Subgroups — #18074599

Order 4864.

794 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564613	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#10597294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597294	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562230	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562074	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3482	C₂	1	1	yes	maximal, characteristic
8	#11926568	C₂²	1	1	yes	characteristic
9	C₂×#10597294	—	2	1	no	—
10	C₂×#10597294	—	2	1	no	—
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	C₄×#64520	C₂²	1	1	yes	characteristic
13	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926303	—	2	2	no	—
15	#11926303	—	2	1	no	—
16	#11926303	—	2	1	no	—
17	#11926286	—	2	2	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#557	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#556	—	2	1	no	—
24	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#552	—	2	2	no	—
26	C₁₉×#552	—	2	1	no	—
27	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
28	C₁₉×#548	—	2	1	no	—
29	C₁₉×#547	—	2	1	no	—
30	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
31	C₁₉×#533	—	2	1	no	—
32	C₁₉×#533	C₂²	1	1	yes	characteristic
33	C₁₉×#529	—	2	1	no	—
34	C₁₉×#529	—	2	2	no	—
35	C₄×#41×C₁₉	—	2	1	no	—
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
41	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	—	2	1	no	—
44	C₁₉×C₄⋊Q₈	—	2	1	no	—
45	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×#126	—	2	2	no	—
48	C₁₉×#126	—	2	2	no	—
49	C₁₉×#126	—	2	2	no	—
50	C₁₉×#125	—	2	2	no	—
51	C₁₉×#125	—	2	2	no	—
52	C₁₉×#125	—	2	1	no	—
53	C₁₉×#125	D₄	1	2	yes	—
54	C₁₉×#124	—	2	2	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×#123	—	2	2	no	—
58	C₁₉×#123	—	2	2	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	—	2	1	no	—
63	C₁₉×C₂²⋊Q₈	—	2	1	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	1	no	—
66	C₁₉×#121	—	2	2	no	—
67	C₁₉×#121	—	2	1	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	—	2	1	no	—
72	C₄×Q₈×C₁₉	—	2	1	no	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	2	1	no	—
85	C₄×D₄×C₁₉	—	2	1	no	—
86	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
89	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
90	C₁₉×#117	—	2	2	no	—
91	C₁₉×#117	—	2	2	no	—
92	C₁₉×#117	—	2	1	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	D₄	1	1	yes	characteristic
96	C₁₉×#117	D₄	1	1	yes	characteristic
97	C₁₉×#117	D₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	2	no	—
101	C₂×C₄²×C₁₉	—	2	1	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄×Dic₁₉	—	2	1	no	—
105	C₂×C₄×Dic₁₉	—	2	1	no	—
106	C₂×C₄×Dic₁₉	—	2	1	no	—
107	C₂×#64520	—	2	1	no	—
108	C₂×#64520	—	2	1	no	—
109	C₂×#64520	—	2	1	no	—
110	#10597294	—	2	4	no	—
111	#10597294	—	2	4	no	—
112	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
113	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
114	#10597260	—	2	1	no	—
115	#10597260	—	2	1	no	—
116	C₄×C₁₉⋊C₈	—	2	1	no	—
117	C₄×C₁₉⋊C₈	—	2	1	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	4	1	no	—
121	#41×C₁₉	—	4	1	no	—
122	#41×C₁₉	—	4	2	no	—
123	#41×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	—	4	2	no	—
129	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×Dic₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	2	2	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	1	no	—
173	C₂²⋊C₄×C₁₉	—	2	1	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	1	no	—
176	C₂²⋊C₄×C₁₉	—	2	1	no	—
177	C₂²⋊C₄×C₁₉	—	2	1	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₄²×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₄×Dic₁₉	—	2	2	no	—
193	C₄×Dic₁₉	—	2	2	no	—
194	C₄×Dic₁₉	—	2	2	no	—
195	C₄×Dic₁₉	—	4	1	no	—
196	C₄×Dic₁₉	—	4	1	no	—
197	C₄×Dic₁₉	—	4	1	no	—
198	#64520	—	2	2	no	—
199	#64520	—	2	2	no	—
