Subgroups — #18087939

Order 4864.

1192 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14576838	C₂	1	1	yes	maximal, characteristic
2	#14572080	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926316	C₂	1	2	yes	maximal, complemented
4	C₂×#11926315	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#413	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	1	yes	characteristic
7	C₂²×#64520	C₂²	1	1	yes	characteristic
8	#11927027	—	2	4	no	—
9	#11927022	—	2	1	no	—
10	#11927019	—	2	1	no	—
11	#11927019	C₄	1	4	yes	—
12	#41×Dic₁₉	—	2	4	no	—
13	C₂×#10597372	—	2	2	no	—
14	C₂×#10597372	C₂²	1	2	yes	—
15	#11926511	—	2	2	no	—
16	#11926511	C₄	1	4	yes	complemented
17	#11926508	—	2	2	no	—
18	#11926316	—	2	4	no	—
19	#11926315	—	2	4	no	—
20	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
22	C₁₉×#413	—	2	2	no	—
23	C₁₉×#413	C₄	1	4	yes	complemented
24	C₂×C₁₉×#101	—	2	1	no	—
25	C₂×C₁₉×#100	—	2	1	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	—	2	2	no	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×#41×C₁₉	D₄	1	2	yes	—
33	C₂×#41×C₁₉	Q₈	1	2	yes	—
34	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₉	—	2	2	no	—
40	C₂×M₁₆×C₁₉	—	2	2	no	—
41	C₂×M₁₆×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
47	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
48	Q₈×Dic₁₉	—	2	8	no	—
49	D₄×Dic₁₉	—	2	8	no	—
50	D₄×Dic₁₉	—	2	16	no	—
51	#10597372	—	2	4	no	—
52	#10597372	—	2	4	no	—
53	#10597372	—	2	4	no	—
54	#10597372	—	2	2	no	—
55	#10597372	—	2	2	no	—
56	#10597372	D₄	1	4	yes	—
57	#10597372	D₄	1	4	yes	—
58	C₂×C₄⋊Dic₁₉	—	2	4	no	—
59	C₂×C₄⋊Dic₁₉	—	2	2	no	—
60	C₂×C₄×Dic₁₉	—	2	4	no	—
61	C₂×C₄×Dic₁₉	—	2	2	no	—
62	C₂×#64520	—	2	2	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	2	no	—
67	C₂×#64520	—	2	2	no	—
68	C₂×#64520	—	2	2	no	—
69	C₂×#64520	C₂×C₄	1	2	yes	complemented
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
72	C₁₉×#101	—	2	4	no	—
73	C₁₉×#100	—	2	4	no	—
74	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
75	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	#41×C₁₉	—	2	4	no	—
80	#41×C₁₉	—	2	4	no	—
81	#41×C₁₉	—	2	4	no	—
82	#41×C₁₉	—	2	4	no	—
83	#41×C₁₉	—	2	4	no	—
84	#41×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	2	no	—
93	C₂×D₄×C₁₉	C₄²	1	4	yes	—
94	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
95	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
96	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	2	yes	—
113	C₂²×C₄×C₁₉	#41	1	2	yes	—
114	C₂²×Dic₁₉	—	2	8	no	—
115	C₂²×Dic₁₉	—	2	4	no	—
116	M₁₆×C₁₉	—	2	4	no	—
117	M₁₆×C₁₉	—	2	4	no	—
118	M₁₆×C₁₉	—	4	2	no	—
119	M₁₆×C₁₉	—	4	2	no	—
120	C₂×C₈×C₁₉	—	2	4	no	—
121	C₂×C₈×C₁₉	—	4	2	no	—
122	C₂×C₈×C₁₉	—	4	2	no	—
123	C₂²⋊Dic₁₉	—	2	8	no	—
124	C₂²⋊Dic₁₉	—	2	4	no	—
125	C₂²⋊Dic₁₉	C₂²⋊C₄	1	8	yes	—
126	C₄⋊Dic₁₉	—	2	8	no	—
127	C₄⋊Dic₁₉	—	2	4	no	—
128	C₄⋊Dic₁₉	—	2	4	no	—
129	C₄×Dic₁₉	—	2	8	no	—
130	C₄×Dic₁₉	—	2	4	no	—
131	C₄×Dic₁₉	—	2	4	no	—
132	#64520	—	2	4	no	—
133	#64520	—	4	1	no	—
134	#64520	—	4	1	no	—
135	#64520	—	4	2	no	—
136	#64520	—	4	1	no	—
137	#64520	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	4	no	—
141	C₂×C₁₉⋊C₈	—	4	2	no	—
142	#10756	—	19	1	no	maximal, Sylow
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	2	no	—
147	C₂³×C₁₉	#95	1	4	yes	—
148	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
149	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₉	#117	1	2	yes	—
153	Q₈×C₁₉	—	2	4	no	—
154	Q₈×C₁₉	—	2	4	no	—
155	D₄×C₁₉	—	2	8	no	—
156	D₄×C₁₉	—	2	8	no	—
