Subgroups — #18088406

Order 4864.

802 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×#11926567	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14566038	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926316	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926315	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926314	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926567	—	2	1	no	—
13	#11926567	—	2	1	no	—
14	#11926567	—	2	2	no	—
15	C₂×Dic₁₉⋊C₈	C₄	1	4	yes	complemented
16	M₁₆×Dic₁₉	—	2	1	no	—
17	M₁₆×Dic₁₉	—	2	1	no	—
18	M₁₆×Dic₁₉	C₄	1	2	yes	complemented
19	M₁₆×Dic₁₉	C₄	1	2	yes	complemented
20	C₂×#10597272	—	2	1	no	—
21	C₂×C₈×Dic₁₉	—	2	1	no	—
22	#11926413	—	2	1	no	—
23	#11926409	—	2	1	no	—
24	#11926402	C₄	1	4	yes	—
25	C₄×Dic₁₉⋊C₄	—	2	2	no	—
26	#11926316	—	2	2	no	—
27	#11926315	—	2	2	no	—
28	#11926314	—	2	2	no	—
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#344	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
46	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₁₉×#117	—	2	1	no	—
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	—	2	1	no	—
52	C₁₉×#117	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
57	#10597372	—	2	1	no	—
58	#10597372	—	2	1	no	—
59	#10597372	—	2	1	no	—
60	#10597372	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×Dic₁₉⋊C₄	—	2	4	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
70	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	C₂×C₄	1	2	yes	—
83	C₂×#64520	D₄	1	2	yes	—
84	C₂×#64520	Q₈	1	2	yes	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₉⋊#95	—	2	4	no	—
88	#10597272	—	2	2	no	—
89	#10597272	—	2	2	no	—
90	Dic₁₉⋊C₈	—	2	4	no	—
91	Dic₁₉⋊C₈	—	2	4	no	—
92	C₈×Dic₁₉	—	2	2	no	—
93	C₈×Dic₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	4	4	no	—
112	C₂²×Dic₁₉	C₄²	1	2	yes	—
113	C₂²×Dic₁₉	C₄²	1	2	yes	—
114	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
116	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
117	C₂²×Dic₁₉	C₄⋊C₄	1	2	yes	—
118	M₁₆×C₁₉	—	2	2	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	2	2	no	—
121	M₁₆×C₁₉	—	4	1	no	—
122	M₁₆×C₁₉	—	4	1	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	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₂²⋊C₄×C₁₉	—	2	2	no	—
135	C₂²⋊C₄×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	C₂²⋊Dic₁₉	—	2	2	no	—
139	C₂²⋊Dic₁₉	—	2	2	no	—
140	C₄⋊Dic₁₉	—	4	1	no	—
141	C₄⋊Dic₁₉	—	4	1	no	—
142	Dic₁₉⋊C₄	—	4	8	no	—
143	C₄×Dic₁₉	—	4	1	no	—
144	C₄×Dic₁₉	—	4	1	no	—
145	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
147	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
148	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
149	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
150	C₄×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
152	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
153	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
154	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
