Subgroups — #18091237

Order 4864.

894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926586	C₂	1	1	yes	maximal, characteristic
2	#14566259	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926413	C₂	1	1	yes	maximal, characteristic
4	#14563355	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597372	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₉⋊C₄	—	2	2	no	—
12	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926586	—	2	2	no	—
14	#11926586	—	2	2	no	—
15	C₂×#10597275	—	2	1	no	—
16	C₂×#10597274	—	2	1	no	—
17	#11926440	—	2	2	no	—
18	#11926417	—	2	2	no	—
19	#11926413	—	2	1	no	—
20	#11926413	—	2	2	no	—
21	#11926413	—	2	2	no	—
22	#11926409	—	2	1	no	—
23	#11926307	—	2	2	no	—
24	#11926305	—	2	2	no	—
25	#11926305	C₄	1	4	yes	complemented
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#343	—	2	2	no	—
30	C₂³×C₄×C₁₉	D₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	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	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
45	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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×C₂²⋊Dic₁₉	—	2	1	no	—
55	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
56	#10597372	—	2	1	no	—
57	#10597372	—	2	1	no	—
58	#10597372	—	2	1	no	—
59	#10597372	—	2	1	no	—
60	#10597372	—	2	1	no	—
61	#10597372	—	2	1	no	—
62	#10597372	C₂×C₄	1	2	yes	—
63	#10597372	Q₈	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	—	2	1	no	—
67	C₂×C₄⋊Dic₁₉	—	2	1	no	—
68	C₂×C₄⋊Dic₁₉	—	2	1	no	—
69	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
72	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
73	C₂×Dic₁₉⋊C₄	—	2	8	no	—
74	C₂×Dic₁₉⋊C₄	—	2	4	no	—
75	C₂×Dic₁₉⋊C₄	—	4	8	no	—
76	C₂×C₄×Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×C₄×Dic₁₉	—	2	1	no	—
80	C₂×C₄×Dic₁₉	—	2	1	no	—
81	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
83	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
84	C₁₉⋊#95	—	2	4	no	—
85	#10597275	—	2	4	no	—
86	#10597274	—	2	4	no	—
87	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	4	4	no	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×Dic₁₉	—	2	4	no	—
107	C₂²×Dic₁₉	—	2	4	no	—
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	2	2	no	—
112	C₂²×Dic₁₉	—	2	1	no	—
113	C₂²×Dic₁₉	—	2	1	no	—
114	C₂²×Dic₁₉	—	2	2	no	—
115	C₂²×Dic₁₉	—	4	4	no	—
116	C₂²×Dic₁₉	—	4	1	no	—
117	C₂²×Dic₁₉	—	4	1	no	—
118	M₁₆×C₁₉	—	2	2	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	2	2	no	—
121	M₁₆×C₁₉	—	2	2	no	—
122	M₁₆×C₁₉	—	2	2	no	—
123	M₁₆×C₁₉	—	4	1	no	—
124	M₁₆×C₁₉	—	4	1	no	—
125	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	complemented
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	2	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	—	4	1	no	—
135	C₄⋊C₄×C₁₉	—	4	1	no	—
136	C₂²⋊Dic₁₉	—	2	2	no	—
137	C₂²⋊Dic₁₉	—	2	2	no	—
138	C₂²⋊Dic₁₉	—	4	1	no	—
139	C₂²⋊Dic₁₉	—	4	1	no	—
140	C₄⋊Dic₁₉	—	2	2	no	—
141	C₄⋊Dic₁₉	—	2	1	no	—
142	C₄⋊Dic₁₉	—	2	2	no	—
143	C₄⋊Dic₁₉	—	2	1	no	—
144	C₄⋊Dic₁₉	—	2	2	no	—
145	C₄⋊Dic₁₉	—	2	1	no	—
146	C₄⋊Dic₁₉	—	2	1	no	—
147	C₄⋊Dic₁₉	—	4	1	no	—
