Subgroups — #18087871

Order 4864.

1208 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	C₂×#11926518	C₂	1	1	yes	maximal, characteristic
3	#14563346	C₂	1	2	yes	maximal, complemented
4	C₂×#11926301	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic
6	#11927027	—	2	4	no	—
7	#11927022	C₄	1	2	yes	complemented
8	#11927019	—	2	2	no	—
9	#11927019	C₄	1	2	yes	complemented
10	#41×Dic₁₉	—	2	4	no	—
11	C₂×#10597372	—	2	2	no	—
12	C₂×#10597372	C₂²	1	2	yes	—
13	C₂×#10597372	C₂²	1	2	yes	—
14	#11926518	—	2	2	no	—
15	#11926518	C₄	1	4	yes	complemented
16	C₂×#10597291	—	2	2	no	—
17	#11926305	—	2	4	no	—
18	#11926301	—	2	4	no	—
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#408	—	2	2	no	—
23	C₁₉×#408	C₄	1	4	yes	complemented
24	C₁₉×#407	—	2	2	no	—
25	C₂×#41×C₁₉	—	2	2	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	C₂×C₄	1	2	yes	—
30	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₉	D₄	1	2	yes	—
32	C₂×#41×C₁₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	D₄	1	2	yes	—
36	C₂³×C₄×C₁₉	D₄	1	2	yes	—
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	—	2	2	no	—
44	C₂×M₁₆×C₁₉	—	2	2	no	—
45	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
48	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
49	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
50	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
51	Q₈×Dic₁₉	—	2	8	no	—
52	D₄×Dic₁₉	—	2	16	no	—
53	D₄×Dic₁₉	—	2	8	no	—
54	#10597372	—	2	4	no	—
55	#10597372	—	2	4	no	—
56	#10597372	—	2	4	no	—
57	#10597372	—	2	2	no	—
58	#10597372	—	2	2	no	—
59	#10597372	—	2	2	no	—
60	#10597372	—	2	2	no	—
61	#10597372	—	2	2	no	—
62	#10597372	C₂×C₄	1	4	yes	—
63	#10597372	C₂×C₄	1	4	yes	complemented
64	#10597372	D₄	1	4	yes	—
65	C₂×C₄⋊Dic₁₉	—	2	4	no	—
66	C₂×C₄⋊Dic₁₉	—	2	2	no	—
67	C₂×C₄⋊Dic₁₉	—	2	2	no	—
68	C₂×C₄×Dic₁₉	—	2	4	no	—
69	C₂×C₄×Dic₁₉	—	2	2	no	—
70	C₂×C₄×Dic₁₉	D₄	1	4	yes	—
71	C₁₉×C₂²⋊C₈	—	2	8	no	—
72	#10597291	—	2	8	no	—
73	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
75	#41×C₁₉	—	2	4	no	—
76	#41×C₁₉	—	2	4	no	—
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	C₂×Q₈×C₁₉	—	2	2	no	—
84	C₂×Q₈×C₁₉	—	2	2	no	—
85	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
86	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	2	no	—
91	C₂×D₄×C₁₉	C₄²	1	2	yes	—
92	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
94	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	2	yes	—
112	C₂²×Dic₁₉	—	2	8	no	—
113	C₂²×Dic₁₉	—	2	4	no	—
114	C₂²×Dic₁₉	—	4	2	no	—
115	M₁₆×C₁₉	—	2	4	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	M₁₆×C₁₉	—	4	1	no	—
118	M₁₆×C₁₉	—	4	2	no	—
119	M₁₆×C₁₉	—	4	1	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	4	no	—
124	C₂×C₈×C₁₉	—	4	2	no	—
125	C₂²⋊Dic₁₉	—	2	8	no	—
126	C₂²⋊Dic₁₉	—	2	4	no	—
127	C₂²⋊Dic₁₉	—	2	4	no	—
128	C₂²⋊Dic₁₉	—	2	4	no	—
129	C₂²⋊Dic₁₉	—	4	2	no	—
130	C₄⋊Dic₁₉	—	2	8	no	—
131	C₄⋊Dic₁₉	—	2	4	no	—
132	C₄⋊Dic₁₉	—	2	4	no	—
133	C₄⋊Dic₁₉	—	2	4	no	—
134	C₄⋊Dic₁₉	—	4	2	no	—
135	C₄×Dic₁₉	—	2	8	no	—
136	C₄×Dic₁₉	—	2	4	no	—
137	C₄×Dic₁₉	—	2	4	no	—
138	C₄×Dic₁₉	—	4	2	no	—
139	C₄×Dic₁₉	C₂²⋊C₄	1	8	yes	—
140	#10743	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	#95	1	4	yes	—
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₉	#120	1	2	yes	—
150	C₂³×C₁₉	#123	1	2	yes	—
151	Q₈×C₁₉	—	2	4	no	—
152	Q₈×C₁₉	—	2	4	no	—
153	D₄×C₁₉	—	2	8	no	—
154	D₄×C₁₉	—	2	8	no	—
155	D₄×C₁₉	—	2	4	no	—
156	D₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	#95	1	4	yes	—
164	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#117	1	2	yes	—
