Group #18071100 — subgroups

Subgroups — #18071100

Order 4864.

640 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563703	C₂	1	1	yes	maximal, characteristic, complemented
2	#14563397	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561456	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×#10597260	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	C₂²	1	2	yes	—
10	#11926299	C₂²	1	2	yes	—
11	C₂×C₁₉×#127	C₄	1	1	yes	characteristic
12	C₂×C₁₉×#121	—	2	1	no	—
13	C₂×C₁₉×#121	—	2	1	no	—
14	C₂×C₁₉×#121	C₄	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#390	—	2	1	no	—
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#390	C₂²	1	2	yes	—
19	C₁₉×#384	C₄	1	1	yes	characteristic
20	C₂²×D₄×C₁₉	—	2	2	no	—
21	C₂²×D₄×C₁₉	—	2	1	no	—
22	C₂²×D₄×C₁₉	—	2	1	no	—
23	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₁₉×#127	—	4	2	no	—
28	C₁₉×#121	—	4	4	no	—
29	C₁₉×#121	—	4	4	no	—
30	C₁₉×#121	—	4	4	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	—	4	2	no	—
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₁₉⋊C₈	—	2	2	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
46	#10597260	—	4	2	no	—
47	C₂⁴×C₁₉	—	2	2	no	—
48	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×D₄×C₁₉	—	2	4	no	—
50	C₂×D₄×C₁₉	—	4	2	no	—
51	C₂×D₄×C₁₉	—	4	2	no	—
52	C₂×D₄×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	4	2	no	—
54	C₂×D₄×C₁₉	—	4	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂×D₄×C₁₉	—	4	4	no	—
57	C₂×D₄×C₁₉	—	4	4	no	—
58	C₂×D₄×C₁₉	—	4	4	no	—
59	C₂×D₄×C₁₉	—	4	2	no	—
60	C₂×D₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	2	2	no	—
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₄⋊C₄×C₁₉	—	4	2	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₂²⋊C₄×C₁₉	—	4	4	no	—
81	C₂²⋊C₄×C₁₉	—	4	4	no	—
82	C₂²⋊C₄×C₁₉	—	4	4	no	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	—	2	2	no	—
85	C₄²×C₁₉	—	4	1	no	—
86	C₄²×C₁₉	—	4	1	no	—
87	C₂×C₁₉⋊C₈	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	#7704	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	2	1	no	—
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	—	2	1	no	—
98	C₂³×C₁₉	—	2	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	—	4	2	no	—
101	C₂³×C₁₉	—	4	2	no	—
102	C₂³×C₁₉	—	4	2	no	—
103	C₂³×C₁₉	—	4	2	no	—
104	C₂³×C₁₉	—	4	2	no	—
105	C₂³×C₁₉	—	4	2	no	—
106	C₂³×C₁₉	—	4	2	no	—
107	C₂³×C₁₉	#100	1	2	yes	—
108	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	D₄×C₁₉	—	8	4	no	—
110	D₄×C₁₉	—	8	4	no	—
111	D₄×C₁₉	—	8	4	no	—
112	D₄×C₁₉	—	8	8	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	4	no	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	#99	1	2	yes	—
133	C₂×C₄×C₁₉	#104	1	2	yes	—
134	C₂×C₄×C₁₉	#131	1	2	yes	—
135	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
137	C₁₉⋊C₈	—	4	4	no	—
138	C₁₉⋊C₈	—	8	2	no	—
139	#2856	D₁₉	1	1	yes	characteristic
140	#1817	—	19	1	no	—
141	#1749	—	19	1	no	—
142	#1270	—	19	4	no	—
143	C₂²×C₁₉	—	2	2	no	—
144	C₂²×C₁₉	—	2	2	no	—
145	C₂²×C₁₉	—	2	2	no	—
146	C₂²×C₁₉	—	4	1	no	—
147	C₂²×C₁₉	—	4	1	no	—
148	C₂²×C₁₉	—	4	1	no	—
149	C₂²×C₁₉	—	4	1	no	—
150	C₂²×C₁₉	—	8	2	no	—
151	C₂²×C₁₉	—	8	2	no	—
152	C₂²×C₁₉	—	8	2	no	—
153	C₂²×C₁₉	—	8	2	no	—
154	C₂²×C₁₉	—	8	2	no	—
155	C₂²×C₁₉	—	8	2	no	—
156	C₂²×C₁₉	—	8	2	no	—
157	C₂²×C₁₉	#408	1	1	yes	characteristic
158	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
159	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
160	C₂²×C₁₉	#418	1	1	yes	characteristic
161	C₂²×C₁₉	#418	1	1	yes	characteristic
162	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
163	C₂²×C₁₉	#421	1	1	yes	characteristic
164	C₄×C₁₉	—	2	2	no	—
165	C₄×C₁₉	—	2	2	no	—
166	C₄×C₁₉	—	2	2	no	—
167	C₄×C₁₉	—	2	2	no	—
168	C₄×C₁₉	—	2	2	no	—
169	C₄×C₁₉	—	4	1	no	—
170	C₄×C₁₉	—	8	2	no	—
171	C₂×#127	Dic₁₉	1	1	yes	characteristic
172	C₂×#121	—	2	1	no	—
173	C₂×#121	—	2	1	no	—
174	C₂×#121	Dic₁₉	1	2	yes	—
