Group #18074252 — subgroups

Subgroups — #18074252

Order 4864.

1050 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 159 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	#14563627	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562303	C₂	1	2	yes	maximal, complemented
3	#14562064	C₂	1	2	yes	maximal, complemented
4	#14561956	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926568	C₂²	1	2	yes	—
8	C₂×#10597290	—	2	1	no	—
9	#11926313	—	2	1	no	—
10	#11926288	—	2	4	no	—
11	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926268	—	2	2	no	—
13	C₂²×#41×C₁₉	C₄	1	2	yes	—
14	C₁₉×#550	—	2	4	no	—
15	C₁₉×#550	—	2	4	no	—
16	C₂×C₁₉×#127	—	2	1	no	—
17	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	—	2	2	no	—
19	C₂×C₁₉×#121	C₄	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×#41×C₁₉	—	2	4	no	—
24	C₂×#41×C₁₉	—	2	4	no	—
25	C₂×#41×C₁₉	—	4	8	no	—
26	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	2	no	—
34	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₁₉×#127	—	2	8	no	—
36	C₁₉×#127	—	2	2	no	—
37	C₁₉×#127	D₄	1	4	yes	—
38	C₁₉×#121	—	2	16	no	—
39	C₁₉×#121	—	2	4	no	—
40	C₁₉×#121	—	2	4	no	—
41	C₄×Q₈×C₁₉	—	2	2	no	—
42	C₄×Q₈×C₁₉	D₄	1	4	yes	—
43	C₄×D₄×C₁₉	—	2	8	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×#64520	—	2	2	no	—
54	#10597290	—	4	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄×C₁₉⋊C₈	—	2	2	no	—
60	C₂⁴×C₁₉	—	2	2	no	—
61	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
62	#41×C₁₉	—	4	16	no	—
63	#41×C₁₉	—	4	8	no	—
64	#41×C₁₉	—	4	8	no	—
65	C₂×Q₈×C₁₉	—	2	4	no	—
66	C₂×Q₈×C₁₉	—	2	1	no	—
67	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂×D₄×C₁₉	—	2	8	no	—
69	C₂×D₄×C₁₉	—	2	8	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	4	no	—
73	C₂×D₄×C₁₉	—	2	4	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	4	8	no	—
78	C₂×D₄×C₁₉	—	4	4	no	—
79	C₂×D₄×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	8	2	no	—
83	C₂×D₄×C₁₉	—	8	4	no	—
84	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	8	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	4	8	no	—
91	C₂²×C₄×C₁₉	—	4	4	no	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	4	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂²⋊C₄×C₁₉	—	2	8	no	—
101	C₂²⋊C₄×C₁₉	—	2	4	no	—
102	C₄²×C₁₉	—	2	4	no	—
103	C₄²×C₁₉	C₂×D₄	1	2	yes	—
104	C₄²×C₁₉	C₂×D₄	1	2	yes	—
105	#64520	—	4	2	no	—
106	#64520	—	4	2	no	—
107	C₂×C₁₉⋊C₈	—	4	2	no	—
108	C₂×C₁₉⋊C₈	—	4	2	no	—
109	#8385	—	19	1	no	maximal, Sylow
110	C₂³×C₁₉	—	2	2	no	—
111	C₂³×C₁₉	—	2	4	no	—
