Subgroups — #18074393

Order 4864.

768 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563445	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562242	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562143	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562121	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562069	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562052	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3514	C₂	1	1	yes	maximal, characteristic
8	#11926601	C₂²	1	1	yes	characteristic, complemented
9	#11926597	C₂²	1	1	yes	characteristic, complemented
10	C₂×#10597294	—	2	1	no	—
11	C₄×#64520	C₂²	1	1	yes	characteristic, complemented
12	#11926390	C₂²	1	1	yes	characteristic, complemented
13	#11926303	—	2	1	no	—
14	#11926286	—	2	1	no	—
15	#11926284	—	2	1	no	—
16	#11926281	—	2	1	no	—
17	#11926278	—	2	1	no	—
18	#11926278	—	2	2	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#559	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#555	—	2	1	no	—
25	C₁₉×#551	—	2	2	no	—
26	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#548	—	2	1	no	—
28	C₁₉×#546	—	2	1	no	—
29	C₁₉×#546	—	2	1	no	—
30	D₄²×C₁₉	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#542	—	2	1	no	—
32	C₁₉×#538	—	2	2	no	—
33	C₁₉×#532	C₂²	1	1	yes	characteristic
34	C₁₉×#529	—	2	1	no	—
35	C₁₉×#529	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#124	—	2	1	no	—
37	C₁₉×#518	—	2	1	no	—
38	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#126	—	2	2	no	—
48	C₁₉×#126	—	2	2	no	—
49	C₁₉×#126	—	2	1	no	—
50	C₁₉×#125	D₄	1	1	yes	characteristic
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	—	2	2	no	—
53	C₁₉×#124	—	2	2	no	—
54	C₁₉×#124	—	2	1	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#124	—	2	1	no	—
57	C₁₉×#124	—	2	1	no	—
58	C₁₉×#124	D₄	1	1	yes	characteristic
59	C₁₉×#123	—	2	2	no	—
60	C₁₉×#123	—	2	2	no	—
61	C₁₉×#123	—	2	2	no	—
62	C₁₉×#123	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	1	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₉×#121	—	2	2	no	—
69	C₁₉×#121	—	2	2	no	—
70	C₁₉×#121	—	2	1	no	—
71	C₁₉×#121	—	2	1	no	—
72	C₁₉×#121	—	2	1	no	—
73	C₁₉×#121	D₄	1	1	yes	characteristic
74	C₁₉×#121	D₄	1	2	yes	—
75	C₁₉×#120	—	2	2	no	—
76	C₁₉×#120	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	1	no	—
78	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	—	2	2	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	2	1	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	—	2	1	no	—
87	C₄×D₄×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	2	1	no	—
89	C₄×D₄×C₁₉	—	2	1	no	—
90	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
93	C₄×D₄×C₁₉	D₄	1	2	yes	—
94	C₁₉×#117	—	2	2	no	—
95	C₁₉×#117	—	2	1	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄×Dic₁₉	—	2	1	no	—
105	C₂×#64520	—	2	1	no	—
106	#10597294	—	2	4	no	—
107	C₁₉⋊#95	—	2	1	no	—
108	C₁₉⋊#95	—	2	1	no	—
109	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
111	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
112	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
113	#10597260	—	2	1	no	—
114	#10597260	—	2	1	no	—
115	C₄×C₁₉⋊C₈	—	2	1	no	—
116	C₄×C₁₉⋊C₈	—	2	1	no	—
117	C₂⁴×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	4	1	no	—
120	#41×C₁₉	—	8	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	8	2	no	—
124	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×Dic₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
160	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
162	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	2	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	1	no	—
172	C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	1	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₁₉	—	2	2	no	—