175	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
176	C₂×C₂²⋊C₈	—	38	1	no	—
177	C₂×C₂²⋊C₈	—	38	1	no	—
178	C₂×#97	—	38	1	no	—
179	#390	—	2	1	no	—
180	#390	—	2	1	no	—
181	#390	C₂×D₁₉	1	2	yes	—
182	#384	Dic₁₉	1	1	yes	characteristic
183	#336	—	19	2	no	—
184	#336	—	19	2	no	—
185	#336	—	38	1	no	—
186	C₂×C₁₉	—	4	2	no	—
187	C₂×C₁₉	—	16	2	no	—
188	C₂×C₁₉	#1471	1	1	yes	characteristic
189	C₂×C₁₉	#1484	1	1	yes	characteristic
190	C₂×C₁₉	#1496	1	1	yes	characteristic
191	C₂×C₁₉	#1507	1	1	yes	characteristic
192	C₂×C₁₉	#1510	1	1	yes	characteristic
193	C₂×C₁₉	#1530	1	1	yes	characteristic
194	C₂×C₁₉	#1555	1	1	yes	characteristic
195	C₂²×D₄	—	2	2	no	—
196	C₂²×D₄	—	2	1	no	—
197	C₂²×D₄	—	2	1	no	—
198	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
199	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
200	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂²×C₈	—	38	2	no	—
203	C₂²×C₈	—	38	2	no	—
204	#127	—	4	2	no	—
205	#121	—	4	4	no	—
206	#121	—	4	4	no	—
207	#121	—	4	4	no	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	—	2	1	no	—
210	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
211	C₂×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₄²	—	4	2	no	—
215	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
216	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
219	C₂²⋊C₈	—	38	4	no	—
220	C₂²⋊C₈	—	76	2	no	—
221	#97	—	76	2	no	—
222	C₁₉	#7704	1	1	yes	characteristic, complemented, Sylow
223	C₂⁴	—	2	2	no	—
224	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	4	2	no	—
227	C₂×D₄	—	4	2	no	—
228	C₂×D₄	—	4	2	no	—
229	C₂×D₄	—	4	2	no	—
230	C₂×D₄	—	4	2	no	—
231	C₂×D₄	—	4	2	no	—
232	C₂×D₄	—	4	4	no	—
233	C₂×D₄	—	4	4	no	—
234	C₂×D₄	—	4	4	no	—
235	C₂×D₄	—	4	2	no	—
236	C₂×D₄	—	4	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	4	1	no	—
245	C₂²×C₄	—	4	1	no	—
246	C₂²×C₄	—	4	1	no	—
247	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
251	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂×C₈	—	38	4	no	—
254	C₂×C₈	—	76	2	no	—
255	C₂×C₈	—	76	2	no	—
256	C₂×C₈	—	76	2	no	—
257	C₂×C₈	—	76	2	no	—
258	C₂×C₈	—	76	2	no	—
259	C₄⋊C₄	—	4	2	no	—
260	C₄⋊C₄	—	4	2	no	—
261	C₄⋊C₄	—	4	2	no	—
262	C₂²⋊C₄	—	4	4	no	—
263	C₂²⋊C₄	—	4	4	no	—
264	C₂²⋊C₄	—	4	4	no	—
265	C₄²	—	2	2	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	4	1	no	—
268	C₄²	—	4	1	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	4	2	no	—
276	C₂³	—	4	2	no	—
277	C₂³	—	4	2	no	—
278	C₂³	—	4	2	no	—
279	C₂³	—	4	2	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	2	no	—
282	C₂³	#10597290	1	2	yes	—
283	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
284	D₄	—	8	4	no	—
285	D₄	—	8	4	no	—
286	D₄	—	8	4	no	—
287	D₄	—	8	8	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	#10597291	1	2	yes	—
308	C₂×C₄	#10597294	1	2	yes	—
309	C₂×C₄	#10597378	1	2	yes	—
310	C₂×C₄	#10597378	1	2	yes	—
311	C₂×C₄	#10597394	1	2	yes	—
312	C₈	—	76	4	no	—
313	C₈	—	152	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	4	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	1	no	—
320	C₂²	—	4	1	no	—
321	C₂²	—	8	2	no	—
322	C₂²	—	8	2	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	#11926511	1	1	yes	characteristic
329	C₂²	C₂×#10597291	1	1	yes	characteristic
330	C₂²	C₂×#10597290	1	1	yes	characteristic
331	C₂²	#11926549	1	1	yes	characteristic
332	C₂²	#11926549	1	1	yes	characteristic
333	C₂²	C₂×#10597294	1	1	yes	characteristic
334	C₂²	#11926561	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	4	1	no	—
341	C₄	—	8	2	no	—
342	C₂	—	4	2	no	—
343	C₂	—	16	2	no	—
344	C₂	#14561995	1	1	yes	characteristic
345	C₂	#14562052	1	1	yes	characteristic
346	C₂	#14562104	1	1	yes	characteristic
347	C₂	#14562151	1	1	yes	characteristic
348	C₂	#14562164	1	1	yes	characteristic
349	C₂	#14562246	1	1	yes	characteristic
350	C₂	#14562349	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563703

