Group #18074312 — subgroups

Subgroups — #18074312

Order 4864.

802 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14562320	C₂	1	2	yes	maximal, complemented
3	#14562060	C₂	1	2	yes	maximal, complemented
4	#14561956	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#555	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	#11926290	—	2	4	no	—
11	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
12	#11926268	—	2	2	no	—
13	C₁₉×#555	—	2	4	no	—
14	C₁₉×#555	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#124	—	2	2	no	—
17	C₂×C₁₉×#121	—	2	1	no	—
18	C₂×C₁₉×#121	C₄	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	—	2	1	no	—
22	C₂×C₁₉×#117	C₄	1	2	yes	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	—	2	2	no	—
30	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
31	C₁₉×#124	—	2	16	no	—
32	C₁₉×#121	—	2	8	no	—
33	C₁₉×#121	—	2	4	no	—
34	C₁₉×#121	—	2	4	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₄×D₄×C₁₉	—	2	2	no	—
38	C₄×D₄×C₁₉	D₄	1	4	yes	—
39	C₁₉×#117	—	2	8	no	—
40	C₁₉×#117	—	2	4	no	—
41	C₁₉×#117	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
50	C₂×C₄²×C₁₉	—	2	2	no	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#64520	—	2	2	no	—
53	#10597290	—	4	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₄⋊(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	C₂⁴×C₁₉	—	2	1	no	—
60	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×Q₈×C₁₉	—	2	4	no	—
62	C₂×Q₈×C₁₉	—	8	2	no	—
63	C₂×D₄×C₁₉	—	2	8	no	—
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	4	2	no	—
70	C₂×D₄×C₁₉	—	8	4	no	—
71	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	4	no	—
77	C₂²×C₄×C₁₉	—	4	4	no	—
78	C₂²×C₄×C₁₉	—	4	2	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	2	4	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
90	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
91	C₂²⋊C₄×C₁₉	—	2	8	no	—
92	C₂²⋊C₄×C₁₉	—	2	8	no	—
93	C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₂²⋊C₄×C₁₉	—	2	4	no	—
95	C₄²×C₁₉	—	2	8	no	—
96	C₄²×C₁₉	C₂×D₄	1	2	yes	—
97	C₄²×C₁₉	C₂×D₄	1	2	yes	—
98	#64520	—	4	2	no	—
99	#64520	—	4	2	no	—
100	C₂×C₁₉⋊C₈	—	4	2	no	—
101	C₂×C₁₉⋊C₈	—	4	2	no	—
102	#8397	—	19	1	no	maximal, Sylow
103	C₂³×C₁₉	—	2	2	no	—
104	C₂³×C₁₉	—	2	2	no	—
105	C₂³×C₁₉	—	2	2	no	—
106	C₂³×C₁₉	—	2	2	no	—
107	C₂³×C₁₉	—	4	2	no	—
108	C₂³×C₁₉	—	4	2	no	—
109	C₂³×C₁₉	—	4	2	no	—
110	C₂³×C₁₉	—	4	2	no	—
111	C₂³×C₁₉	—	4	1	no	—
112	C₂³×C₁₉	—	4	1	no	—
113	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	Q₈×C₁₉	—	8	4	no	—
115	D₄×C₁₉	—	2	4	no	—
116	D₄×C₁₉	—	4	2	no	—
117	D₄×C₁₉	—	4	2	no	—
118	D₄×C₁₉	—	4	2	no	—
119	D₄×C₁₉	—	8	8	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	4	no	—
130	C₂×C₄×C₁₉	—	4	4	no	—
131	C₂×C₄×C₁₉	—	4	4	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#120	1	2	yes	—
136	C₂×C₄×C₁₉	#120	1	2	yes	—
137	C₂×C₄×C₁₉	#135	1	2	yes	—
138	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
140	C₁₉⋊C₈	—	8	2	no	—
141	C₁₉⋊C₈	—	8	2	no	—
142	C₂×#555	D₁₉	1	1	yes	characteristic
143	#1800	—	19	1	no	—
144	#1549	—	19	2	no	—
145	#1486	—	19	2	no	—
146	#1460	—	19	1	no	—
147	C₂²×C₁₉	—	2	1	no	—
148	C₂²×C₁₉	—	2	1	no	—
149	C₂²×C₁₉	—	4	2	no	—
150	C₂²×C₁₉	—	4	2	no	—
151	C₂²×C₁₉	—	4	2	no	—
152	C₂²×C₁₉	—	4	2	no	—
153	C₂²×C₁₉	—	4	2	no	—
154	C₂²×C₁₉	—	4	2	no	—
155	C₂²×C₁₉	—	8	2	no	—
156	C₂²×C₁₉	—	8	2	no	—
157	C₂²×C₁₉	—	8	2	no	—
158	C₂²×C₁₉	—	8	2	no	—
159	C₂²×C₁₉	#379	1	1	yes	characteristic
160	C₂²×C₁₉	#416	1	1	yes	characteristic
161	C₂²×C₁₉	#417	1	1	yes	characteristic
162	C₄×C₁₉	—	2	2	no	—
163	C₄×C₁₉	—	2	1	no	—
164	C₄×C₁₉	—	4	4	no	—
165	C₄×C₁₉	—	4	2	no	—
166	C₄×C₁₉	—	4	2	no	—
167	C₄×C₁₉	#413	1	2	yes	—
168	C₄×C₁₉	#449	1	2	yes	—
169	C₄×C₁₉	#452	1	2	yes	—
170	#555	—	2	4	no	—
171	#555	—	2	4	no	—