157	D₄×C₁₉	—	2	4	no	—
158	D₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	#95	1	4	yes	—
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₉	#120	1	2	yes	—
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#121	1	2	yes	—
178	C₂×C₄×C₁₉	#121	1	2	yes	—
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₁₉	#123	1	2	yes	—
182	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₂×Dic₁₉	—	2	8	no	—
185	C₂×Dic₁₉	—	8	4	no	—
186	C₂×Dic₁₉	—	8	8	no	—
187	C₈×C₁₉	—	4	4	no	—
188	C₁₉⋊C₈	—	4	2	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	#3428	—	19	1	no	—
191	C₂×#413	D₁₉	1	1	yes	characteristic
192	#2879	—	19	1	no	—
193	C₂×#344	—	19	2	no	—
194	C₂×#344	—	19	2	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	4	2	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	1	no	—
199	C₂²×C₁₉	—	4	1	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	4	no	—
203	C₂²×C₁₉	—	8	2	no	—
204	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
205	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
206	C₂²×C₁₉	#379	1	1	yes	characteristic
207	C₂²×C₁₉	#380	1	2	yes	—
208	C₂²×C₁₉	#381	1	1	yes	characteristic
209	C₄×C₁₉	—	2	4	no	—
210	C₄×C₁₉	#385	1	2	yes	—
211	C₄×C₁₉	#385	1	1	yes	characteristic
212	C₄×C₁₉	#385	1	1	yes	characteristic
213	C₄×C₁₉	#386	1	1	yes	characteristic
214	C₄×C₁₉	#386	1	1	yes	characteristic
215	C₄×C₁₉	#386	1	2	yes	—
216	Dic₁₉	—	4	8	no	—
217	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
218	C₂²×M₁₆	—	19	1	no	—
219	C₂²×M₁₆	—	19	1	no	—
220	C₂²×M₁₆	C₂×D₁₉	1	2	yes	—
221	#520	—	38	4	no	—
222	#519	—	38	1	no	—
223	#518	—	19	4	no	—
224	#518	—	38	1	no	—
225	C₄×#41	—	38	4	no	—
226	C₂×#117	—	19	2	no	—
227	C₂×#117	—	38	2	no	—
228	#413	—	2	2	no	—
229	#413	Dic₁₉	1	4	yes	complemented
230	C₂×#101	—	2	1	no	—
231	C₂×#100	—	2	1	no	—
232	#408	—	19	4	no	—
233	#408	—	38	2	no	—
234	#407	—	38	2	no	—
235	#344	—	38	4	no	—
236	#344	—	38	4	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	2	2	no	—
242	C₂×C₁₉	—	4	4	no	—
243	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	Dic₃₈	1	2	yes	—
249	C₂×#41	C₄×D₁₉	1	2	yes	—
250	C₂×#41	C₂×Dic₁₉	1	2	yes	—
251	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
252	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂²×D₄	C₄×D₁₉	1	2	yes	—
254	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂³×C₄	D₇₆	1	2	yes	—
256	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	19	2	no	—
263	C₂×M₁₆	—	38	1	no	—
264	C₂×M₁₆	—	38	1	no	—
265	C₂×M₁₆	—	38	2	no	—
266	C₂×M₁₆	—	38	2	no	—
267	C₂×M₁₆	—	38	1	no	—
268	C₂×M₁₆	—	38	2	no	—
269	C₂×M₁₆	—	38	2	no	—
270	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	complemented
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	19	2	no	—
273	C₂²×C₈	—	38	1	no	—
274	C₄×Q₈	—	38	8	no	—
275	C₄×D₄	—	38	16	no	—
276	C₄×D₄	—	38	8	no	—
277	#117	—	19	4	no	—
278	#117	—	19	4	no	—
279	#117	—	38	4	no	—
280	#117	—	38	4	no	—
281	#117	—	38	4	no	—
282	#117	—	38	2	no	—
283	#117	—	38	2	no	—
284	C₂×C₄⋊C₄	—	38	4	no	—
285	C₂×C₄⋊C₄	—	38	2	no	—
286	C₂×C₂²⋊C₄	—	19	4	no	—
287	C₂×C₂²⋊C₄	—	38	4	no	—
288	C₂×C₄²	—	38	4	no	—
289	C₂×C₄²	—	38	2	no	—
290	#101	—	2	4	no	—
291	#100	—	2	4	no	—
292	C₂²⋊C₈	—	38	8	no	—
293	C₁₉	#10756	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
295	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
307	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₄×Dic₁₉	1	4	yes	—
313	C₂×D₄	Dic₁₉⋊C₄	1	4	yes	—
314	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