112	C₂³×C₁₉	—	2	2	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	4	4	no	—
115	C₂³×C₁₉	—	4	4	no	—
116	C₂³×C₁₉	—	4	2	no	—
117	C₂³×C₁₉	—	4	2	no	—
118	C₂³×C₁₉	—	4	2	no	—
119	C₂³×C₁₉	—	4	2	no	—
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	Q₈×C₁₉	—	2	4	no	—
122	Q₈×C₁₉	—	2	2	no	—
123	Q₈×C₁₉	#100	1	4	yes	complemented
124	D₄×C₁₉	—	4	4	no	—
125	D₄×C₁₉	—	4	16	no	—
126	D₄×C₁₉	—	4	4	no	—
127	D₄×C₁₉	—	4	2	no	—
128	D₄×C₁₉	—	4	4	no	—
129	D₄×C₁₉	—	4	2	no	—
130	D₄×C₁₉	—	4	4	no	—
131	D₄×C₁₉	—	8	4	no	—
132	D₄×C₁₉	—	8	8	no	—
133	C₂×C₄×C₁₉	—	2	4	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	16	no	—
140	C₂×C₄×C₁₉	—	4	4	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	4	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#120	1	2	yes	—
147	C₂×C₄×C₁₉	#120	1	2	yes	—
148	C₂×C₄×C₁₉	#135	1	2	yes	—
149	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
151	C₁₉⋊C₈	—	8	2	no	—
152	C₁₉⋊C₈	—	8	2	no	—
153	C₂×#550	D₁₉	1	1	yes	characteristic
154	#1800	—	19	1	no	—
155	#1545	—	19	2	no	—
156	#1487	—	19	2	no	—
157	#1460	—	19	1	no	—
158	C₂²×C₁₉	—	2	1	no	—
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	4	2	no	—
161	C₂²×C₁₉	—	4	4	no	—
162	C₂²×C₁₉	—	4	2	no	—
163	C₂²×C₁₉	—	4	4	no	—
164	C₂²×C₁₉	—	4	2	no	—
165	C₂²×C₁₉	—	4	4	no	—
166	C₂²×C₁₉	—	8	2	no	—
167	C₂²×C₁₉	—	8	2	no	—
168	C₂²×C₁₉	—	8	4	no	—
169	C₂²×C₁₉	—	8	4	no	—
170	C₂²×C₁₉	#379	1	1	yes	characteristic
171	C₂²×C₁₉	#416	1	1	yes	characteristic
172	C₂²×C₁₉	#417	1	1	yes	characteristic
173	C₄×C₁₉	—	2	2	no	—
174	C₄×C₁₉	—	2	4	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	4	2	no	—
177	C₄×C₁₉	—	4	2	no	—
178	C₄×C₁₉	C₂×#100	1	2	yes	—
179	C₄×C₁₉	#449	1	2	yes	—
180	C₄×C₁₉	#452	1	2	yes	—
181	C₂²×#41	Dic₁₉	1	2	yes	—
182	#550	—	2	4	no	—
183	#550	—	2	4	no	—
184	C₂×#127	—	2	1	no	—
185	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
186	C₂×#121	—	2	2	no	—
187	C₂×#121	Dic₁₉	1	2	yes	—
188	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
189	C₂×C₄×D₄	—	2	1	no	—
190	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
191	#431	—	19	2	no	—
192	#423	—	19	2	no	—
193	C₂×#100	—	38	1	no	—
194	#343	—	38	1	no	—
195	#331	—	38	4	no	—
196	Q₈⋊C₈	—	38	4	no	—
197	#323	—	38	2	no	—
198	C₂×C₁₉	—	2	1	no	—
199	C₂×C₁₉	—	2	1	no	—
200	C₂×C₁₉	—	8	2	no	—
201	C₂×C₁₉	—	8	4	no	—
202	C₂×C₁₉	#1783	1	1	yes	characteristic
203	C₂×C₁₉	#1788	1	1	yes	characteristic
204	C₂×C₁₉	#1795	1	1	yes	characteristic
205	C₂×#41	—	2	4	no	—
206	C₂×#41	—	2	4	no	—
207	C₂×#41	—	4	8	no	—
208	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
209	C₂²×D₄	—	2	2	no	—