155	#64520	—	2	2	no	—
156	#64520	—	2	2	no	—
157	#64520	—	2	2	no	—
158	#64520	—	4	1	no	—
159	#64520	—	4	1	no	—
160	#64520	—	4	1	no	—
161	#64520	—	4	1	no	—
162	#64520	C₄⋊C₄	1	4	yes	complemented
163	C₂×C₁₉⋊C₈	—	2	2	no	—
164	C₂×C₁₉⋊C₈	—	2	2	no	—
165	C₂×C₁₉⋊C₈	—	2	2	no	—
166	C₂×C₁₉⋊C₈	—	2	2	no	—
167	C₂×C₁₉⋊C₈	—	2	2	no	—
168	C₂×C₁₉⋊C₈	—	2	2	no	—
169	#10855	—	19	1	no	maximal, Sylow
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
172	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
177	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
208	C₂×Dic₁₉	—	2	4	no	—
209	C₂×Dic₁₉	—	2	4	no	—
210	C₂×Dic₁₉	—	2	4	no	—
211	C₂×Dic₁₉	—	4	2	no	—
212	C₂×Dic₁₉	—	4	2	no	—
213	C₂×Dic₁₉	—	4	2	no	—
214	C₂×Dic₁₉	—	4	4	no	—
215	C₂×Dic₁₉	—	4	2	no	—
216	C₂×Dic₁₉	#95	1	2	yes	—
217	C₂×Dic₁₉	#95	1	2	yes	—
218	C₂×Dic₁₉	#95	1	2	yes	—
219	C₂×Dic₁₉	#95	1	2	yes	—
220	C₈×C₁₉	—	2	4	no	—
221	C₈×C₁₉	—	4	2	no	—
222	C₁₉⋊C₈	—	2	4	no	—
223	C₁₉⋊C₈	—	4	2	no	—
224	C₂×#423	—	19	1	no	—
225	C₂×C₄×M₁₆	—	19	1	no	—
226	#2285	—	19	1	no	—
227	C₂×#344	—	19	1	no	—
228	C₂×#344	—	19	1	no	—
229	C₂×#344	—	19	1	no	—
230	C₂×#344	D₁₉	1	1	yes	characteristic
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	4	1	no	—
235	C₂²×C₁₉	—	4	1	no	—
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
239	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂²×C₁₉	#389	1	1	yes	characteristic
242	C₂²×C₁₉	#389	1	1	yes	characteristic
243	C₂²×C₁₉	#390	1	1	yes	characteristic
244	C₂²×C₁₉	#391	1	1	yes	characteristic
245	C₄×C₁₉	—	8	2	no	—
246	C₄×C₁₉	#380	1	1	yes	characteristic
247	C₄×C₁₉	#380	1	1	yes	characteristic
248	C₄×C₁₉	#382	1	1	yes	characteristic
249	C₄×C₁₉	#384	1	1	yes	characteristic
250	C₄×C₁₉	#389	1	1	yes	characteristic
251	C₄×C₁₉	#389	1	1	yes	characteristic
252	C₄×C₁₉	#390	1	1	yes	characteristic
253	C₄×C₁₉	#391	1	1	yes	characteristic
254	Dic₁₉	—	2	2	no	—
255	Dic₁₉	—	2	2	no	—
256	Dic₁₉	—	2	2	no	—
257	Dic₁₉	—	8	2	no	—
258	Dic₁₉	#344	1	4	yes	complemented
259	C₂²×M₁₆	—	19	1	no	—
260	C₂²×M₁₆	—	19	1	no	—
261	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
262	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
263	C₂×#117	—	19	1	no	—
264	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
265	C₂²×C₄²	—	19	1	no	—
266	#423	—	38	2	no	—
267	#423	—	38	1	no	—
268	#423	—	38	1	no	—
269	C₂×C₄⋊C₈	—	19	4	no	—
270	C₄×M₁₆	—	19	2	no	—
271	C₄×M₁₆	—	19	2	no	—
272	C₄×M₁₆	—	38	1	no	—
273	C₄×M₁₆	—	38	1	no	—
274	C₂×#97	—	38	1	no	—
275	C₂×C₄×C₈	—	38	1	no	—
276	#384	—	38	1	no	—
277	#382	—	38	1	no	—
278	#380	—	19	4	no	—
279	C₄×C₄⋊C₄	—	38	2	no	—
280	#344	—	2	2	no	—
281	#344	—	38	2	no	—
282	#344	—	38	2	no	—
283	#344	—	38	2	no	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	2	1	no	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#344	1	2	yes	—
292	C₂³×C₄	—	19	2	no	—
293	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	19	2	no	—
304	C₂×M₁₆	—	19	2	no	—
305	C₂×M₁₆	—	19	2	no	—
306	C₂×M₁₆	—	38	1	no	—