200	#64520	—	4	1	no	—
201	#64520	—	4	1	no	—
202	#64520	—	4	2	no	—
203	C₂×C₁₉⋊C₈	—	4	1	no	—
204	C₂×C₁₉⋊C₈	—	4	1	no	—
205	C₂×C₁₉⋊C₈	—	4	1	no	—
206	#8442	—	19	1	no	maximal, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	#120	1	1	yes	characteristic
210	Q₈×C₁₉	—	2	1	no	—
211	Q₈×C₁₉	—	2	1	no	—
212	Q₈×C₁₉	—	2	1	no	—
213	Q₈×C₁₉	—	4	4	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	Q₈×C₁₉	—	4	1	no	—
217	Q₈×C₁₉	—	4	1	no	—
218	Q₈×C₁₉	#104	1	2	yes	complemented
219	D₄×C₁₉	—	2	1	no	—
220	D₄×C₁₉	—	2	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	4	no	—
225	D₄×C₁₉	#104	1	2	yes	complemented
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×Dic₁₉	—	4	2	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	—	4	2	no	—
261	C₁₉⋊C₈	—	4	2	no	—
262	C₁₉⋊C₈	—	4	2	no	—
263	C₁₉⋊C₈	—	8	1	no	—
264	#3482	D₁₉	1	1	yes	characteristic
265	#1994	—	19	1	no	—
266	C₄×#104	—	19	1	no	—
267	C₄×#104	—	19	1	no	—
268	#1526	—	19	1	no	—
269	#1489	—	19	1	no	—
270	#1489	—	19	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	2	2	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	1	no	—
278	C₂²×C₁₉	—	4	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	#379	1	1	yes	characteristic
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	2	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	1	no	—
289	C₄×C₁₉	—	4	2	no	—
290	C₄×C₁₉	—	4	2	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
293	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
294	C₄×C₁₉	#421	1	1	yes	characteristic
295	C₄×C₁₉	#421	1	1	yes	characteristic
296	C₄×C₁₉	#454	1	1	yes	characteristic
297	C₄×C₁₉	#456	1	1	yes	characteristic
298	Dic₁₉	—	4	4	no	—
299	#557	Dic₁₉	1	1	yes	characteristic, complemented
300	#556	—	2	1	no	—
301	#556	Dic₁₉	1	1	yes	characteristic, complemented
302	#552	—	2	2	no	—
303	#552	—	2	1	no	—
304	D₄×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
305	#548	—	2	1	no	—
306	#547	—	2	1	no	—
307	#547	Dic₁₉	1	1	yes	characteristic, complemented
308	#533	—	2	1	no	—
309	#533	C₂×D₁₉	1	1	yes	characteristic
310	#529	—	2	1	no	—
311	#529	—	2	2	no	—
312	C₄×#41	—	2	1	no	—
313	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
314	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
315	C₂×C₄×Q₈	—	2	1	no	—
316	#423	—	19	1	no	—
317	C₂×#104	—	38	1	no	—
318	C₂×#104	—	38	1	no	—
319	C₄×M₁₆	—	19	1	no	—
320	C₄×M₁₆	—	19	1	no	—
321	C₄³	—	19	1	no	—
322	#339	—	38	2	no	—
323	#339	—	38	1	no	—
324	#339	—	38	1	no	—
325	#330	—	38	2	no	—
326	Q₈⋊C₈	—	38	1	no	—
327	Q₈⋊C₈	—	38	1	no	—
328	D₄⋊C₈	—	38	1	no	—
329	D₄⋊C₈	—	38	1	no	—
330	C₂×C₁₉	—	4	1	no	—
331	C₂×C₁₉	—	4	2	no	—
332	C₂×C₁₉	—	8	1	no	—
333	C₂×C₁₉	#1789	1	1	yes	characteristic
334	C₂×C₁₉	#1789	1	1	yes	characteristic
335	C₂×C₁₉	#1793	1	1	yes	characteristic
336	C₂×#41	—	2	1	no	—
337	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
338	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂²×Q₈	—	2	1	no	—
340	C₂×M₁₆	—	38	1	no	—
341	C₂×M₁₆	—	38	1	no	—
342	C₂×M₁₆	—	38	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
346	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
347	#126	—	2	2	no	—
348	#126	—	2	2	no	—
349	#126	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	#125	—	2	1	no	—
353	#125	C₂²⋊D₁₉	1	2	yes	—
354	#124	—	2	2	no	—
355	#124	—	2	1	no	—
356	#123	—	2	2	no	—
357	#123	—	2	2	no	—
358	#123	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	#121	—	2	2	no	—
367	#121	—	2	1	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
376	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
378	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
387	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
388	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
389	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
390	#117	—	2	2	no	—