191	C₄×Dic₁₉	—	4	1	no	—
192	#64520	—	2	2	no	—
193	#64520	—	4	1	no	—
194	C₂×C₁₉⋊C₈	—	4	1	no	—
195	C₂×C₁₉⋊C₈	—	4	1	no	—
196	C₂×C₁₉⋊C₈	—	4	1	no	—
197	#8412	—	19	1	no	maximal, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	2	no	—
201	C₂³×C₁₉	—	4	4	no	—
202	C₂³×C₁₉	—	8	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	#120	1	1	yes	characteristic
205	Q₈×C₁₉	—	2	1	no	—
206	Q₈×C₁₉	—	2	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	8	2	no	—
210	D₄×C₁₉	—	2	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	4	2	no	—
214	D₄×C₁₉	—	4	2	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	8	1	no	—
219	D₄×C₁₉	—	8	2	no	—
220	D₄×C₁₉	—	8	2	no	—
221	D₄×C₁₉	#104	1	2	yes	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	8	1	no	—
238	C₂×C₄×C₁₉	—	8	2	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	—	8	2	no	—
241	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×Dic₁₉	—	4	2	no	—
248	C₂×Dic₁₉	—	8	1	no	—
249	C₂×Dic₁₉	—	8	1	no	—
250	C₁₉⋊C₈	—	4	2	no	—
251	C₁₉⋊C₈	—	8	1	no	—
252	C₁₉⋊C₈	—	8	1	no	—
253	#3514	D₁₉	1	1	yes	characteristic
254	#1759	—	19	1	no	—
255	#1529	—	19	1	no	—
256	#1505	—	19	1	no	—
257	#1500	—	19	1	no	—
258	#1488	—	19	1	no	—
259	#1484	—	19	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	4	1	no	—
265	C₂²×C₁₉	—	4	1	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	16	4	no	—
273	C₂²×C₁₉	#379	1	1	yes	characteristic
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	2	1	no	—
276	C₄×C₁₉	—	2	1	no	—
277	C₄×C₁₉	—	2	1	no	—
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	2	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
287	C₄×C₁₉	#421	1	1	yes	characteristic
288	Dic₁₉	—	8	2	no	—
289	#559	Dic₁₉	1	1	yes	characteristic, complemented
290	#556	Dic₁₉	1	1	yes	characteristic, complemented
291	#555	—	2	1	no	—
292	#551	—	2	2	no	—
293	D₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
294	#548	—	2	1	no	—
295	#546	—	2	1	no	—
296	#546	—	2	1	no	—
297	D₄²	Dic₁₉	1	1	yes	characteristic, complemented
298	#542	—	2	1	no	—
299	#538	—	2	2	no	—
300	#532	C₂×D₁₉	1	1	yes	characteristic
301	#529	—	2	1	no	—
302	#529	C₂×D₁₉	1	1	yes	characteristic
303	C₂×#124	—	2	1	no	—
304	#518	—	2	1	no	—
305	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
306	#432	—	19	1	no	—
307	#431	—	19	1	no	—
308	C₂×#104	—	38	1	no	—
309	C₄×M₁₆	—	19	1	no	—
310	#376	—	19	1	no	—
311	#339	—	38	1	no	—
312	#330	—	38	1	no	—
313	#329	—	38	1	no	—
314	#328	—	38	1	no	—
315	#327	—	38	1	no	—
316	#327	—	38	2	no	—
317	Q₈⋊C₈	—	38	1	no	—
318	D₄⋊C₈	—	38	2	no	—
319	D₄⋊C₈	—	38	1	no	—
320	C₂×C₁₉	—	4	1	no	—
321	C₂×C₁₉	—	4	2	no	—
322	C₂×C₁₉	—	8	2	no	—
323	C₂×C₁₉	—	8	1	no	—
324	C₂×C₁₉	#1789	1	1	yes	characteristic
325	C₂×C₁₉	#1794	1	1	yes	characteristic
326	C₂×C₁₉	#1795	1	1	yes	characteristic
327	C₂×#41	—	2	1	no	—
328	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂×M₁₆	—	38	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
335	#127	C₂×Dic₁₉	1	1	yes	characteristic
336	#126	—	2	2	no	—
337	#126	—	2	2	no	—
338	#126	—	2	1	no	—
339	#125	C₂²⋊D₁₉	1	1	yes	characteristic
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	—	2	2	no	—
343	#124	—	2	1	no	—
344	#124	—	2	1	no	—
345	#124	—	2	1	no	—
346	#124	—	2	1	no	—
347	#124	C₂²⋊D₁₉	1	1	yes	characteristic
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	#123	—	2	2	no	—
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	C₂²⋊D₁₉	1	1	yes	characteristic
363	#121	C₂²⋊D₁₉	1	2	yes	—
364	#120	—	2	2	no	—
365	#120	—	2	2	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
368	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
369	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
380	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
381	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
