Subgroups — #18074152

Order 4864.

782 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563734	C₂	1	2	yes	maximal, complemented
2	C₄×#10597291	C₂	1	1	yes	maximal, characteristic
3	#14562155	C₂	1	2	yes	maximal, complemented
4	#14561973	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#556	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597291	—	2	1	no	—
7	#11926508	C₂²	1	2	yes	—
8	C₄×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
9	#11926311	—	2	1	no	—
10	#11926303	—	2	4	no	—
11	#11926281	—	2	4	no	—
12	#11926270	—	2	1	no	—
13	#11926268	—	2	1	no	—
14	C₁₉×#556	—	2	4	no	—
15	C₁₉×#556	—	2	4	no	—
16	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#126	—	2	1	no	—
18	C₂×C₁₉×#126	—	2	1	no	—
19	C₂×C₁₉×#124	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#117	C₄	1	1	yes	characteristic, complemented
26	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×C₄⋊Q₈	—	2	2	no	—
33	C₁₉×C₄⋊Q₈	—	2	2	no	—
34	C₁₉×#126	—	2	8	no	—
35	C₁₉×#126	—	2	8	no	—
36	C₁₉×#124	—	2	8	no	—
37	C₁₉×C₂²⋊Q₈	—	2	2	no	—
38	C₁₉×C₂²⋊Q₈	—	2	2	no	—
39	C₁₉×C₂²⋊Q₈	—	2	2	no	—
40	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
41	C₄×Q₈×C₁₉	—	2	8	no	—
42	C₄×Q₈×C₁₉	—	2	2	no	—
43	C₄×Q₈×C₁₉	—	2	2	no	—
44	C₄×D₄×C₁₉	—	2	2	no	—
45	C₄×D₄×C₁₉	—	2	2	no	—
46	C₁₉×#117	—	2	2	no	—
47	C₁₉×#117	—	2	2	no	—
48	C₁₉×#117	—	2	2	no	—
49	C₁₉×#117	D₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
69	C₂×C₄×Dic₁₉	—	2	2	no	—
70	C₂×#64520	—	2	2	no	—
71	#10597291	—	2	4	no	—
72	C₁₉⋊#95	—	2	2	no	—
73	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
75	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×Q₈×C₁₉	—	4	2	no	—
81	C₂×Q₈×C₁₉	—	4	2	no	—
82	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	1	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	4	2	no	—
94	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	2	4	no	—
103	C₄⋊C₄×C₁₉	—	2	4	no	—
104	C₄⋊C₄×C₁₉	—	2	4	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	4	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
112	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂²⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	4	no	—
116	C₂²⋊C₄×C₁₉	—	2	4	no	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	2	4	no	—
120	C₄²×C₁₉	—	2	4	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	4	no	—
124	C₂²⋊Dic₁₉	—	2	4	no	—
125	C₂²⋊Dic₁₉	—	4	2	no	—
126	C₄×Dic₁₉	—	4	4	no	—
127	#64520	—	4	4	no	—
128	C₂×C₁₉⋊C₈	—	4	2	no	—
129	#8365	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	4	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₁₉	#120	1	2	yes	—
141	Q₈×C₁₉	—	4	2	no	—
142	Q₈×C₁₉	—	4	8	no	—
143	Q₈×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	1	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	#104	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#120	1	2	yes	—
171	C₂×Dic₁₉	—	4	4	no	—
172	C₂×Dic₁₉	—	8	2	no	—
173	C₂×Dic₁₉	—	8	2	no	—
174	C₁₉⋊C₈	—	8	2	no	—
175	C₂×#556	D₁₉	1	1	yes	characteristic
176	#1826	—	19	2	no	—
177	C₄×#99	—	19	1	no	—
178	#1508	—	19	2	no	—
179	#1465	—	19	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	#379	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
194	C₂²×C₁₉	#421	1	1	yes	characteristic
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	2	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	4	1	no	—
201	C₄×C₁₉	—	4	2	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	#410	1	2	yes	—
205	Dic₁₉	—	8	4	no	—
206	#556	—	2	4	no	—
207	#556	—	2	4	no	—
208	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic, complemented
209	C₂×#126	—	2	1	no	—
210	C₂×#126	—	2	1	no	—
211	C₂×#124	—	2	1	no	—