172	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
173	C₂×#124	—	2	2	no	—
174	C₂×#121	—	2	1	no	—
175	C₂×#121	Dic₁₉	1	2	yes	—
176	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
177	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
178	C₂×#117	—	2	1	no	—
179	C₂×#117	Dic₁₉	1	2	yes	—
180	#431	—	19	2	no	—
181	#423	—	19	2	no	—
182	C₂×#100	—	38	1	no	—
183	#343	—	38	1	no	—
184	#332	—	38	4	no	—
185	D₄⋊C₈	—	38	4	no	—
186	#323	—	38	2	no	—
187	C₂×C₁₉	—	2	1	no	—
188	C₂×C₁₉	—	2	1	no	—
189	C₂×C₁₉	—	8	2	no	—
190	C₂×C₁₉	—	8	2	no	—
191	C₂×C₁₉	#1785	1	1	yes	characteristic
192	C₂×C₁₉	#1788	1	1	yes	characteristic
193	C₂×C₁₉	#1795	1	1	yes	characteristic
194	C₂²×Q₈	—	2	1	no	—
195	C₂²×D₄	—	2	2	no	—
196	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
197	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
198	C₂³×C₄	—	2	1	no	—
199	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
200	C₂×M₁₆	—	38	2	no	—
201	C₄⋊Q₈	—	2	2	no	—
202	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
203	#124	—	2	16	no	—
204	#121	—	2	8	no	—
205	#121	—	2	4	no	—
206	#121	—	2	4	no	—
207	C₄×D₄	—	2	2	no	—
208	C₄×D₄	—	2	2	no	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	C₂²⋊D₁₉	1	4	yes	—
211	#117	—	2	8	no	—
212	#117	—	2	4	no	—
213	#117	—	2	4	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
217	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
224	C₄⋊C₈	—	38	2	no	—
225	C₄⋊C₈	—	38	2	no	—
226	C₄⋊C₈	—	38	2	no	—
227	#100	—	76	2	no	—
228	C₂²⋊C₈	—	38	2	no	—
229	C₄×C₈	—	38	2	no	—
230	C₁₉	#8397	1	1	yes	characteristic, complemented, Sylow
231	C₂⁴	—	2	1	no	—
232	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
233	C₂×Q₈	—	2	4	no	—
234	C₂×Q₈	—	8	2	no	—
235	C₂×D₄	—	2	8	no	—
236	C₂×D₄	—	2	1	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	4	2	no	—
242	C₂×D₄	—	8	4	no	—
243	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
254	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
257	M₁₆	—	76	2	no	—
258	M₁₆	—	76	2	no	—
259	C₂×C₈	—	76	2	no	—
260	C₂×C₈	—	76	2	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
266	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
267	C₂²⋊C₄	—	2	8	no	—
268	C₂²⋊C₄	—	2	8	no	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	2	4	no	—
271	C₄²	—	2	8	no	—
272	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
273	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	4	2	no	—
279	C₂³	—	4	2	no	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	2	no	—
282	C₂³	—	4	1	no	—
283	C₂³	—	4	1	no	—
284	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
285	Q₈	—	8	4	no	—
286	D₄	—	2	4	no	—
287	D₄	—	4	2	no	—
288	D₄	—	4	2	no	—
289	D₄	—	4	2	no	—
290	D₄	—	8	8	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	#10597395	1	1	yes	characteristic
305	C₂×C₄	#10597396	1	2	yes	—
306	C₂×C₄	#10597397	1	1	yes	characteristic
307	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
308	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
309	C₂×C₄	#10597399	1	2	yes	—
310	C₂×C₄	#10597399	1	2	yes	—
311	C₈	—	152	2	no	—
312	C₈	—	152	2	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	8	2	no	—
322	C₂²	—	8	2	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	#11926400	1	1	yes	characteristic
326	C₂²	#11926540	1	1	yes	characteristic
327	C₂²	#11926545	1	1	yes	characteristic
328	C₄	—	2	2	no	—
329	C₄	—	2	1	no	—
330	C₄	—	4	4	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	2	no	—
333	C₄	#11926528	1	2	yes	—
334	C₄	#11926689	1	2	yes	—
335	C₄	#11926706	1	2	yes	—
336	C₂	—	2	1	no	—
337	C₂	—	2	1	no	—
338	C₂	—	8	2	no	—
339	C₂	—	8	2	no	—
340	C₂	#14563563	1	1	yes	characteristic
341	C₂	#14563575	1	1	yes	characteristic
342	C₂	#14563605	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563627