315	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	38	8	no	—
321	C₂²×C₄	—	38	4	no	—
322	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
323	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
324	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
325	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₁₉	1	2	yes	—
329	C₂²×C₄	D₄×D₁₉	1	2	yes	—
330	C₂²×C₄	#64543	1	2	yes	—
331	C₂²×C₄	#64543	1	2	yes	—
332	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
335	M₁₆	—	2	4	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	4	2	no	—
338	M₁₆	—	4	2	no	—
339	M₁₆	—	38	4	no	—
340	M₁₆	—	76	2	no	—
341	M₁₆	—	76	1	no	—
342	M₁₆	—	76	1	no	—
343	M₁₆	—	76	1	no	—
344	M₁₆	—	76	1	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	38	4	no	—
349	C₂×C₈	—	38	2	no	—
350	C₂×C₈	—	38	2	no	—
351	C₂×C₈	—	76	2	no	—
352	C₄⋊C₄	—	38	8	no	—
353	C₄⋊C₄	—	38	4	no	—
354	C₄⋊C₄	—	38	4	no	—
355	C₂²⋊C₄	—	19	8	no	—
356	C₂²⋊C₄	—	38	8	no	—
357	C₂²⋊C₄	—	38	4	no	—
358	C₄²	—	38	8	no	—
359	C₄²	—	38	4	no	—
360	C₄²	—	38	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	8	1	no	—
364	C₂³	—	8	2	no	—
365	C₂³	C₁₉⋊#95	1	4	yes	—
366	C₂³	#10597323	1	2	yes	—
367	C₂³	C₂²⋊C₄×D₁₉	1	2	yes	—
368	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
369	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
370	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	38	8	no	—
384	C₂×C₄	—	152	4	no	—
385	C₂×C₄	—	152	8	no	—
386	C₂×C₄	C₁₉⋊#95	1	4	yes	—
387	C₂×C₄	#10597324	1	2	yes	—
388	C₂×C₄	#10597324	1	2	yes	—
389	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
390	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
391	C₂×C₄	#10597328	1	1	yes	characteristic
392	C₂×C₄	#10597328	1	1	yes	characteristic
393	C₂×C₄	#10597332	1	1	yes	characteristic
394	C₂×C₄	#10597332	1	1	yes	characteristic
395	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
399	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
400	C₂×C₄	#10597381	1	2	yes	—
401	C₂×C₄	#10597383	1	2	yes	—
402	C₂×C₄	#10597385	1	2	yes	—
403	C₂×C₄	#10597385	1	2	yes	—
404	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
405	C₈	—	4	4	no	—
406	C₈	—	76	2	no	—
407	C₈	—	76	2	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
418	C₂²	C₂²⋊C₄×Dic₁₉	1	2	yes	—
419	C₂²	#11926399	1	1	yes	characteristic
420	C₂²	#11926402	1	2	yes	—
421	C₂²	#11926405	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	76	8	no	—
424	C₄	#11926416	1	2	yes	—
425	C₄	#11926419	1	1	yes	characteristic
426	C₄	#11926419	1	1	yes	characteristic
427	C₄	#11926421	1	1	yes	characteristic
428	C₄	#11926421	1	1	yes	characteristic
429	C₄	#11926424	1	2	yes	—
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	2	2	no	—
435	C₂	—	4	4	no	—
436	C₂	#14561857	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926421
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#413	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#413	D₁₉
hypocenter	C₁₉	#10756
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
3. C₂×#11926316	C₂	semidirect
4. C₂×#11926315	C₂	semidirect
16. #11926511	C₄	semidirect
23. C₁₉×#413	C₄	semidirect
44. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
69. C₂×#64520	C₂×C₄	semidirect
71. C₂²×C₁₉⋊C₈	C₂×C₄	semidirect
229. #413	Dic₁₉	semidirect
270. C₂×M₁₆	C₂×Dic₁₉	semidirect
293. C₁₉	#10756	semidirect

Maximal subgroups

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

subgroup	index
#14576838	2
#14572080	2
C₂×#11926316	2
C₂×#11926315	2
C₂×C₁₉×#413	2
#10756	19