212	C₂×C₂²⋊Q₈	Dic₁₉	1	1	yes	characteristic, complemented
213	C₂×C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
214	C₂×C₄×Q₈	—	2	1	no	—
215	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
216	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
217	C₂×#117	Dic₁₉	1	1	yes	characteristic, complemented
218	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
219	C₂×#99	—	38	1	no	—
220	#407	—	19	2	no	—
221	C₄×C₂²⋊C₄	—	19	2	no	—
222	#342	—	38	1	no	—
223	#339	—	38	4	no	—
224	#328	—	38	4	no	—
225	#324	—	38	1	no	—
226	#323	—	38	1	no	—
227	C₂×C₁₉	—	2	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	4	2	no	—
230	C₂×C₁₉	—	8	1	no	—
231	C₂×C₁₉	#1782	1	1	yes	characteristic
232	C₂×C₁₉	#1789	1	1	yes	characteristic
233	C₂×C₁₉	#1796	1	1	yes	characteristic
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
239	C₂×M₁₆	—	38	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	#126	—	2	8	no	—
243	#126	—	2	8	no	—
244	#124	—	2	8	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
249	C₄×Q₈	—	2	8	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	—	2	2	no	—
257	#117	C₂²⋊D₁₉	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	38	2	no	—
271	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	38	2	no	—
277	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
278	#99	—	38	4	no	—
279	C₂²⋊C₈	—	38	2	no	—
280	C₂²⋊C₈	—	38	2	no	—
281	#95	—	38	2	no	—
282	C₁₉	#8365	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
284	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	76	2	no	—
303	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
310	M₁₆	—	76	4	no	—
311	C₂×C₈	—	76	2	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
321	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
322	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	38	4	no	—
330	C₂²⋊C₄	—	76	2	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	76	4	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
347	C₂³	#10597399	1	2	yes	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	8	no	—
350	Q₈	—	4	2	no	—
351	D₄	—	4	4	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	76	4	no	—
375	C₂×C₄	—	152	2	no	—
376	C₂×C₄	—	152	2	no	—
377	C₂×C₄	#10597294	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
380	C₂×C₄	#10597399	1	2	yes	—
381	C₈	—	152	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	#11926400	1	1	yes	characteristic
395	C₂²	C₂×#10597294	1	1	yes	characteristic
396	C₂²	#11926561	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	152	4	no	—
407	C₄	#11926518	1	2	yes	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	4	2	no	—
411	C₂	—	8	1	no	—
412	C₂	#14563553	1	1	yes	characteristic
413	C₂	#14563579	1	1	yes	characteristic
414	C₂	#14563610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926400
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#556	C₂
socle	C₂²×C₁₉	#379
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#556	D₁₉
hypocenter	C₁₉	#8365
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#556

Complements

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

N	H ≅ G/N	type
1. #14563734	C₂	semidirect
3. #14562155	C₂	semidirect
16. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
20. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
23. C₂×C₄×Q₈×C₁₉	C₄	semidirect
25. C₂×C₁₉×#117	C₄	semidirect
208. C₂×C₄⋊Q₈	Dic₁₉	semidirect
212. C₂×C₂²⋊Q₈	Dic₁₉	semidirect
215. C₂×C₄×Q₈	Dic₁₉	semidirect
217. C₂×#117	Dic₁₉	semidirect
282. C₁₉	#8365	semidirect

Maximal subgroups

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

subgroup	index
#14563734	2
C₄×#10597291	2
#14562155	2
#14561973	2
C₂×C₁₉×#556	2
#8365	19