C₂

yes

maximal, characteristic, complemented

#14562320

C₂

yes

maximal, complemented

#14562060

C₂

yes

maximal, complemented

#14561956

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#555

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

#11926313

—

#11926290

—

D₄⋊(C₁₉⋊C₈)

—

#11926268

—

C₁₉×#555

—

C₁₉×#555

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#124

—

C₂×C₁₉×#121

—

C₂×C₁₉×#121

C₄

yes

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#117

—

C₂×C₁₉×#117

C₄

yes

—

C₂²×Q₈×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

D₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

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

—

C₂×Q₈×C₁₉

—

C₂×Q₈×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×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

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

#64520

—

100

C₂×C₁₉⋊C₈

—

101

C₂×C₁₉⋊C₈

—

102

#8397

—

maximal, Sylow

103

C₂³×C₁₉

—

104

C₂³×C₁₉

—

105

C₂³×C₁₉

—

106

C₂³×C₁₉

—

107

C₂³×C₁₉

—

108

C₂³×C₁₉

—

109

C₂³×C₁₉

—

110

C₂³×C₁₉

—

111

C₂³×C₁₉

—

112

C₂³×C₁₉

—

113

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

114

Q₈×C₁₉

—

115

D₄×C₁₉

—

116

D₄×C₁₉

—

117

D₄×C₁₉

—

118

D₄×C₁₉

—

119

D₄×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

—

133

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

134

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

135

C₂×C₄×C₁₉

#120

yes

—

136

C₂×C₄×C₁₉

#120

yes

—

137

C₂×C₄×C₁₉

#135

yes

—

138

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

139

C₂×C₄×C₁₉

#137

yes

characteristic

140

C₁₉⋊C₈

—

141

C₁₉⋊C₈

—

142

C₂×#555

D₁₉

yes

characteristic

143

#1800

—

144

#1549

—

145

#1486

—

146

#1460

—

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

—

158

C₂²×C₁₉

—

159

C₂²×C₁₉

#379

yes

characteristic

160

C₂²×C₁₉

#416

yes

characteristic

161

C₂²×C₁₉

#417

yes

characteristic

162

C₄×C₁₉

—

163

C₄×C₁₉

—

164

C₄×C₁₉

—

165

C₄×C₁₉

—

166

C₄×C₁₉

—

167

C₄×C₁₉

#413

yes

—

168

C₄×C₁₉

#449

yes

—

169

C₄×C₁₉

#452

yes

—

170

#555

—

171

#555

—

172

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

173

C₂×#124

—

174

C₂×#121

—

175

C₂×#121

Dic₁₉

yes

—

176

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

177

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

178

C₂×#117

—

179

C₂×#117

Dic₁₉

yes

—

180

#431

—

181

#423

—

182

C₂×#100

—

183

#343

—

184

#332

—

185

D₄⋊C₈

—

186

#323

—

187

C₂×C₁₉

—

188

C₂×C₁₉

—

189

C₂×C₁₉

—

190

C₂×C₁₉

—

191

C₂×C₁₉

#1785

yes

characteristic

192

C₂×C₁₉

#1788

yes

characteristic

193

C₂×C₁₉

#1795

yes

characteristic

194

C₂²×Q₈

—

195

C₂²×D₄

—

196

C₂²×D₄

C₂×Dic₁₉

yes

characteristic

197

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

198

C₂³×C₄

—

199

C₂³×C₄

C₂×Dic₁₉

yes

—

200

C₂×M₁₆

—

201

C₄⋊Q₈

—

202

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

203

#124

—

204

#121

—

205

#121

—

206

#121

—

207

C₄×D₄

—

208

C₄×D₄

—

209

C₄×D₄

—

210

C₄×D₄

C₂²⋊D₁₉

yes

—

211

#117

—

212

#117

—

213

#117

—

214

C₂×C₄⋊C₄

—

215

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

216

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

217

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

218

C₂×C₂²⋊C₄

—

219

