Subgroups — #18082544

Order 4864.

566 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597334	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	1	yes	maximal, characteristic
5	#14561475	C₂	1	1	yes	maximal, characteristic
6	#14561474	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597334	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₃₈	—	2	1	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	1	no	—
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₁₉	—	2	1	no	—
15	C₂×C₈×Dic₁₉	—	2	1	no	—
16	#11926448	—	2	1	no	—
17	#11926443	C₄	1	1	yes	characteristic
18	#11926441	—	2	1	no	—
19	#11926440	C₄	1	1	yes	characteristic
20	#11926413	C₄	1	1	yes	characteristic
21	C₄×Dic₁₉⋊C₄	—	2	1	no	—
22	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×Dic₃₈	—	2	1	no	—
28	C₂²×C₈×C₁₉	—	2	1	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×Dic₁₉⋊C₄	—	2	1	no	—
38	C₂×Dic₁₉⋊C₄	—	2	1	no	—
39	C₂×Dic₁₉⋊C₄	—	2	1	no	—
40	C₂×Dic₁₉⋊C₄	—	2	1	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	—	2	1	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	#10597334	—	2	2	no	—
51	#10597334	C₈	1	4	yes	complemented
52	C₄×Dic₃₈	—	4	2	no	—
53	C₄×Dic₃₈	—	4	2	no	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₄×C₈×C₁₉	Q₈	1	2	yes	complemented
58	C₁₉×#95	—	2	1	no	—
59	C₁₉⋊#95	—	2	1	no	—
60	C₁₉⋊#95	—	2	1	no	—
61	C₁₉⋊#95	—	2	1	no	—
62	Dic₁₉⋊C₈	—	4	2	no	—
63	Dic₁₉⋊C₈	—	4	2	no	—
64	C₈×Dic₁₉	—	2	4	no	—
65	C₈×Dic₁₉	—	2	4	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₄×C₁₉⋊C₈	Q₈	1	2	yes	complemented
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Dic₃₈	—	2	4	no	—
82	C₂×Dic₃₈	—	4	2	no	—
83	C₂×Dic₃₈	—	4	2	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	2	no	—
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₂×C₈×C₁₉	—	4	1	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
94	C₄²×C₁₉	—	4	1	no	—
95	C₄²×C₁₉	—	4	1	no	—
96	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₄²×C₁₉	#41	1	1	yes	characteristic
99	C₄²×C₁₉	#41	1	1	yes	characteristic
100	C₄⋊Dic₁₉	—	2	1	no	—
101	C₄⋊Dic₁₉	—	2	1	no	—
102	C₄⋊Dic₁₉	—	2	1	no	—
103	C₄⋊Dic₁₉	—	4	2	no	—
104	C₄⋊Dic₁₉	C₂×C₈	1	2	yes	—
105	Dic₁₉⋊C₄	—	2	4	no	—
106	Dic₁₉⋊C₄	—	4	2	no	—
107	Dic₁₉⋊C₄	—	4	2	no	—
108	Dic₁₉⋊C₄	—	4	2	no	—
109	C₄×Dic₁₉	—	2	1	no	—
110	C₄×Dic₁₉	—	2	1	no	—
111	C₄×Dic₁₉	—	2	2	no	—
112	C₄×Dic₁₉	—	2	2	no	—
113	C₄×Dic₁₉	—	4	1	no	—
114	C₄×Dic₁₉	—	4	1	no	—
115	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
116	C₄×Dic₁₉	M₁₆	1	2	yes	—
117	C₄×Dic₁₉	D₈	1	2	yes	—
118	C₄×Dic₁₉	SD₁₆	1	2	yes	—
119	C₄×Dic₁₉	SD₁₆	1	2	yes	—
120	C₄×Dic₁₉	Q₁₆	1	2	yes	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	2	2	no	—
123	C₂×C₁₉⋊C₈	—	2	2	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	#9870	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	2	no	—
156	C₂×Dic₁₉	—	4	1	no	—
157	C₂×Dic₁₉	—	4	1	no	—
158	C₂×Dic₁₉	—	4	1	no	—
159	C₂×Dic₁₉	—	4	1	no	—
160	C₂×Dic₁₉	—	4	1	no	—
161	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
162	C₂×Dic₁₉	C₂²⋊C₈	1	2	yes	—
163	C₂×Dic₁₉	#102	1	2	yes	—
164	C₂×Dic₁₉	#102	1	2	yes	—
165	C₂×Dic₁₉	#103	1	2	yes	—
166	C₂×Dic₁₉	#103	1	2	yes	—
167	C₂×Dic₁₉	#104	1	2	yes	—
168	C₂×Dic₁₉	#104	1	2	yes	—
169	Dic₃₈	—	4	8	no	—
170	C₈×C₁₉	—	2	4	no	—
171	C₈×C₁₉	—	8	1	no	—
