Subgroups — #18088256

Order 4864.

734 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926308	C₂	1	1	yes	maximal, characteristic
3	#14563351	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	#14563331	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₉	—	2	2	no	—
13	C₂×C₈×Dic₁₉	—	2	2	no	—
14	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
15	#11926308	C₄	1	4	yes	complemented
16	#11926306	C₄	1	4	yes	complemented
17	#11926305	—	2	2	no	—
18	#11926303	—	2	2	no	—
19	#11926298	—	2	2	no	—
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₁₉×#336	—	2	2	no	—
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	—	2	1	no	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂²×C₈×C₁₉	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₉	D₄	1	2	yes	—
39	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
40	C₁₉×#117	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
48	#10597372	—	2	1	no	—
49	#10597372	—	2	1	no	—
50	#10597372	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
59	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	C₂×C₄	1	2	yes	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	C₂²×C₁₉⋊C₈	—	2	1	no	—
68	C₂²×C₁₉⋊C₈	—	2	1	no	—
69	C₂²×C₁₉⋊C₈	—	2	1	no	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
72	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₈×Dic₁₉	—	2	8	no	—
75	C₂⁴×C₁₉	#41	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×Dic₁₉	—	2	8	no	—
92	C₂²×Dic₁₉	—	2	2	no	—
93	C₂²×Dic₁₉	—	2	2	no	—
94	C₂²×Dic₁₉	—	2	2	no	—
95	C₂²×Dic₁₉	—	2	2	no	—
96	M₁₆×C₁₉	—	2	2	no	—
97	M₁₆×C₁₉	—	2	2	no	—
98	M₁₆×C₁₉	—	4	1	no	—
99	M₁₆×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₂²⋊C₄×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₂²⋊Dic₁₉	—	4	1	no	—
117	C₂²⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	2	2	no	—
119	C₄⋊Dic₁₉	—	2	2	no	—
120	C₄×Dic₁₉	—	2	2	no	—
121	C₄×Dic₁₉	—	2	2	no	—
122	C₄×Dic₁₉	—	2	2	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
126	#64520	—	2	2	no	—
127	#64520	—	2	2	no	—
128	#64520	—	4	1	no	—
129	#64520	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	4	1	no	—
138	C₂×C₁₉⋊C₈	—	4	1	no	—
139	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
140	#10818	—	19	1	no	maximal, Sylow
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	#117	1	1	yes	characteristic
143	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
144	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
145	C₂³×C₁₉	#123	1	1	yes	characteristic
146	C₂³×C₁₉	#123	1	1	yes	characteristic
147	C₂³×C₁₉	#126	1	1	yes	characteristic
148	C₂³×C₁₉	#126	1	1	yes	characteristic
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
179	C₂×Dic₁₉	—	2	8	no	—
180	C₂×Dic₁₉	—	2	8	no	—
181	C₂×Dic₁₉	—	2	8	no	—
182	C₂×Dic₁₉	—	2	4	no	—
183	C₂×Dic₁₉	—	4	2	no	—
184	C₂×Dic₁₉	—	4	4	no	—
185	C₈×C₁₉	—	2	4	no	—
186	C₈×C₁₉	—	4	2	no	—
187	C₁₉⋊C₈	—	2	4	no	—
188	C₁₉⋊C₈	—	4	2	no	—
189	C₂²×C₄×C₈	—	19	1	no	—
190	C₂×#341	—	19	1	no	—
191	#1735	—	19	1	no	—
192	C₂×#339	—	19	1	no	—
193	C₂×#339	—	19	1	no	—
194	#1729	—	19	1	no	—
195	#1729	D₁₉	1	1	yes	characteristic
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	2	no	—
199	C₂²×C₁₉	—	2	2	no	—
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₁₉	#381	1	1	yes	characteristic
204	C₂²×C₁₉	#383	1	1	yes	characteristic
205	C₂²×C₁₉	#387	1	1	yes	characteristic
206	C₂²×C₁₉	#387	1	1	yes	characteristic