C₂×C₂²⋊C₄

—

220

C₂×C₂²⋊C₄

—

221

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

222

C₂×C₄²

—

223

C₂×C₄²

C₂²×D₁₉

yes

characteristic

224

C₄⋊C₈

—

225

C₄⋊C₈

—

226

C₄⋊C₈

—

227

#100

—

228

C₂²⋊C₈

—

229

C₄×C₈

—

230

C₁₉

#8397

yes

characteristic, complemented, Sylow

231

C₂⁴

—

232

C₂⁴

C₂²⋊Dic₁₉

yes

—

233

C₂×Q₈

—

234

C₂×Q₈

—

235

C₂×D₄

—

236

C₂×D₄

—

237

C₂×D₄

—

238

C₂×D₄

—

239

C₂×D₄

—

240

C₂×D₄

—

241

C₂×D₄

—

242

C₂×D₄

—

243

C₂×D₄

C₂²⋊Dic₁₉

yes

—

244

C₂²×C₄

—

245

C₂²×C₄

—

246

C₂²×C₄

—

247

C₂²×C₄

—

248

C₂²×C₄

—

249

C₂²×C₄

—

250

C₂²×C₄

—

251

C₂²×C₄

—

252

C₂²×C₄

—

253

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

254

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

255

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

256

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

257

M₁₆

—

258

M₁₆

—

259

C₂×C₈

—

260

C₂×C₈

—

261

C₄⋊C₄

—

262

C₄⋊C₄

—

263

C₄⋊C₄

—

264

C₄⋊C₄

—

265

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

266

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

267

C₂²⋊C₄

—

268

C₂²⋊C₄

—

269

C₂²⋊C₄

—

270

C₂²⋊C₄

—

271

C₄²

—

272

C₄²

C₂×C₂²⋊D₁₉

yes

—

273

C₄²

C₂×C₂²⋊D₁₉

yes

—

274

C₂³

—

275

C₂³

—

276

C₂³

—

277

C₂³

—

278

C₂³

—

279

C₂³

—

280

C₂³

—

281

C₂³

—

282

C₂³

—

283

C₂³

—

284

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

285

Q₈

—

286

D₄

—

287

D₄

—

288

D₄

—

289

D₄

—

290

D₄

—

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

#10597395

yes

characteristic

305

C₂×C₄

#10597396

yes

—

306

C₂×C₄

#10597397

yes

characteristic

307

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

308

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

309

C₂×C₄

#10597399

yes

—

310

C₂×C₄

#10597399

yes

—

311

C₈

—

152

—

312

C₈

—

152

—

313

C₂²

—

314

C₂²

—

315

C₂²

—

316

C₂²

—

317

C₂²

—

318

C₂²

—

319

C₂²

—

320

C₂²

—

321

C₂²

—

322

C₂²

—

323

C₂²

—

324

C₂²

—

325

C₂²

#11926400

yes

characteristic

326

C₂²

#11926540

yes

characteristic

327

C₂²

#11926545

yes

characteristic

328

C₄

—

329

C₄

—

330

C₄

—

331

C₄

—

332

C₄

—

333

C₄

#11926528

yes

—

334

C₄

#11926689

yes

—

335

C₄

#11926706

yes

—

336

C₂

—

337

C₂

—

338

C₂

—

339

C₂

—

340

C₂

#14563563

yes

characteristic

341

C₂

#14563575

yes

characteristic

342

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×#555	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#555	D₁₉
hypocenter	C₁₉	#8397
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#555

subgroup

G/H

center

C₂²

#11926400

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₂×C₁₉×#555

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×#555

N	H ≅ G/N	type
1. #14563627	C₂	semidirect
2. #14562320	C₂	semidirect
3. #14562060	C₂	semidirect
4. #14561956	C₂	semidirect
230. C₁₉	#8397	semidirect

H ≅ G/N

type

1. #14563627

C₂

semidirect

2. #14562320

C₂

semidirect

3. #14562060

C₂

semidirect

4. #14561956

C₂

semidirect

230. C₁₉

#8397

semidirect

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

subgroup	index
#14563627	2
#14562320	2
#14562060	2
#14561956	2
C₂×C₁₉×#555	2
#8397	19

subgroup

index

C₂×C₁₉×#555

Subgroups — #18074312

Conjugacy classes of subgroups

Complements

Maximal subgroups