172	C₁₉⋊C₈	—	2	4	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	C₄×C₄⋊Q₈	—	19	1	no	—
175	#1842	—	19	1	no	—
176	C₄²×C₈	—	19	1	no	—
177	#1279	—	19	1	no	—
178	#1279	—	19	1	no	—
179	#1279	—	19	1	no	—
180	#1279	D₁₉	1	1	yes	characteristic
181	C₂²×C₁₉	#391	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
183	C₂²×C₁₉	#408	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	8	1	no	—
192	C₄×C₁₉	C₈×Q₈	1	1	yes	characteristic
193	C₄×C₁₉	C₈×Q₈	1	1	yes	characteristic
194	C₄×C₁₉	#446	1	1	yes	characteristic
195	C₄×C₁₉	#446	1	1	yes	characteristic
196	C₄×C₁₉	#486	1	1	yes	characteristic
197	C₄×C₁₉	#487	1	1	yes	characteristic
198	C₄×C₁₉	#498	1	1	yes	characteristic
199	C₄×C₁₉	#500	1	1	yes	characteristic
200	Dic₁₉	—	2	2	no	—
201	Dic₁₉	—	2	2	no	—
202	Dic₁₉	—	4	2	no	—
203	Dic₁₉	—	8	1	no	—
204	Dic₁₉	D₄⋊C₈	1	4	yes	—
205	Dic₁₉	Q₈⋊C₈	1	4	yes	—
206	C₂×C₄⋊Q₈	—	19	1	no	—
207	C₂×C₄×Q₈	—	38	1	no	—
208	C₂×C₄⋊C₈	—	19	1	no	—
209	C₂×C₄⋊C₈	—	38	1	no	—
210	C₂×C₄⋊C₈	—	38	1	no	—
211	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₄×C₈	—	19	1	no	—
213	C₂×C₄×C₈	—	38	1	no	—
214	C₂×C₄×C₈	—	38	1	no	—
215	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
216	#391	—	38	1	no	—
217	#389	—	19	1	no	—
218	#389	—	19	1	no	—
219	#389	—	38	1	no	—
220	#384	—	19	1	no	—
221	C₄×C₄⋊C₄	—	19	1	no	—
222	C₄×C₄⋊C₄	—	38	1	no	—
223	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
224	C₄³	—	19	1	no	—
225	C₂×C₁₉	C₂×D₄⋊C₈	1	1	yes	characteristic
226	C₂×C₁₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
227	C₂×C₁₉	#1492	1	1	yes	characteristic
228	C₂×C₁₉	#1493	1	1	yes	characteristic
229	C₂×C₁₉	#1984	1	1	yes	characteristic
230	C₂×C₁₉	#1990	1	1	yes	characteristic
231	C₂×C₁₉	#1994	1	1	yes	characteristic
232	C₂²×Q₈	—	38	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	38	1	no	—
236	C₂²×C₈	—	38	1	no	—
237	C₄⋊Q₈	—	19	4	no	—
238	C₄⋊Q₈	—	38	2	no	—
239	C₄×Q₈	—	76	2	no	—
240	C₄×Q₈	—	76	2	no	—
241	C₂×C₄⋊C₄	—	19	1	no	—
242	C₂×C₄⋊C₄	—	19	1	no	—
243	C₂×C₄⋊C₄	—	38	1	no	—
244	C₂×C₄⋊C₄	—	38	1	no	—
245	C₂×C₄⋊C₄	—	38	1	no	—
246	C₂×C₄⋊C₄	—	38	1	no	—
247	C₂×C₄⋊C₄	—	38	1	no	—
248	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	19	1	no	—
252	C₂×C₄²	—	19	1	no	—
253	C₂×C₄²	—	19	1	no	—
254	C₂×C₄²	—	19	1	no	—
255	C₂×C₄²	—	19	1	no	—
256	C₂×C₄²	—	19	1	no	—
257	C₂×C₄²	—	38	1	no	—
258	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	38	1	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	—	76	2	no	—
264	C₄⋊C₈	—	76	2	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	19	2	no	—
267	C₄×C₈	—	38	4	no	—
268	C₄×C₈	—	38	4	no	—
269	C₄×C₈	—	38	1	no	—
270	C₄×C₈	Dic₃₈	1	2	yes	complemented
271	#95	—	2	1	no	—
272	#95	—	38	1	no	—
273	#95	—	38	1	no	—
274	#95	—	38	1	no	—
275	C₁₉	#9870	1	1	yes	characteristic, complemented, Sylow
276	C₂×Q₈	—	38	4	no	—
277	C₂×Q₈	—	76	2	no	—
278	C₂×Q₈	—	76	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	19	1	no	—
282	C₂²×C₄	—	19	1	no	—
283	C₂²×C₄	—	19	1	no	—
284	C₂²×C₄	—	19	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
289	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	38	2	no	—
297	C₂×C₈	—	38	2	no	—
298	C₂×C₈	—	38	2	no	—
299	C₂×C₈	—	76	1	no	—
300	C₂×C₈	—	76	1	no	—
301	C₂×C₈	—	76	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	19	2	no	—
306	C₄⋊C₄	—	38	4	no	—