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
214	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
217	C₂×M₁₆	—	38	2	no	—
218	#127	—	2	8	no	—
219	#127	—	2	2	no	—
220	#127	C₂²⋊D₁₉	1	4	yes	—
221	#121	—	2	16	no	—
222	#121	—	2	4	no	—
223	#121	—	2	4	no	—
224	C₄×Q₈	—	2	2	no	—
225	C₄×Q₈	C₂²⋊D₁₉	1	4	yes	—
226	C₄×D₄	—	2	8	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
236	C₄⋊C₈	—	38	2	no	—
237	C₄⋊C₈	—	38	2	no	—
238	C₄⋊C₈	—	38	2	no	—
239	#100	—	76	2	no	—
240	C₂²⋊C₈	—	38	2	no	—
241	C₄×C₈	—	38	2	no	—
242	C₁₉	#8385	1	1	yes	characteristic, complemented, Sylow
243	C₂⁴	—	2	2	no	—
244	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
245	#41	—	4	16	no	—
246	#41	—	4	8	no	—
247	#41	—	4	8	no	—
248	C₂×Q₈	—	2	4	no	—
249	C₂×Q₈	—	2	1	no	—
250	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	4	8	no	—
261	C₂×D₄	—	4	4	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	8	2	no	—
266	C₂×D₄	—	8	4	no	—
267	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
276	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
279	M₁₆	—	76	2	no	—
280	M₁₆	—	76	2	no	—
281	C₂×C₈	—	76	2	no	—
282	C₂×C₈	—	76	2	no	—
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	4	no	—
289	C₄²	—	2	4	no	—
290	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
291	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	2	no	—
302	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
303	Q₈	—	2	4	no	—
304	Q₈	—	2	2	no	—
305	Q₈	#10597290	1	4	yes	complemented
306	D₄	—	4	4	no	—
307	D₄	—	4	16	no	—
308	D₄	—	4	2	no	—
309	D₄	—	4	4	no	—
310	D₄	—	4	2	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	4	no	—
313	D₄	—	8	4	no	—
314	D₄	—	8	8	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	16	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	#10597395	1	1	yes	characteristic
327	C₂×C₄	#10597396	1	2	yes	—
328	C₂×C₄	#10597397	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
331	C₂×C₄	#10597399	1	2	yes	—
332	C₂×C₄	#10597399	1	2	yes	—
333	C₈	—	152	2	no	—
334	C₈	—	152	2	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	4	no	—
346	C₂²	—	8	4	no	—
347	C₂²	#11926400	1	1	yes	characteristic
348	C₂²	#11926540	1	1	yes	characteristic
349	C₂²	#11926545	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	C₂×#10597290	1	2	yes	—
356	C₄	#11926689	1	2	yes	—
357	C₄	#11926706	1	2	yes	—
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	—	8	4	no	—
361	C₂	—	8	2	no	—
362	C₂	#14563556	1	1	yes	characteristic
363	C₂	#14563575	1	1	yes	characteristic
364	C₂	#14563605	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563627