391	#117	—	2	2	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	C₂²⋊D₁₉	1	1	yes	characteristic
396	#117	C₂²⋊D₁₉	1	1	yes	characteristic
397	#117	C₂²⋊D₁₉	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄²	—	2	2	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	38	1	no	—
404	C₂×C₄²	—	38	1	no	—
405	C₂×C₄²	—	38	1	no	—
406	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
407	C₄⋊C₈	—	38	1	no	—
408	C₄⋊C₈	—	38	1	no	—
409	#104	—	38	4	no	—
410	#104	—	38	4	no	—
411	#97	—	38	1	no	—
412	#97	—	38	1	no	—
413	C₄×C₈	—	38	1	no	—
414	C₄×C₈	—	38	1	no	—
415	C₁₉	#8442	1	1	yes	characteristic, complemented, Sylow
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	2	no	—
421	#41	—	4	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	4	2	no	—
426	C₂×Q₈	—	4	2	no	—
427	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
428	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
433	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	76	1	no	—
443	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
446	M₁₆	—	38	2	no	—
447	M₁₆	—	38	2	no	—
448	M₁₆	—	76	1	no	—
449	M₁₆	—	76	1	no	—
450	M₁₆	—	76	2	no	—
451	C₂×C₈	—	76	1	no	—
452	C₂×C₈	—	76	1	no	—
453	C₂×C₈	—	76	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
473	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	38	2	no	—
495	C₄²	—	38	2	no	—
496	C₄²	—	38	2	no	—
497	C₄²	—	76	1	no	—
498	C₄²	—	76	1	no	—
499	C₄²	—	76	1	no	—
500	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
501	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
502	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
503	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	#10597399	1	1	yes	characteristic
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	#10597294	1	2	yes	complemented
516	D₄	—	2	1	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	#10597294	1	2	yes	complemented
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	76	2	no	—
550	C₂×C₄	—	76	2	no	—
551	C₂×C₄	—	76	2	no	—
552	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
554	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
555	C₂×C₄	#10597399	1	1	yes	characteristic
556	C₂×C₄	#10597399	1	1	yes	characteristic
557	C₂×C₄	#10597399	1	1	yes	characteristic
558	C₈	—	76	2	no	—
559	C₈	—	76	2	no	—
560	C₈	—	152	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	#11926400	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	76	4	no	—
583	C₄	C₂×#10597294	1	1	yes	characteristic
584	C₄	C₂×#10597294	1	1	yes	characteristic
585	C₄	#11926561	1	1	yes	characteristic
586	C₄	#11926561	1	1	yes	characteristic
587	C₄	#11926717	1	1	yes	characteristic
588	C₄	#11926727	1	1	yes	characteristic
589	C₂	—	4	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	8	1	no	—
592	C₂	#14563579	1	1	yes	characteristic
593	C₂	#14563579	1	1	yes	characteristic
594	C₂	#14563594	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3482	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3482	D₁₉
hypocenter	C₁₉	#8442
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3482

Complements

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

N	H ≅ G/N	type
1. #14564613	C₂	semidirect
2. C₄×#10597294	C₂	semidirect
3. C₄×#10597294	C₂	semidirect
4. #14562230	C₂	semidirect
5. #14562074	C₂	semidirect
6. #14562074	C₂	semidirect
22. C₁₉×#557	C₄	semidirect
24. C₁₉×#556	C₄	semidirect
27. D₄×Q₈×C₁₉	C₄	semidirect
30. C₁₉×#547	C₄	semidirect
218. Q₈×C₁₉	#104	semidirect
225. D₄×C₁₉	#104	semidirect
299. #557	Dic₁₉	semidirect
301. #556	Dic₁₉	semidirect
304. D₄×Q₈	Dic₁₉	semidirect
307. #547	Dic₁₉	semidirect
415. C₁₉	#8442	semidirect
515. Q₈	#10597294	semidirect
522. D₄	#10597294	semidirect

Maximal subgroups

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

subgroup	index
#14564613	2
C₄×#10597294	2
#14562230	2
#14562074	2
C₁₉×#3482	2
#8442	19