148	C₄⋊Dic₁₉	—	4	1	no	—
149	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	complemented
150	Dic₁₉⋊C₄	—	4	16	no	—
151	Dic₁₉⋊C₄	—	8	4	no	—
152	C₄×Dic₁₉	—	2	2	no	—
153	C₄×Dic₁₉	—	2	2	no	—
154	C₄×Dic₁₉	—	2	2	no	—
155	C₄×Dic₁₉	—	2	2	no	—
156	C₄×Dic₁₉	—	2	2	no	—
157	C₄×Dic₁₉	—	4	1	no	—
158	C₄×Dic₁₉	—	4	1	no	—
159	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	complemented
160	#11340	—	19	1	no	maximal, Sylow
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₁₉	#120	1	1	yes	characteristic
165	C₂³×C₁₉	#120	1	1	yes	characteristic
166	C₂³×C₁₉	#121	1	1	yes	characteristic
167	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
202	C₂×Dic₁₉	—	2	4	no	—
203	C₂×Dic₁₉	—	2	8	no	—
204	C₂×Dic₁₉	—	2	8	no	—
205	C₂×Dic₁₉	—	2	4	no	—
206	C₂×Dic₁₉	—	2	4	no	—
207	C₂×Dic₁₉	—	2	4	no	—
208	C₂×Dic₁₉	—	4	2	no	—
209	C₂×Dic₁₉	—	4	2	no	—
210	C₂×Dic₁₉	—	4	4	no	—
211	C₂×Dic₁₉	—	4	1	no	—
212	C₂×Dic₁₉	—	4	1	no	—
213	C₂×Dic₁₉	—	4	2	no	—
214	C₂×Dic₁₉	—	4	2	no	—
215	C₂×Dic₁₉	—	4	2	no	—
216	C₂×Dic₁₉	—	8	2	no	—
217	C₂×Dic₁₉	—	8	2	no	—
218	C₈×C₁₉	—	2	4	no	—
219	C₈×C₁₉	—	4	2	no	—
220	C₂×#428	—	19	1	no	—
221	#2317	—	19	1	no	—
222	C₂×#384	—	19	1	no	—
223	C₂×#343	D₁₉	1	1	yes	characteristic
224	#1736	—	19	1	no	—
225	C₂×#339	—	19	1	no	—
226	C₂×#339	—	19	1	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	#385	1	1	yes	characteristic
236	C₂²×C₁₉	#385	1	1	yes	characteristic
237	C₂²×C₁₉	#389	1	1	yes	characteristic
238	C₂²×C₁₉	#392	1	1	yes	characteristic
239	C₂²×C₁₉	#395	1	1	yes	characteristic
240	C₂²×C₁₉	#395	1	1	yes	characteristic
241	C₂²×C₁₉	#398	1	1	yes	characteristic
242	C₂²×C₁₉	#453	1	2	yes	—
243	C₂²×C₁₉	#456	1	2	yes	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	#384	1	1	yes	characteristic
246	C₄×C₁₉	#385	1	1	yes	characteristic
247	C₄×C₁₉	#389	1	1	yes	characteristic
248	C₄×C₁₉	#389	1	1	yes	characteristic
249	C₄×C₁₉	#395	1	1	yes	characteristic
250	C₄×C₁₉	#398	1	1	yes	characteristic
251	C₄×C₁₉	#398	1	1	yes	characteristic
252	C₄×C₁₉	#399	1	1	yes	characteristic
253	Dic₁₉	—	2	8	no	—
254	Dic₁₉	—	4	4	no	—
255	Dic₁₉	—	8	1	no	—
256	Dic₁₉	—	8	2	no	—
257	Dic₁₉	—	8	1	no	—
258	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
259	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
260	C₂×#117	—	19	1	no	—
261	C₂×#117	—	19	1	no	—
262	C₂²×C₄⋊C₄	—	19	1	no	—
263	C₂²×C₄⋊C₄	—	38	2	no	—
264	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
265	C₂²×C₄²	—	19	1	no	—
266	#428	—	38	2	no	—
267	#428	—	38	2	no	—
268	C₂×#107	—	38	1	no	—
269	C₂×#106	—	38	1	no	—
270	#389	—	38	2	no	—
271	#385	—	38	2	no	—
272	#384	—	38	2	no	—
273	#384	—	38	1	no	—
274	#384	—	38	2	no	—
275	#382	—	38	1	no	—
276	#343	—	2	2	no	—
277	#340	—	38	2	no	—
278	#339	—	19	4	no	—
279	#339	—	38	2	no	—
280	C₂×C₁₉	—	2	1	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	2	1	no	—
284	C₂×C₁₉	#1444	1	1	yes	characteristic
285	C₂×C₁₉	#1859	1	2	yes	—
286	C₂×C₁₉	#2002	1	1	yes	characteristic
287	C₂×C₁₉	#2005	1	1	yes	characteristic
288	C₂×C₁₉	#2060	1	2	yes	—
289	C₂³×C₄	—	38	1	no	—
290	C₂³×C₄	—	38	1	no	—
291	C₂³×C₄	D₇₆	1	2	yes	—
292	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