C₂

yes

maximal, characteristic, complemented

#14562303

C₂

yes

maximal, complemented

#14562064

C₂

yes

maximal, complemented

#14561956

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#550

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

#11926313

—

#11926288

—

Q₈⋊(C₁₉⋊C₈)

—

#11926268

—

C₂²×#41×C₁₉

C₄

yes

—

C₁₉×#550

—

C₁₉×#550

—

C₂×C₁₉×#127

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂×#41×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₁₉×#127

—

C₁₉×#127

—

C₁₉×#127

D₄

yes

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

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

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

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

—

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

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

100

C₂²⋊C₄×C₁₉

—

101

C₂²⋊C₄×C₁₉

—

102

C₄²×C₁₉

—

103

C₄²×C₁₉

C₂×D₄

yes

—

104

C₄²×C₁₉

C₂×D₄

yes

—

105

#64520

—

106

#64520

—

107

C₂×C₁₉⋊C₈

—

108

C₂×C₁₉⋊C₈

—

109

#8385

—

maximal, Sylow

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

C₂×C₂²⋊C₄

yes

characteristic

121

Q₈×C₁₉

—

122

Q₈×C₁₉

—

123

Q₈×C₁₉

#100

yes

complemented

124

D₄×C₁₉

—

125

D₄×C₁₉

—

126

D₄×C₁₉

—

127

D₄×C₁₉

—

128

D₄×C₁₉

—

129

D₄×C₁₉

—

130

D₄×C₁₉

—

131

D₄×C₁₉

—

132

D₄×C₁₉

—

133

C₂×C₄×C₁₉

—

134

C₂×C₄×C₁₉

—

135

C₂×C₄×C₁₉

—

136

C₂×C₄×C₁₉

—

137

C₂×C₄×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

C₂×C₂²⋊C₄

yes

characteristic

145

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

146

C₂×C₄×C₁₉

#120

yes

—

147

C₂×C₄×C₁₉

#120

yes

—

148

C₂×C₄×C₁₉

#135

yes

—

149

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

150

C₂×C₄×C₁₉

#137

yes

characteristic

151

C₁₉⋊C₈

—

152

C₁₉⋊C₈

—

153

C₂×#550

D₁₉

yes

characteristic

154

#1800

—

155

#1545

—

156

#1487

—

157

#1460

—

158

C₂²×C₁₉

—

159

C₂²×C₁₉

—

160

C₂²×C₁₉

—

161

C₂²×C₁₉

—

162

C₂²×C₁₉

—

163

C₂²×C₁₉

—

164

C₂²×C₁₉

—

165

C₂²×C₁₉

—

166

C₂²×C₁₉

—

167

C₂²×C₁₉

—

168

C₂²×C₁₉

—

169

C₂²×C₁₉

—

170

C₂²×C₁₉

#379

yes

characteristic

171

C₂²×C₁₉

#416

yes

characteristic

172

C₂²×C₁₉

#417

yes

characteristic

173

C₄×C₁₉

—

174

C₄×C₁₉

—

175

C₄×C₁₉

—

176

C₄×C₁₉

—

177

C₄×C₁₉

—

178

C₄×C₁₉

C₂×#100

yes

—

179

C₄×C₁₉

#449

yes

—

180

C₄×C₁₉

#452

yes

—

181

C₂²×#41

Dic₁₉

yes

—

182

#550

—

183

#550

—

184

C₂×#127

—

185

C₂×#127

C₂×D₁₉

yes

characteristic

186

C₂×#121

—

187

C₂×#121

Dic₁₉

yes

—

188

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

189

C₂×C₄×D₄

—

190

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

191

#431

—

192

#423

—

193

C₂×#100

—

194

#343

—

195

#331

—

196

Q₈⋊C₈

—

197

#323

—

198

C₂×C₁₉

—

199

C₂×C₁₉

—

200

C₂×C₁₉

—

201

C₂×C₁₉

—

202

C₂×C₁₉

#1783

yes

characteristic

203

C₂×C₁₉

#1788

yes

characteristic

204

C₂×C₁₉

#1795

yes

characteristic

205

C₂×#41

—

206

C₂×#41

—

207

C₂×#41

—

208

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

209

C₂²×D₄

—

210

C₂²×D₄

—

211

C₂²×D₄

—

212

C₂²×D₄

—

213

C₂²×D₄

C₂×Dic₁₉

yes

—

214

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

215

C₂³×C₄

—

216

C₂³×C₄

C₂×Dic₁₉

yes

—

217

C₂×M₁₆

—

218

#127

—

219

#127

—

220

#127

C₂²⋊D₁₉

yes

—

221

#121

—

222

#121

—

223

#121

—

224

C₄×Q₈

—

225

C₄×Q₈

C₂²⋊D₁₉

yes

—

226

C₄×D₄

—

227

C₄×D₄

—

228

C₄×D₄

—

229

C₂×C₄⋊C₄

—

230

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

231

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

232

C₂×C₂²⋊C₄

—

233

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