382	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
383	#117	—	2	2	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂²⋊D₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	38	1	no	—
393	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
394	C₄⋊C₈	—	38	1	no	—
395	C₄⋊C₈	—	38	1	no	—
396	#104	—	38	4	no	—
397	C₂²⋊C₈	—	38	1	no	—
398	C₂²⋊C₈	—	38	1	no	—
399	#97	—	38	1	no	—
400	#97	—	38	1	no	—
401	C₄×C₈	—	38	1	no	—
402	C₄×C₈	—	38	1	no	—
403	#95	—	38	1	no	—
404	#95	—	38	1	no	—
405	C₁₉	#8412	1	1	yes	characteristic, complemented, Sylow
406	C₂⁴	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	4	1	no	—
409	#41	—	8	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	8	2	no	—
413	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
414	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	—	8	2	no	—
425	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
426	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
427	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	76	1	no	—
436	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
439	M₁₆	—	38	2	no	—
440	M₁₆	—	76	1	no	—
441	C₂×C₈	—	76	1	no	—
442	C₂×C₈	—	76	1	no	—
443	C₂×C₈	—	76	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
454	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
455	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
456	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
457	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	38	2	no	—
481	C₄²	—	76	1	no	—
482	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
483	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
484	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
485	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	8	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	#10597399	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	8	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	1	no	—
508	D₄	—	8	2	no	—
509	D₄	#10597294	1	2	yes	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	76	2	no	—
530	C₂×C₄	—	152	1	no	—
531	C₂×C₄	—	152	1	no	—
532	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
534	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
535	C₂×C₄	#10597399	1	1	yes	characteristic
536	C₂×C₄	#10597399	1	1	yes	characteristic
537	C₂×C₄	#10597399	1	1	yes	characteristic
538	C₈	—	76	2	no	—
539	C₈	—	152	1	no	—
540	C₈	—	152	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	16	4	no	—
554	C₂²	#11926400	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	152	2	no	—
568	C₄	C₂×#10597294	1	1	yes	characteristic
569	C₄	#11926561	1	1	yes	characteristic
570	C₂	—	4	1	no	—
571	C₂	—	4	2	no	—
572	C₂	—	8	1	no	—
573	C₂	—	8	2	no	—
574	C₂	#14563579	1	1	yes	characteristic
575	C₂	#14563599	1	1	yes	characteristic
576	C₂	#14563605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3514	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3514	D₁₉
hypocenter	C₁₉	#8412
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3514

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #14563445	C₂	semidirect
2. #14562242	C₂	semidirect
3. #14562143	C₂	semidirect
4. #14562121	C₂	semidirect
5. #14562069	C₂	semidirect
6. #14562052	C₂	semidirect
8. #11926601	C₂²	semidirect
9. #11926597	C₂²	semidirect
11. C₄×#64520	C₂²	semidirect
12. #11926390	C₂²	semidirect
22. C₁₉×#559	C₄	semidirect
23. C₁₉×#556	C₄	semidirect
26. D₄×Q₈×C₁₉	C₄	semidirect
30. D₄²×C₁₉	C₄	semidirect
289. #559	Dic₁₉	semidirect
290. #556	Dic₁₉	semidirect
293. D₄×Q₈	Dic₁₉	semidirect
297. D₄²	Dic₁₉	semidirect
405. C₁₉	#8412	semidirect

Maximal subgroups

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

subgroup	index
#14563445	2
#14562242	2
#14562143	2
#14562121	2
#14562069	2
#14562052	2
C₁₉×#3514	2
#8412	19