C₂

yes

maximal, characteristic, complemented

#14563397

C₂

yes

maximal, characteristic, complemented

#14561456

C₂

yes

maximal, complemented

C₁₉×#2856

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

—

#11926299

C₂²

yes

—

#11926299

C₂²

yes

—

C₂×C₁₉×#127

C₄

yes

characteristic

C₂×C₁₉×#121

—

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#390

—

C₁₉×#390

—

C₁₉×#390

C₂²

yes

—

C₁₉×#384

C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₁₉×#127

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

—

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

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×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

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7704

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

100

C₂³×C₁₉

—

101

C₂³×C₁₉

—

102

C₂³×C₁₉

—

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

#100

yes

—

108

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

109

D₄×C₁₉

—

110

D₄×C₁₉

—

111

D₄×C₁₉

—

112

D₄×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

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

—

130

C₂×C₄×C₁₉

—

131

C₂×C₄×C₁₉

—

132

C₂×C₄×C₁₉

#99

yes

—

133

C₂×C₄×C₁₉

#104

yes

—

134

C₂×C₄×C₁₉

#131

yes

—

135

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

136

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

137

C₁₉⋊C₈

—

138

C₁₉⋊C₈

—

139

#2856

D₁₉

yes

characteristic

140

#1817

—

141

#1749

—

142

#1270

—

143

C₂²×C₁₉

—

144

C₂²×C₁₉

—

145

C₂²×C₁₉

—

146

C₂²×C₁₉

—

147

C₂²×C₁₉

—

148

C₂²×C₁₉

—

149

C₂²×C₁₉

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

—

153

C₂²×C₁₉

—

154

C₂²×C₁₉

—

155

C₂²×C₁₉

—

156

C₂²×C₁₉

—

157

C₂²×C₁₉

#408

yes

characteristic

158

C₂²×C₁₉

C₂×#99

yes

characteristic

159

C₂²×C₁₉

C₂×#100

yes

characteristic

160

C₂²×C₁₉

#418

yes

characteristic

161

C₂²×C₁₉

#418

yes

characteristic

162

C₂²×C₁₉

C₂×#104

yes

characteristic

163

C₂²×C₁₉

#421

yes

characteristic

164

C₄×C₁₉

—

165

C₄×C₁₉

—

166

C₄×C₁₉

—

167

C₄×C₁₉

—

168

C₄×C₁₉

—

169

C₄×C₁₉

—

170

C₄×C₁₉

—

171

C₂×#127

Dic₁₉

yes

characteristic

172

C₂×#121

—

173

C₂×#121

—

174

C₂×#121

Dic₁₉

yes

—

175

C₂²×C₄²

C₂×D₁₉

yes

characteristic

176

C₂×C₂²⋊C₈

—

177

C₂×C₂²⋊C₈

—

178

C₂×#97

—

179

#390

—

180

#390

—

181

#390

C₂×D₁₉

yes

—

182

#384

Dic₁₉

yes

characteristic

183

#336

—

184

#336

—

185

#336

—

186

C₂×C₁₉

—

187

C₂×C₁₉

—

188

C₂×C₁₉

#1471

yes

characteristic

189

C₂×C₁₉

#1484

yes

characteristic

190

C₂×C₁₉

#1496

yes

characteristic

191

C₂×C₁₉

#1507

yes

characteristic

192

C₂×C₁₉

#1510

yes

characteristic

193

C₂×C₁₉

#1530

yes

characteristic

194

C₂×C₁₉

#1555

yes

characteristic

195

C₂²×D₄

—

196

C₂²×D₄

—

197

C₂²×D₄

—

198

C₂²×D₄

C₂×Dic₁₉

yes

—

199

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

200

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

201

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

202

C₂²×C₈

—

203

C₂²×C₈

—

204

#127

—

205

#121

—

206

#121

—

207

#121

—

208

C₂×C₄⋊C₄

—

209

C₂×C₄⋊C₄

—

210

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

211

C₂×C₂²⋊C₄

—

212

C₂×C₂²⋊C₄

—

213

C₂×C₂²⋊C₄

—

214

C₂×C₄²

—

215

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

216

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

217

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

218

C₂×C₄²