307	C₂×M₁₆	—	38	1	no	—
308	C₂×M₁₆	—	38	1	no	—
309	C₂×M₁₆	—	38	1	no	—
310	C₂×M₁₆	—	38	1	no	—
311	C₂×M₁₆	—	38	1	no	—
312	C₂×M₁₆	—	38	1	no	—
313	C₂×M₁₆	—	38	1	no	—
314	C₂×M₁₆	—	38	1	no	—
315	C₂×M₁₆	Dic₃₈	1	2	yes	—
316	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
317	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	19	2	no	—
320	C₂²×C₈	—	38	1	no	—
321	C₂²×C₈	C₄×D₁₉	1	2	yes	—
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	2	1	no	—
326	#117	—	38	1	no	—
327	#117	—	38	1	no	—
328	#117	—	38	1	no	—
329	#117	—	38	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	38	4	no	—
332	C₂×C₄⋊C₄	—	38	1	no	—
333	C₂×C₂²⋊C₄	—	19	2	no	—
334	C₂×C₂²⋊C₄	C₄×D₁₉	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	19	1	no	—
337	C₂×C₄²	—	19	1	no	—
338	C₂×C₄²	—	19	2	no	—
339	C₂×C₄²	—	19	2	no	—
340	C₂×C₄²	—	19	1	no	—
341	C₂×C₄²	—	19	1	no	—
342	C₂×C₄²	—	19	1	no	—
343	C₂×C₄²	—	19	1	no	—
344	C₂×C₄²	—	19	2	no	—
345	C₂×C₄²	—	38	1	no	—
346	C₄⋊C₈	—	38	4	no	—
347	C₄⋊C₈	—	38	4	no	—
348	#97	—	38	2	no	—
349	#97	—	38	2	no	—
350	C₄×C₈	—	38	2	no	—
351	C₄×C₈	—	38	2	no	—
352	#95	—	38	4	no	—
353	C₁₉	#10855	1	1	yes	characteristic, complemented, Sylow
354	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	19	2	no	—
357	C₂²×C₄	—	19	2	no	—
358	C₂²×C₄	—	19	2	no	—
359	C₂²×C₄	—	19	2	no	—
360	C₂²×C₄	—	19	2	no	—
361	C₂²×C₄	—	19	2	no	—
362	C₂²×C₄	—	38	2	no	—
363	C₂²×C₄	—	76	4	no	—
364	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₁₉	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	—	4	1	no	—
382	M₁₆	—	4	1	no	—
383	M₁₆	—	4	1	no	—
384	M₁₆	—	4	1	no	—
385	M₁₆	—	19	4	no	—
386	M₁₆	—	38	2	no	—
387	M₁₆	—	38	2	no	—
388	M₁₆	—	38	2	no	—
389	M₁₆	—	76	1	no	—
390	M₁₆	—	76	1	no	—
391	M₁₆	—	76	1	no	—
392	M₁₆	—	76	1	no	—
393	M₁₆	Dic₁₉⋊C₄	1	4	yes	complemented
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	38	2	no	—
401	C₂×C₈	—	38	2	no	—
402	C₂×C₈	—	38	2	no	—
403	C₂×C₈	—	38	2	no	—
404	C₂×C₈	—	38	2	no	—
405	C₂×C₈	—	38	2	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	76	8	no	—
409	C₄⋊C₄	—	76	1	no	—
410	C₄⋊C₄	—	76	1	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	38	2	no	—
414	C₂²⋊C₄	—	38	2	no	—
415	C₄²	—	4	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	19	1	no	—
418	C₄²	—	19	1	no	—
419	C₄²	—	19	1	no	—
420	C₄²	—	19	1	no	—
421	C₄²	—	19	2	no	—
422	C₄²	—	19	2	no	—
423	C₄²	—	19	2	no	—
424	C₄²	—	19	2	no	—
425	C₄²	—	19	2	no	—
426	C₄²	—	19	2	no	—
427	C₄²	—	76	1	no	—
428	C₄²	—	76	1	no	—
429	C₂³	—	4	2	no	—
430	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
431	C₂³	C₄²×D₁₉	1	1	yes	characteristic
432	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
433	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
434	C₂³	#10597333	1	1	yes	characteristic
435	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
436	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	19	2	no	—
440	C₂×C₄	—	19	2	no	—
441	C₂×C₄	—	19	2	no	—
442	C₂×C₄	—	19	2	no	—
443	C₂×C₄	—	38	4	no	—