234

C₂×C₄²

—

235

C₂×C₄²

C₂²×D₁₉

yes

characteristic

236

C₄⋊C₈

—

237

C₄⋊C₈

—

238

C₄⋊C₈

—

239

#100

—

240

C₂²⋊C₈

—

241

C₄×C₈

—

242

C₁₉

#8385

yes

characteristic, complemented, Sylow

243

C₂⁴

—

244

C₂⁴

C₂²⋊Dic₁₉

yes

—

245

#41

—

246

#41

—

247

#41

—

248

C₂×Q₈

—

249

C₂×Q₈

—

250

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

251

C₂×D₄

—

252

C₂×D₄

—

253

C₂×D₄

—

254

C₂×D₄

—

255

C₂×D₄

—

256

C₂×D₄

—

257

C₂×D₄

—

258

C₂×D₄

—

259

C₂×D₄

—

260

C₂×D₄

—

261

C₂×D₄

—

262

C₂×D₄

—

263

C₂×D₄

—

264

C₂×D₄

—

265

C₂×D₄

—

266

C₂×D₄

—

267

C₂×D₄

C₂²⋊Dic₁₉

yes

—

268

C₂²×C₄

—

269

C₂²×C₄

—

270

C₂²×C₄

—

271

C₂²×C₄

—

272

C₂²×C₄

—

273

C₂²×C₄

—

274

C₂²×C₄

—

275

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

276

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

277

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

278

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

279

M₁₆

—

280

M₁₆

—

281

C₂×C₈

—

282

C₂×C₈

—

283

C₄⋊C₄

—

284

C₄⋊C₄

—

285

C₄⋊C₄

—

286

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

287

C₂²⋊C₄

—

288

C₂²⋊C₄

—

289

C₄²

—

290

C₄²

C₂×C₂²⋊D₁₉

yes

—

291

C₄²

C₂×C₂²⋊D₁₉

yes

—

292

C₂³

—

293

C₂³

—

294

C₂³

—

295

C₂³

—

296

C₂³

—

297

C₂³

—

298

C₂³

—

299

C₂³

—

300

C₂³

—

301

C₂³

—

302

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

303

Q₈

—

304

Q₈

—

305

Q₈

#10597290

yes

complemented

306

D₄

—

307

D₄

—

308

D₄

—

309

D₄

—

310

D₄

—

311

D₄

—

312

D₄

—

313

D₄

—

314

D₄

—

315

C₂×C₄

—

316

C₂×C₄

—

317

C₂×C₄

—

318

C₂×C₄

—

319

C₂×C₄

—

320

C₂×C₄

—

321

C₂×C₄

—

322

C₂×C₄

—

323

C₂×C₄

—

324

C₂×C₄

—

325

C₂×C₄

—

326

C₂×C₄

#10597395

yes

characteristic

327

C₂×C₄

#10597396

yes

—

328

C₂×C₄

#10597397

yes

characteristic

329

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

330

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

331

C₂×C₄

#10597399

yes

—

332

C₂×C₄

#10597399

yes

—

333

C₈

—

152

—

334

C₈

—

152

—

335

C₂²

—

336

C₂²

—

337

C₂²

—

338

C₂²

—

339

C₂²

—

340

C₂²

—

341

C₂²

—

342

C₂²

—

343

C₂²

—

344

C₂²

—

345

C₂²

—

346

C₂²

—

347

C₂²

#11926400

yes

characteristic

348

C₂²

#11926540

yes

characteristic

349

C₂²

#11926545

yes

characteristic

350

C₄

—

351

C₄

—

352

C₄

—

353

C₄

—

354

C₄

—

355

C₄

C₂×#10597290

yes

—

356

C₄

#11926689

yes

—

357

C₄

#11926706

yes

—

358

C₂

—

359

C₂

—

360

C₂

—

361

C₂

—

362

C₂

#14563556

yes

characteristic

363

C₂

#14563575

yes

characteristic

364

C₂

#14563605

yes

characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#550	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#550	D₁₉
hypocenter	C₁₉	#8385
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#550

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#550

C₂

socle

C₂²×C₁₉

#379

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#550

N	H ≅ G/N	type
1. #14563627	C₂	semidirect
2. #14562303	C₂	semidirect
3. #14562064	C₂	semidirect
4. #14561956	C₂	semidirect
123. Q₈×C₁₉	#100	semidirect
242. C₁₉	#8385	semidirect
305. Q₈	#10597290	semidirect

H ≅ G/N

type

1. #14563627

C₂

semidirect

2. #14562303

C₂

semidirect

3. #14562064

C₂

semidirect

4. #14561956

C₂

semidirect

123. Q₈×C₁₉

#100

semidirect

242. C₁₉

#8385

semidirect

305. Q₈

#10597290

semidirect

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

subgroup	index
#14563627	2
#14562303	2
#14562064	2
#14561956	2
C₂×C₁₉×#550	2
#8385	19

subgroup

index

C₂×C₁₉×#550

Subgroups — #18074252

Conjugacy classes of subgroups

Complements

Maximal subgroups