C₂²×D₁₉

yes

characteristic

219

C₂²⋊C₈

—

220

C₂²⋊C₈

—

221

#97

—

222

C₁₉

#7704

yes

characteristic, complemented, Sylow

223

C₂⁴

—

224

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

225

C₂×D₄

—

226

C₂×D₄

—

227

C₂×D₄

—

228

C₂×D₄

—

229

C₂×D₄

—

230

C₂×D₄

—

231

C₂×D₄

—

232

C₂×D₄

—

233

C₂×D₄

—

234

C₂×D₄

—

235

C₂×D₄

—

236

C₂×D₄

—

237

C₂²×C₄

—

238

C₂²×C₄

—

239

C₂²×C₄

—

240

C₂²×C₄

—

241

C₂²×C₄

—

242

C₂²×C₄

—

243

C₂²×C₄

—

244

C₂²×C₄

—

245

C₂²×C₄

—

246

C₂²×C₄

—

247

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

248

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

249

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

250

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

251

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

252

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

253

C₂×C₈

—

254

C₂×C₈

—

255

C₂×C₈

—

256

C₂×C₈

—

257

C₂×C₈

—

258

C₂×C₈

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

—

262

C₂²⋊C₄

—

263

C₂²⋊C₄

—

264

C₂²⋊C₄

—

265

C₄²

—

266

C₄²

—

267

C₄²

—

268

C₄²

—

269

C₂³

—

270

C₂³

—

271

C₂³

—

272

C₂³

—

273

C₂³

—

274

C₂³

—

275

C₂³

—

276

C₂³

—

277

C₂³

—

278

C₂³

—

279

C₂³

—

280

C₂³

—

281

C₂³

—

282

C₂³

#10597290

yes

—

283

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

284

D₄

—

285

D₄

—

286

D₄

—

287

D₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

—

295

C₂×C₄

—

296

C₂×C₄

—

297

C₂×C₄

—

298

C₂×C₄

—

299

C₂×C₄

—

300

C₂×C₄

—

301

C₂×C₄

—

302

C₂×C₄

—

303

C₂×C₄

—

304

C₂×C₄

—

305

C₂×C₄

—

306

C₂×C₄

—

307

C₂×C₄

#10597291

yes

—

308

C₂×C₄

#10597294

yes

—

309

C₂×C₄

#10597378

yes

—

310

C₂×C₄

#10597378

yes

—

311

C₂×C₄

#10597394

yes

—

312

C₈

—

313

C₈

—

152

—

314

C₂²

—

315

C₂²

—

316

C₂²

—

317

C₂²

—

318

C₂²

—

319

C₂²

—

320

C₂²

—

321

C₂²

—

322

C₂²

—

323

C₂²

—

324

C₂²

—

325

C₂²

—

326

C₂²

—

327

C₂²

—

328

C₂²

#11926511

yes

characteristic

329

C₂²

C₂×#10597291

yes

characteristic

330

C₂²

C₂×#10597290

yes

characteristic

331

C₂²

#11926549

yes

characteristic

332

C₂²

#11926549

yes

characteristic

333

C₂²

C₂×#10597294

yes

characteristic

334

C₂²

#11926561

yes

characteristic

335

C₄

—

336

C₄

—

337

C₄

—

338

C₄

—

339

C₄

—

340

C₄

—

341

C₄

—

342

C₂

—

343

C₂

—

344

C₂

#14561995

yes

characteristic

345

C₂

#14562052

yes

characteristic

346

C₂

#14562104

yes

characteristic

347

C₂

#14562151

yes

characteristic

348

C₂

#14562164

yes

characteristic

349

C₂

#14562246

yes

characteristic

350

C₂

#14562349

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#2856	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2856	D₁₉
hypocenter	C₁₉	#7704
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2856

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#2856

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2856

N	H ≅ G/N	type
1. #14563703	C₂	semidirect
2. #14563397	C₂	semidirect
3. #14561456	C₂	semidirect
222. C₁₉	#7704	semidirect

H ≅ G/N

type

1. #14563703

C₂

semidirect

2. #14563397

C₂

semidirect

3. #14561456

C₂

semidirect

222. C₁₉

#7704

semidirect

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

subgroup	index
#14563703	2
#14563397	2
#14561456	2
C₁₉×#2856	2
#7704	19

subgroup

index

C₁₉×#2856

Subgroups — #18071100

Conjugacy classes of subgroups

Complements

Maximal subgroups