444	C₂×C₄	—	38	4	no	—
445	C₂×C₄	—	38	4	no	—
446	C₂×C₄	—	76	2	no	—
447	C₂×C₄	—	76	2	no	—
448	C₂×C₄	—	76	2	no	—
449	C₂×C₄	—	76	4	no	—
450	C₂×C₄	—	76	2	no	—
451	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
452	C₂×C₄	#10597318	1	1	yes	characteristic
453	C₂×C₄	#10597323	1	1	yes	characteristic
454	C₂×C₄	#10597324	1	1	yes	characteristic
455	C₂×C₄	#10597324	1	1	yes	characteristic
456	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
458	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
459	C₂×C₄	#10597330	1	1	yes	characteristic
460	C₂×C₄	#10597330	1	1	yes	characteristic
461	C₂×C₄	#10597331	1	1	yes	characteristic
462	C₂×C₄	#10597331	1	1	yes	characteristic
463	C₂×C₄	#10597333	1	1	yes	characteristic
464	C₂×C₄	#10597334	1	1	yes	characteristic
465	C₂×C₄	#10597334	1	1	yes	characteristic
466	C₂×C₄	#10597335	1	1	yes	characteristic
467	C₂×C₄	#10597335	1	1	yes	characteristic
468	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
469	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
470	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
471	C₂×C₄	#10597342	1	1	yes	characteristic
472	C₂×C₄	#10597342	1	1	yes	characteristic
473	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
474	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
475	C₂×C₄	#10597385	1	1	yes	characteristic
476	C₂×C₄	#10597385	1	1	yes	characteristic
477	C₂×C₄	#10597386	1	1	yes	characteristic
478	C₂×C₄	#10597390	1	1	yes	characteristic
479	C₈	—	2	4	no	—
480	C₈	—	4	2	no	—
481	C₈	—	38	4	no	—
482	C₈	—	76	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	#95×D₁₉	1	1	yes	characteristic
491	C₂²	#11926395	1	1	yes	characteristic
492	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
493	C₂²	#11926439	1	1	yes	characteristic
494	C₂²	#11926441	1	1	yes	characteristic
495	C₂²	#11926444	1	1	yes	characteristic
496	C₂²	#11926448	1	1	yes	characteristic
497	C₄	—	8	2	no	—
498	C₄	—	19	4	no	—
499	C₄	—	38	2	no	—
500	C₄	—	38	2	no	—
501	C₄	—	38	2	no	—
502	C₄	—	152	2	no	—
503	C₄	#11926402	1	1	yes	characteristic
504	C₄	#11926403	1	1	yes	characteristic
505	C₄	#11926408	1	1	yes	characteristic
506	C₄	#11926413	1	1	yes	characteristic
507	C₄	#11926439	1	1	yes	characteristic
508	C₄	#11926441	1	1	yes	characteristic
509	C₄	#11926444	1	1	yes	characteristic
510	C₄	#11926448	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
518	C₂	D₁₉×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#344	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#344	D₁₉
hypocenter	C₁₉	#10855
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
15. C₂×Dic₁₉⋊C₈	C₄	semidirect
18. M₁₆×Dic₁₉	C₄	semidirect
19. M₁₆×Dic₁₉	C₄	semidirect
125. M₁₆×C₁₉	C₄⋊C₄	semidirect
162. #64520	C₄⋊C₄	semidirect
258. Dic₁₉	#344	semidirect
353. C₁₉	#10855	semidirect
393. 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×#11926567	2
C₂×M₁₆×Dic₁₉	2
#14566038	2
C₂×#11926316	2
C₂×#11926315	2
C₂×#11926314	2
C₂×C₁₉×#344	2
#10855	19