂×M₁₆

—

231

C₂×M₁₆

—

232

C₂²×C₈

—

233

#121

—

234

#120

—

235

C₄×D₄

—

236

C₄×D₄

—

237

C₂×C₄⋊C₄

—

238

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

239

C₂×C₂²⋊C₄

—

240

C₂×C₂²⋊C₄

—

241

C₂×C₂²⋊C₄

—

242

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

characteristic

243

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

244

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

characteristic

245

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

246

C₄⋊C₈

—

247

#100

—

248

C₂²⋊C₈

—

249

C₂²⋊C₈

—

250

C₂²⋊C₈

—

251

C₂²⋊C₈

—

252

C₂²⋊C₈

—

253

#97

—

254

#95

—

255

C₁₉

#9503

yes

characteristic, complemented, Sylow

256

C₂⁴

—

257

C₂⁴

—

258

C₂⁴

—

259

C₂⁴

—

260

C₂⁴

—

261

C₂⁴

—

262

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

263

C₂⁴

C₂²×Dic₁₉

yes

characteristic

264

C₂×D₄

—

265

C₂×D₄

—

266

C₂×D₄

—

267

C₂×D₄

—

268

C₂×D₄

—

269

C₂×D₄

—

270

C₂×D₄

—

271

C₂×D₄

—

272

C₂×D₄

—

273

C₂×D₄

—

274

C₂×D₄

—

275

C₂×D₄

—

276

C₂×D₄

—

277

C₂×D₄

—

278

C₂×D₄

—

279

C₂²×C₄

—

280

C₂²×C₄

—

281

C₂²×C₄

—

282

C₂²×C₄

—

283

C₂²×C₄

—

284

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

285

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

286

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

287

C₂²×C₄

D₄×D₁₉

yes

—

288

C₂²×C₄

#64543

yes

—

289

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

290

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

291

M₁₆

—

292

M₁₆

—

293

C₂×C₈

—

294

C₂×C₈

—

295

C₂×C₈

—

152

—

296

C₄⋊C₄

—

297

C₄⋊C₄

—

298

C₂²⋊C₄

—

299

C₂²⋊C₄

—

300

C₂²⋊C₄

—

301

C₂²⋊C₄

—

302

C₂²⋊C₄

—

303

C₂²⋊C₄

—

304

C₄²

—

305

C₄²

—

306

C₂³

—

307

C₂³

—

308

C₂³

—

309

C₂³

—

310

C₂³

—

311

C₂³

—

312

C₂³

—

313

C₂³

—

314

C₂³

—

315

C₂³

—

316

C₂³

—

317

C₂³

—

318

C₂³

—

319

C₂³

—

320

C₂³

—

321

C₂³

—

322

C₂³

—

323

C₂³

—

324

C₂³

—

325

C₂³

—

326

C₂³

—

327

C₂³

#10597290

yes

complemented

328

C₂³

D₄×Dic₁₉

yes

—

329

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

330

D₄

—

331

D₄

—

332

D₄

—

333

D₄

—

334

D₄

—

335

C₂×C₄

—

336

C₂×C₄

—

337

C₂×C₄

—

338

C₂×C₄

—

339

C₂×C₄

—

340

C₂×C₄

—

341

C₂×C₄

—

342

C₂×C₄

—

343

C₂×C₄

—

344

C₂×C₄

—

345

C₂×C₄

—

346

C₂×C₄

—

347

C₂×C₄

—

348

C₂×C₄

—

349

C₂×C₄

—

350

C₂×C₄

—

351

C₂×C₄

#10597381

yes

characteristic

352

C₂×C₄

#10597383

yes

characteristic

353

C₂×C₄

#10597385

yes

—

354

C₈

—

355

C₈

—

152

—

356

C₂²

—

357

C₂²

—

358

C₂²

—

359

C₂²

—

360

C₂²

—

361

C₂²

—

362

C₂²

—

363

C₂²

—

364

C₂²

—

365

C₂²

—

366

C₂²

—

367

C₂²

—

368

C₂²

—

369

C₂²

—

370

C₂²

—

371

C₂²

—

372

C₂²

—

373

C₂²

—

374

C₂²

—

375

C₂²

—

376

C₂²

—

377

C₂²

#11926424

yes

characteristic

378

C₂²

C₂×#10597290

yes

characteristic

379

C₂²

#11926528

yes

characteristic

380

C₄

—

381

C₄

—

382

C₄

—

383

C₄

—

384

C₄

—

385

C₄

—

386

C₄

#11926730

yes

—

387

C₂

—

388

C₂

—

389

C₂

—

390

C₂

—

391

C₂

—

392

C₂

#14564044

yes

characteristic

393

C₂

#14564099

yes

characteristic

394

C₂

#14564183

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2408	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2408	D₁₉
hypocenter	C₁₉	#9503
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2408

subgroup

G/H

center

C₂²

#11926424

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2408

C₂

socle

C₂²×C₁₉

#386

cosocle

C₂³×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2408

N	H ≅ G/N	type
1. #14572664	C₂	semidirect
2. #14563556	C₂	semidirect
3. #14561973	C₂	semidirect
4. #14561541	C₂	semidirect
47. C₂×#64520	D₄	semidirect
130. C₂³×C₁₉	#100	semidirect
255. C₁₉	#9503	semidirect
327. C₂³	#10597290	semidirect

H ≅ G/N

type

1. #14572664

C₂

semidirect

2. #14563556

C₂

semidirect

3. #14561973

C₂

semidirect

4. #14561541

C₂

semidirect

47. C₂×#64520

D₄

semidirect

130. C₂³×C₁₉

#100

semidirect

255. C₁₉

#9503

semidirect

327. C₂³

#10597290

semidirect

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

subgroup	index
#14572664	2
#14563556	2
#14561973	2
#14561541	2
C₁₉×#2408	2
#9503	19

subgroup

index

C₁₉×#2408

Subgroups — #18080479

Conjugacy classes of subgroups

Complements

Maximal subgroups