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	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#121	1	2	yes	—
177	C₂×C₄×C₁₉	#121	1	2	yes	—
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
182	C₂×Dic₁₉	—	2	8	no	—
183	C₂×Dic₁₉	—	4	4	no	—
184	C₂×Dic₁₉	—	8	4	no	—
185	C₂×Dic₁₉	—	8	8	no	—
186	C₂×Dic₁₉	—	8	4	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	2	no	—
189	#3428	—	19	1	no	—
190	C₂×#410	—	19	1	no	—
191	#2879	D₁₉	1	1	yes	characteristic
192	#1733	—	19	2	no	—
193	C₂×H(3,ℤ/4)	—	19	2	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	4	2	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	4	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
204	C₂²×C₁₉	#379	1	1	yes	characteristic
205	C₂²×C₁₉	#381	1	1	yes	characteristic
206	C₂²×C₁₉	#385	1	2	yes	—
207	C₂²×C₁₉	#386	1	2	yes	—
208	C₄×C₁₉	—	2	4	no	—
209	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
210	C₄×C₁₉	#380	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	Dic₁₉	—	4	8	no	—
216	Dic₁₉	—	8	4	no	—
217	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
218	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
219	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
220	#520	—	38	4	no	—
221	#519	—	19	2	no	—
222	#518	—	19	2	no	—
223	#518	—	38	2	no	—
224	C₄×#41	—	38	4	no	—
225	C₂×#117	—	19	2	no	—
226	C₂×#117	—	19	2	no	—
227	C₂×#117	—	38	2	no	—
228	#410	—	19	4	no	—
229	#410	—	38	2	no	—
230	C₂×#99	—	38	2	no	—
231	#408	—	2	2	no	—
232	#408	Dic₁₉	1	4	yes	complemented
233	#407	—	2	2	no	—
234	#339	—	38	4	no	—
235	H(3,ℤ/4)	—	38	4	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	2	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	4	4	no	—
242	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	Dic₃₈	1	2	yes	—
248	C₂×#41	C₄×D₁₉	1	2	yes	—
249	C₂×#41	C₂×Dic₁₉	1	2	yes	—
250	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
251	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
252	C₂²×D₄	C₄×D₁₉	1	1	yes	characteristic
253	C₂²×D₄	D₇₆	1	2	yes	—
254	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
255	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	complemented
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂×Dic₁₉	1	2	yes	complemented
266	C₄×Q₈	—	38	8	no	—
267	C₄×D₄	—	38	8	no	—
268	C₄×D₄	—	38	16	no	—
269	#117	—	19	4	no	—
270	#117	—	19	4	no	—
271	#117	—	19	4	no	—
272	#117	—	38	4	no	—
273	#117	—	38	4	no	—
274	#117	—	38	4	no	—
275	#117	—	38	2	no	—
276	#117	—	38	2	no	—
277	#117	—	38	2	no	—
278	#117	—	38	2	no	—
279	#117	—	38	2	no	—
280	C₂×C₄⋊C₄	—	38	4	no	—
281	C₂×C₄⋊C₄	—	38	2	no	—
282	C₂×C₄⋊C₄	—	38	2	no	—
283	C₂×C₂²⋊C₄	—	38	4	no	—
284	C₂×C₂²⋊C₄	—	38	2	no	—
285	C₂×C₂²⋊C₄	—	38	2	no	—
286	C₂×C₄²	—	19	4	no	—
287	C₂×C₄²	—	38	4	no	—
288	C₂×C₄²	—	38	2	no	—
289	#99	—	38	8	no	—
290	C₂²⋊C₈	—	2	8	no	—
291	C₁₉	#10743	1	1	yes	characteristic, complemented, Sylow
292	C₂⁴	(C₂×D₁₉)⋊C₄	1	2	yes	—
293	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
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	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
305	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
311	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
312	C₂×D₄	C₄⋊Dic₁₉	1	4	yes	—
313	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	38	8	no	—
319	C₂²×C₄	—	38	4	no	—
320	C₂²×C₄	—	76	2	no	—
321	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
322	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
323	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