307	C₄⋊C₄	—	38	1	no	—
308	C₄⋊C₄	—	38	1	no	—
309	C₄⋊C₄	—	38	1	no	—
310	C₄⋊C₄	—	76	2	no	—
311	C₄⋊C₄	—	76	2	no	—
312	C₄⋊C₄	—	76	2	no	—
313	C₄⋊C₄	—	76	2	no	—
314	C₄⋊C₄	C₈×D₁₉	1	2	yes	—
315	C₄²	—	4	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	19	2	no	—
318	C₄²	—	19	2	no	—
319	C₄²	—	19	2	no	—
320	C₄²	—	19	2	no	—
321	C₄²	—	19	2	no	—
322	C₄²	—	19	2	no	—
323	C₄²	—	38	2	no	—
324	C₄²	—	38	2	no	—
325	C₄²	—	38	1	no	—
326	C₄²	—	38	1	no	—
327	C₄²	—	76	1	no	—
328	C₄²	—	76	1	no	—
329	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
330	C₄²	#64541	1	1	yes	characteristic
331	C₄²	#64543	1	1	yes	characteristic
332	C₄²	Q₈×D₁₉	1	1	yes	characteristic
333	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
334	Q₈	—	76	8	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	19	2	no	—
344	C₂×C₄	—	19	2	no	—
345	C₂×C₄	—	19	2	no	—
346	C₂×C₄	—	19	2	no	—
347	C₂×C₄	—	19	2	no	—
348	C₂×C₄	—	19	2	no	—
349	C₂×C₄	—	19	2	no	—
350	C₂×C₄	—	19	2	no	—
351	C₂×C₄	—	38	1	no	—
352	C₂×C₄	—	38	1	no	—
353	C₂×C₄	—	38	1	no	—
354	C₂×C₄	—	38	1	no	—
355	C₂×C₄	—	38	2	no	—
356	C₂×C₄	—	76	1	no	—
357	C₂×C₄	—	76	1	no	—
358	C₂×C₄	—	76	1	no	—
359	C₂×C₄	—	76	1	no	—
360	C₂×C₄	—	76	1	no	—
361	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
362	C₂×C₄	#10597324	1	1	yes	characteristic
363	C₂×C₄	#10597331	1	1	yes	characteristic
364	C₂×C₄	#10597333	1	1	yes	characteristic
365	C₂×C₄	#10597334	1	1	yes	characteristic
366	C₂×C₄	#10597342	1	1	yes	characteristic
367	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
368	C₂×C₄	#10597347	1	1	yes	characteristic
369	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597353	1	1	yes	characteristic
371	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
374	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	8	1	no	—
377	C₈	—	38	4	no	—
378	C₈	—	152	1	no	—
379	C₂²	#11926448	1	1	yes	characteristic
380	C₂²	C₂²⋊C₈×D₁₉	1	1	yes	characteristic
381	C₂²	#11926509	1	1	yes	characteristic
382	C₂²	#102×D₁₉	1	1	yes	characteristic
383	C₂²	#103×D₁₉	1	1	yes	characteristic
384	C₂²	#104×D₁₉	1	1	yes	characteristic
385	C₂²	#104×D₁₉	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	1	no	—
390	C₄	—	19	4	no	—
391	C₄	—	19	4	no	—
392	C₄	—	38	2	no	—
393	C₄	—	38	2	no	—
394	C₄	—	76	2	no	—
395	C₄	—	152	1	no	—
396	C₄	#11926668	1	1	yes	characteristic
397	C₄	C₈×Dic₃₈	1	1	yes	characteristic
398	C₄	#11926672	1	1	yes	characteristic
399	C₄	#11926673	1	1	yes	characteristic
400	C₄	#11926889	1	1	yes	characteristic
401	C₄	#11926893	1	1	yes	characteristic
402	C₄	#11926941	1	1	yes	characteristic
403	C₄	#11926948	1	1	yes	characteristic
404	C₂	D₁₉×D₄⋊C₈	1	1	yes	characteristic
405	C₂	D₁₉×Q₈⋊C₈	1	1	yes	characteristic
406	C₂	#14562084	1	1	yes	characteristic
407	C₂	#14562088	1	1	yes	characteristic
408	C₂	#14564569	1	1	yes	characteristic
409	C₂	#14564594	1	1	yes	characteristic
410	C₂	#14564610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#9870
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
51. #10597334	C₈	semidirect
57. C₄×C₈×C₁₉	Q₈	semidirect
69. C₄×C₁₉⋊C₈	Q₈	semidirect
270. C₄×C₈	Dic₃₈	semidirect
275. C₁₉	#9870	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597334	2
#14563786	2
C₄×C₈×Dic₁₉	2
#14561476	2
#14561475	2
#14561474	2
C₁₉×#1279	2
#9870	19