207	C₂²×C₁₉	#388	1	1	yes	characteristic
208	C₂²×C₁₉	#388	1	1	yes	characteristic
209	C₂²×C₁₉	#443	1	4	yes	—
210	C₄×C₁₉	—	8	2	no	—
211	C₄×C₁₉	#376	1	1	yes	characteristic
212	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₄×C₁₉	#380	1	1	yes	characteristic
214	C₄×C₁₉	#382	1	1	yes	characteristic
215	C₄×C₁₉	#387	1	1	yes	characteristic
216	C₄×C₁₉	#387	1	1	yes	characteristic
217	C₄×C₁₉	#388	1	1	yes	characteristic
218	C₄×C₁₉	#388	1	1	yes	characteristic
219	Dic₁₉	—	2	8	no	—
220	Dic₁₉	—	8	2	no	—
221	C₂²×M₁₆	—	19	1	no	—
222	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
223	C₂³×C₈	—	19	1	no	—
224	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
225	C₂×#117	—	19	1	no	—
226	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
227	C₂²×C₄²	—	19	1	no	—
228	C₂×C₄×C₈	—	19	4	no	—
229	C₂×C₄×C₈	—	38	2	no	—
230	C₂×C₄×C₈	—	38	2	no	—
231	#341	—	19	4	no	—
232	#340	—	19	4	no	—
233	#339	—	38	2	no	—
234	#339	—	38	2	no	—
235	#336	—	2	2	no	—
236	#336	—	38	2	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	2	1	no	—
239	C₂×C₁₉	—	2	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	#1434	1	1	yes	characteristic
242	C₂×C₁₉	#1772	1	2	yes	—
243	C₂×C₁₉	#1937	1	2	yes	—
244	C₂×C₁₉	#1937	1	2	yes	—
245	C₂³×C₄	—	38	1	no	—
246	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	19	2	no	—
253	C₂×M₁₆	—	38	1	no	—
254	C₂×M₁₆	—	38	1	no	—
255	C₂×M₁₆	—	38	1	no	—
256	C₂×M₁₆	—	38	1	no	—
257	C₂×M₁₆	—	38	1	no	—
258	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	19	2	no	—
265	C₂²×C₈	—	19	2	no	—
266	C₂²×C₈	—	19	2	no	—
267	C₂²×C₈	—	38	1	no	—
268	C₂²×C₈	—	38	1	no	—
269	C₂²×C₈	—	38	1	no	—
270	C₂²×C₈	—	38	1	no	—
271	C₂²×C₈	—	38	1	no	—
272	C₂²×C₈	Dic₃₈	1	2	yes	—
273	C₂²×C₈	C₄×D₁₉	1	2	yes	—
274	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	—	2	1	no	—
278	#117	—	2	1	no	—
279	#117	—	38	1	no	—
280	#117	—	38	1	no	—
281	#117	—	38	1	no	—
282	#117	—	38	1	no	—
283	C₂×C₄⋊C₄	—	19	2	no	—
284	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	38	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	19	2	no	—
289	C₂×C₄²	—	19	2	no	—
290	C₂×C₄²	—	19	2	no	—
291	C₂×C₄²	—	38	1	no	—
292	C₂×C₄²	—	38	1	no	—
293	C₂×C₄²	—	38	1	no	—
294	C₂×C₄²	—	38	1	no	—
295	C₄×C₈	—	38	8	no	—
296	C₁₉	#10818	1	1	yes	characteristic, complemented, Sylow
297	C₂⁴	#64541	1	1	yes	characteristic
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	38	8	no	—
300	C₂²×C₄	—	38	2	no	—
301	C₂²×C₄	—	38	2	no	—
302	C₂²×C₄	—	38	2	no	—
303	C₂²×C₄	—	38	2	no	—
304	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
308	C₂²×C₄	#64541	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	#64543	1	1	yes	characteristic
312	C₂²×C₄	#64543	1	1	yes	characteristic
313	C₂²×C₄	#64543	1	1	yes	characteristic
314	C₂²×C₄	#64543	1	1	yes	characteristic
315	C₂²×C₄	#64545	1	1	yes	characteristic
316	C₂²×C₄	#64545	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	38	2	no	—
323	M₁₆	—	38	2	no	—
324	M₁₆	—	76	1	no	—
325	M₁₆	—	76	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	19	4	no	—
336	C₂×C₈	—	38	2	no	—
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	38	2	no	—
339	C₂×C₈	—	38	2	no	—
340	C₂×C₈	—	38	2	no	—
341	C₂×C₈	—	38	2	no	—
342	C₂×C₈	—	38	2	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	1	no	—
345	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	38	2	no	—