324	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₁₉	1	2	yes	—
328	C₂²×C₄	D₄×D₁₉	1	2	yes	—
329	C₂²×C₄	#64543	1	2	yes	—
330	C₂²×C₄	#64543	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
334	M₁₆	—	2	4	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₄⋊C₄	—	38	8	no	—
345	C₄⋊C₄	—	38	4	no	—
346	C₄⋊C₄	—	38	4	no	—
347	C₄⋊C₄	—	38	4	no	—
348	C₄⋊C₄	—	76	2	no	—
349	C₂²⋊C₄	—	38	8	no	—
350	C₂²⋊C₄	—	38	4	no	—
351	C₂²⋊C₄	—	38	4	no	—
352	C₂²⋊C₄	—	38	4	no	—
353	C₂²⋊C₄	—	76	2	no	—
354	C₄²	—	19	8	no	—
355	C₄²	—	38	8	no	—
356	C₄²	—	38	4	no	—
357	C₄²	—	38	4	no	—
358	C₄²	—	76	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	2	no	—
363	C₂³	C₁₉⋊#95	1	4	yes	—
364	C₂³	#10597328	1	2	yes	—
365	C₂³	#10597332	1	2	yes	—
366	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
367	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
368	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	2	4	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	8	no	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	38	8	no	—
382	C₂×C₄	—	76	4	no	—
383	C₂×C₄	—	152	4	no	—
384	C₂×C₄	—	152	8	no	—
385	C₂×C₄	—	152	4	no	—
386	C₂×C₄	C₁₉⋊#95	1	4	yes	—
387	C₂×C₄	#10597323	1	2	yes	—
388	C₂×C₄	#10597324	1	2	yes	—
389	C₂×C₄	#10597324	1	2	yes	—
390	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
391	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
392	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
393	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
396	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
397	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
398	C₂×C₄	#10597381	1	1	yes	characteristic
399	C₂×C₄	#10597381	1	1	yes	characteristic
400	C₂×C₄	#10597383	1	1	yes	characteristic
401	C₂×C₄	#10597383	1	1	yes	characteristic
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	2	no	—
406	C₈	—	4	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	8	2	no	—
416	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
417	C₂²	#11926399	1	1	yes	characteristic
418	C₂²	#11926405	1	1	yes	characteristic
419	C₂²	#11926419	1	2	yes	—
420	C₂²	#11926421	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	76	8	no	—
423	C₄	—	152	4	no	—
424	C₄	C₂²⋊C₄×Dic₁₉	1	2	yes	—
425	C₄	#11926402	1	2	yes	—
426	C₄	#11926416	1	1	yes	characteristic
427	C₄	#11926416	1	1	yes	characteristic
428	C₄	#11926424	1	1	yes	characteristic
429	C₄	#11926424	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	2	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	2	2	no	—
435	C₂	—	4	4	no	—
436	C₂	#14561857	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926424
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2879	C₂
socle	C₂×C₁₉	C₂²⋊#95
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2879	D₁₉
hypocenter	C₁₉	#10743
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #2879

Complements

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

N	H ≅ G/N	type
3. #14563346	C₂	semidirect
4. C₂×#11926301	C₂	semidirect
7. #11927022	C₄	semidirect
9. #11927019	C₄	semidirect
15. #11926518	C₄	semidirect
23. C₁₉×#408	C₄	semidirect
45. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
47. C₂²×C₈×C₁₉	C₂×C₄	semidirect
63. #10597372	C₂×C₄	semidirect
232. #408	Dic₁₉	semidirect
263. C₂×M₁₆	C₂×Dic₁₉	semidirect
265. C₂²×C₈	C₂×Dic₁₉	semidirect
291. C₁₉	#10743	semidirect

Maximal subgroups

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

subgroup	index
#14576838	2
C₂×#11926518	2
#14563346	2
C₂×#11926301	2
C₁₉×#2879	2
#10743	19