293	C₂×M₁₆	—	2	1	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	Dic₃₈	1	2	yes	—
302	C₂×M₁₆	Dic₃₈	1	2	yes	—
303	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
304	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	#117	—	19	2	no	—
308	#117	—	19	2	no	—
309	#117	—	38	1	no	—
310	#117	—	38	1	no	—
311	#117	—	38	1	no	—
312	#117	—	38	1	no	—
313	#117	—	38	1	no	—
314	#117	—	38	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	19	2	no	—
322	C₂×C₄⋊C₄	—	19	2	no	—
323	C₂×C₄⋊C₄	—	19	1	no	—
324	C₂×C₄⋊C₄	—	19	1	no	—
325	C₂×C₄⋊C₄	—	38	1	no	—
326	C₂×C₄⋊C₄	—	38	1	no	—
327	C₂×C₄⋊C₄	—	38	1	no	—
328	C₂×C₄⋊C₄	—	38	1	no	—
329	C₂×C₄⋊C₄	—	38	8	no	—
330	C₂×C₄⋊C₄	—	38	1	no	—
331	C₂×C₄⋊C₄	—	38	4	no	—
332	C₂×C₄⋊C₄	—	76	8	no	—
333	C₂×C₂²⋊C₄	—	38	1	no	—
334	C₂×C₂²⋊C₄	—	38	1	no	—
335	C₂×C₄²	—	19	2	no	—
336	C₂×C₄²	—	19	2	no	—
337	C₂×C₄²	—	19	2	no	—
338	C₂×C₄²	—	38	1	no	—
339	C₂×C₄²	—	38	1	no	—
340	C₂×C₄²	—	38	1	no	—
341	C₂×C₄²	—	38	1	no	—
342	C₂×C₄²	—	38	1	no	—
343	#107	—	38	4	no	—
344	#106	—	38	4	no	—
345	#95	—	38	4	no	—
346	C₁₉	#11340	1	1	yes	characteristic, complemented, Sylow
347	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	38	4	no	—
353	C₂²×C₄	—	38	4	no	—
354	C₂²×C₄	—	38	2	no	—
355	C₂²×C₄	—	38	2	no	—
356	C₂²×C₄	—	38	2	no	—
357	C₂²×C₄	—	38	2	no	—
358	C₂²×C₄	—	38	2	no	—
359	C₂²×C₄	—	38	1	no	—
360	C₂²×C₄	—	38	1	no	—
361	C₂²×C₄	—	76	4	no	—
362	C₂²×C₄	—	76	1	no	—
363	C₂²×C₄	—	76	1	no	—
364	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
365	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
367	C₂²×C₄	#64541	1	1	yes	characteristic
368	C₂²×C₄	#64541	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
372	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
373	C₂²×C₄	#64543	1	1	yes	characteristic
374	C₂²×C₄	#64543	1	1	yes	characteristic
375	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
376	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	4	1	no	—
384	M₁₆	—	4	1	no	—
385	M₁₆	Dic₁₉⋊C₄	1	4	yes	complemented
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	1	no	—
391	C₂×C₈	—	4	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	19	4	no	—
397	C₄⋊C₄	—	38	2	no	—
398	C₄⋊C₄	—	38	1	no	—
399	C₄⋊C₄	—	38	2	no	—
400	C₄⋊C₄	—	38	1	no	—
401	C₄⋊C₄	—	38	2	no	—
402	C₄⋊C₄	—	38	1	no	—
403	C₄⋊C₄	—	38	1	no	—
404	C₄⋊C₄	—	76	16	no	—
405	C₄⋊C₄	—	76	1	no	—
406	C₄⋊C₄	—	76	1	no	—
407	C₄⋊C₄	—	152	4	no	—
408	C₂²⋊C₄	—	38	2	no	—
409	C₂²⋊C₄	—	38	2	no	—
410	C₂²⋊C₄	—	76	1	no	—
411	C₂²⋊C₄	—	76	1	no	—
412	C₄²	—	19	4	no	—
413	C₄²	—	38	2	no	—
414	C₄²	—	38	2	no	—
415	C₄²	—	38	2	no	—
416	C₄²	—	38	2	no	—
417	C₄²	—	38	2	no	—
418	C₄²	—	76	1	no	—
419	C₄²	—	76	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	#10597315	1	1	yes	characteristic
423	C₂³	C₄×D₇₆	1	1	yes	characteristic
424	C₂³	#10597328	1	1	yes	characteristic
425	C₂³	#10597328	1	1	yes	characteristic
426	C₂³	#10597343	1	1	yes	characteristic
427	C₂³	#10597343	1	1	yes	characteristic
428	C₂³	#10597376	1	1	yes	characteristic
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	38	4	no	—
434	C₂×C₄	—	38	8	no	—
435	C₂×C₄	—	38	4	no	—
436	C₂×C₄	—	38	8	no	—