349	C₄⋊C₄	—	38	2	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	76	1	no	—
353	C₂²⋊C₄	—	76	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	19	4	no	—
357	C₄²	—	38	2	no	—
358	C₄²	—	38	2	no	—
359	C₄²	—	38	2	no	—
360	C₄²	—	76	1	no	—
361	C₄²	—	76	1	no	—
362	C₂³	—	2	4	no	—
363	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
364	C₂³	#10597318	1	1	yes	characteristic
365	C₂³	#10597325	1	1	yes	characteristic
366	C₂³	#10597329	1	1	yes	characteristic
367	C₂³	#10597340	1	1	yes	characteristic
368	C₂³	#10597344	1	1	yes	characteristic
369	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	38	8	no	—
373	C₂×C₄	—	38	8	no	—
374	C₂×C₄	—	38	8	no	—
375	C₂×C₄	—	38	4	no	—
376	C₂×C₄	—	76	4	no	—
377	C₂×C₄	—	76	2	no	—
378	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
379	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
380	C₂×C₄	#10597323	1	1	yes	characteristic
381	C₂×C₄	#10597323	1	1	yes	characteristic
382	C₂×C₄	#10597323	1	1	yes	characteristic
383	C₂×C₄	#10597324	1	1	yes	characteristic
384	C₂×C₄	#10597324	1	1	yes	characteristic
385	C₂×C₄	#10597325	1	1	yes	characteristic
386	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
387	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
389	C₂×C₄	#10597329	1	1	yes	characteristic
390	C₂×C₄	#10597336	1	1	yes	characteristic
391	C₂×C₄	#10597336	1	1	yes	characteristic
392	C₂×C₄	#10597338	1	1	yes	characteristic
393	C₂×C₄	#10597338	1	1	yes	characteristic
394	C₂×C₄	#10597338	1	1	yes	characteristic
395	C₂×C₄	#10597338	1	1	yes	characteristic
396	C₂×C₄	#10597339	1	1	yes	characteristic
397	C₂×C₄	#10597339	1	1	yes	characteristic
398	C₂×C₄	#10597340	1	1	yes	characteristic
399	C₂×C₄	#10597344	1	1	yes	characteristic
400	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
401	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
402	C₂×C₄	#10597382	1	1	yes	characteristic
403	C₂×C₄	#10597385	1	1	yes	characteristic
404	C₂×C₄	#10597385	1	1	yes	characteristic
405	C₂×C₄	#10597393	1	1	yes	characteristic
406	C₈	—	2	4	no	—
407	C₈	—	4	2	no	—
408	C₈	—	38	4	no	—
409	C₈	—	76	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
417	C₂²	#11926406	1	1	yes	characteristic
418	C₂²	#11926411	1	1	yes	characteristic
419	C₂²	#11926427	1	1	yes	characteristic
420	C₂²	#11926431	1	1	yes	characteristic
421	C₂²	#11926434	1	1	yes	characteristic
422	C₂²	#11926438	1	1	yes	characteristic
423	C₂²	#11926659	1	4	yes	—
424	C₄	—	8	2	no	—
425	C₄	—	38	8	no	—
426	C₄	—	152	2	no	—
427	C₄	#11926389	1	1	yes	characteristic
428	C₄	#11926391	1	1	yes	characteristic
429	C₄	#11926402	1	1	yes	characteristic
430	C₄	#11926409	1	1	yes	characteristic
431	C₄	#11926427	1	1	yes	characteristic
432	C₄	#11926431	1	1	yes	characteristic
433	C₄	#11926434	1	1	yes	characteristic
434	C₄	#11926438	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	#14561861	1	1	yes	characteristic
440	C₂	#14563515	1	2	yes	—
441	C₂	#14564338	1	2	yes	—
442	C₂	#14564342	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1729	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1729	D₁₉
hypocenter	C₁₉	#10818
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×Dic₁₉	C₄	semidirect
15. #11926308	C₄	semidirect
16. #11926306	C₄	semidirect
296. C₁₉	#10818	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₁₉	2
C₂×#11926308	2
#14563351	2
C₂×#11926305	2
C₂×#11926303	2
#14563331	2
C₁₉×#1729	2
#10818	19