437	C₂×C₄	—	38	4	no	—
438	C₂×C₄	—	38	4	no	—
439	C₂×C₄	—	76	2	no	—
440	C₂×C₄	—	76	2	no	—
441	C₂×C₄	—	76	4	no	—
442	C₂×C₄	—	76	1	no	—
443	C₂×C₄	—	76	1	no	—
444	C₂×C₄	—	76	2	no	—
445	C₂×C₄	—	76	2	no	—
446	C₂×C₄	—	76	2	no	—
447	C₂×C₄	—	152	2	no	—
448	C₂×C₄	—	152	2	no	—
449	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
450	C₂×C₄	#10597316	1	1	yes	characteristic
451	C₂×C₄	#10597324	1	1	yes	characteristic
452	C₂×C₄	#10597324	1	1	yes	characteristic
453	C₂×C₄	#10597324	1	1	yes	characteristic
454	C₂×C₄	#10597324	1	1	yes	characteristic
455	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
456	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
457	C₂×C₄	#10597329	1	1	yes	characteristic
458	C₂×C₄	#10597329	1	1	yes	characteristic
459	C₂×C₄	#10597330	1	1	yes	characteristic
460	C₂×C₄	#10597330	1	1	yes	characteristic
461	C₂×C₄	#10597334	1	1	yes	characteristic
462	C₂×C₄	#10597334	1	1	yes	characteristic
463	C₂×C₄	#10597334	1	1	yes	characteristic
464	C₂×C₄	#10597334	1	1	yes	characteristic
465	C₂×C₄	#10597335	1	1	yes	characteristic
466	C₂×C₄	#10597335	1	1	yes	characteristic
467	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
468	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
469	C₂×C₄	#10597342	1	1	yes	characteristic
470	C₂×C₄	#10597342	1	1	yes	characteristic
471	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
472	C₂×C₄	#10597370	1	1	yes	characteristic
473	C₂×C₄	#10597381	1	1	yes	characteristic
474	C₂×C₄	#10597383	1	1	yes	characteristic
475	C₂×C₄	#10597386	1	1	yes	characteristic
476	C₂×C₄	#10597390	1	1	yes	characteristic
477	C₈	—	2	4	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	#11926418	1	1	yes	characteristic
488	C₂²	#11926418	1	1	yes	characteristic
489	C₂²	#11926442	1	1	yes	characteristic
490	C₂²	#11926453	1	1	yes	characteristic
491	C₂²	#11926465	1	1	yes	characteristic
492	C₂²	#11926465	1	1	yes	characteristic
493	C₂²	#11926474	1	1	yes	characteristic
494	C₂²	#11926714	1	2	yes	—
495	C₂²	#11926729	1	2	yes	—
496	C₄	—	8	2	no	—
497	C₄	—	38	8	no	—
498	C₄	—	76	4	no	—
499	C₄	—	152	2	no	—
500	C₄	—	152	1	no	—
501	C₄	—	152	1	no	—
502	C₄	#11926413	1	1	yes	characteristic
503	C₄	#11926416	1	1	yes	characteristic
504	C₄	#11926441	1	1	yes	characteristic
505	C₄	#11926441	1	1	yes	characteristic
506	C₄	#11926464	1	1	yes	characteristic
507	C₄	#11926478	1	1	yes	characteristic
508	C₄	#11926478	1	1	yes	characteristic
509	C₄	#11926480	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	#14561899	1	1	yes	characteristic
515	C₂	#14563864	1	2	yes	—
516	C₂	#14564652	1	1	yes	characteristic
517	C₂	#14564673	1	1	yes	characteristic
518	C₂	#14564981	1	2	yes	—

	subgroup	G/H
center	C₂³	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#11340
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
25. #11926305	C₄	semidirect
125. M₁₆×C₁₉	C₄⋊C₄	semidirect
149. C₄⋊Dic₁₉	C₄⋊C₄	semidirect
159. C₄×Dic₁₉	C₄⋊C₄	semidirect
346. C₁₉	#11340	semidirect
385. M₁₆	Dic₁₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926586	2
#14566259	2
C₂×#11926413	2
#14563355	2
C₂×#11926305	2
C₂×C₁₉×#343	2
#11340	19