Subgroups — C₁₉×#33569 #18039528

Order 4864.

1082 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3020	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2205	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2204	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2203	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2133	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
10	C₁₉×#575	—	2	2	no	—
11	C₂×C₁₉×#137	—	2	1	no	—
12	C₁₉×#563	—	2	1	no	—
13	C₁₉×#563	C₂²	1	2	yes	complemented
14	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₁₉×#555	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#554	—	2	1	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#547	—	2	2	no	—
19	C₁₉×#544	—	2	2	no	—
20	C₁₉×#542	—	2	2	no	—
21	C₁₉×#536	—	2	1	no	—
22	C₁₉×#536	C₂²	1	2	yes	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₉×#529	—	2	1	no	—
25	C₁₉×#456	—	2	1	no	—
26	C₁₉×#456	—	2	1	no	—
27	C₁₉×#456	—	2	2	no	—
28	C₁₉×#456	C₂²	1	2	yes	—
29	C₁₉×#456	C₂²	1	4	yes	—
30	C₁₉×#456	C₂²	1	2	yes	—
31	C₁₉×#454	—	2	2	no	—
32	C₁₉×#454	C₂²	1	4	yes	—
33	C₁₉×#421	—	2	2	no	—
34	C₂×C₁₉×#104	—	2	1	no	—
35	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#101	C₂²	1	2	yes	—
37	C₁₉×#356	C₂²	1	2	yes	complemented
38	C₁₉×#356	C₂²	1	4	yes	complemented
39	C₁₉×#356	C₂²	1	2	yes	complemented
40	C₁₉×#355	C₂²	1	4	yes	complemented
41	C₁₉×2₋¹⁺⁴	—	2	2	no	—
42	C₁₉×2₋¹⁺⁴	—	2	1	no	—
43	C₁₉×2₋¹⁺⁴	—	4	2	no	—
44	C₁₉×2₋¹⁺⁴	C₂³	1	2	yes	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	4	1	no	—
49	C₂×#41×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	—	4	1	no	—
51	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#137	—	2	2	no	—
54	C₁₉×#137	—	2	2	no	—
55	C₁₉×#137	—	2	4	no	—
56	C₁₉×#137	—	4	2	no	—
57	C₁₉×#137	—	4	2	no	—
58	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
59	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
60	C₁₉×#135	—	4	4	no	—
61	C₂×Q₁₆×C₁₉	—	4	1	no	—
62	C₂×SD₁₆×C₁₉	—	4	1	no	—
63	C₂×M₁₆×C₁₉	—	2	1	no	—
64	C₂×M₁₆×C₁₉	—	2	2	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	—	2	2	no	—
67	C₁₉×C₄⋊Q₈	—	2	1	no	—
68	C₁₉×C₄⋊Q₈	—	2	2	no	—
69	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
72	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	2	no	—
77	C₁₉×#126	—	2	2	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	2	2	no	—
81	C₁₉×#125	—	2	2	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	D₄	1	2	yes	—
86	C₁₉×#124	C₂³	1	2	yes	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×#123	—	2	2	no	—
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	—	2	2	no	—
98	C₁₉×C₂²⋊Q₈	—	2	2	no	—
99	C₁₉×C₂²⋊Q₈	—	2	2	no	—
100	C₁₉×#121	—	2	1	no	—
101	C₁₉×#121	—	2	2	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	—	2	2	no	—
104	C₄×D₄×C₁₉	—	2	2	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	2	no	—
110	C₁₉×#117	D₄	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
114	C₁₉×#104	—	2	2	no	—
115	C₁₉×#104	—	2	2	no	—
116	C₁₉×#104	—	2	4	no	—
117	C₁₉×#104	—	2	4	no	—
118	C₁₉×#101	—	2	2	no	—
119	C₁₉×#101	—	2	1	no	—
120	C₁₉×#101	C₂³	1	2	yes	—
121	C₁₉×#101	C₂³	1	4	yes	—
122	#41×C₁₉	—	2	4	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	4	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	4	2	no	—
127	#41×C₁₉	—	4	1	no	—
128	#41×C₁₉	—	4	2	no	—
129	#41×C₁₉	—	4	2	no	—
130	#41×C₁₉	—	4	2	no	—
131	#41×C₁₉	—	4	4	no	—
132	#41×C₁₉	—	4	2	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	2	no	—
135	#41×C₁₉	—	8	1	no	—
136	#41×C₁₉	—	8	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	1	no	—
139	C₂×Q₈×C₁₉	—	2	1	no	—
140	C₂×Q₈×C₁₉	—	2	1	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	4	1	no	—
144	C₂×Q₈×C₁₉	—	4	1	no	—
145	C₂×Q₈×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	4	2	no	—
147	C₂×Q₈×C₁₉	—	4	4	no	—
148	C₂×Q₈×C₁₉	—	4	2	no	—
149	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
154	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂×D₄×C₁₉	—	2	1	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	1	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	1	no	—
160	C₂×D₄×C₁₉	—	4	1	no	—
161	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	—	2	2	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	Q₁₆×C₁₉	—	4	2	no	—
172	Q₁₆×C₁₉	—	4	2	no	—
173	Q₁₆×C₁₉	—	4	4	no	—
174	SD₁₆×C₁₉	—	4	2	no	—
175	SD₁₆×C₁₉	—	4	2	no	—
176	SD₁₆×C₁₉	—	4	4	no	—
177	SD₁₆×C₁₉	—	4	4	no	—
178	D₈×C₁₉	—	4	4	no	—
179	M₁₆×C₁₉	—	2	4	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	4	2	no	—
182	M₁₆×C₁₉	—	4	1	no	—
183	C₂×C₈×C₁₉	—	4	1	no	—
184	C₂×C₈×C₁₉	—	4	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	2	no	—
210	C₄²×C₁₉	—	2	1	no	—
211	C₄²×C₁₉	—	2	2	no	—
212	C₄²×C₁₉	—	2	1	no	—
213	C₄²×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₉	C₂×D₄	1	2	yes	—
217	C₄²×C₁₉	C₂×D₄	1	2	yes	—
218	#33569	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	4	1	no	—
221	C₂³×C₁₉	#120	1	1	yes	characteristic
222	Q₈×C₁₉	—	2	4	no	—
223	Q₈×C₁₉	—	2	2	no	—
224	Q₈×C₁₉	—	4	2	no	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	1	no	—
229	Q₈×C₁₉	—	4	2	no	—
230	Q₈×C₁₉	—	4	2	no	—
231	Q₈×C₁₉	—	4	2	no	—
232	Q₈×C₁₉	—	4	1	no	—
233	Q₈×C₁₉	—	8	1	no	—
234	Q₈×C₁₉	—	8	1	no	—
235	D₄×C₁₉	—	2	4	no	—
236	D₄×C₁₉	—	2	2	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	D₄×C₁₉	—	4	2	no	—
244	D₄×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	8	1	no	—
246	C₂×C₄×C₁₉	—	2	1	no	—
247	C₂×C₄×C₁₉	—	2	1	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	4	no	—
259	C₂×C₄×C₁₉	—	4	4	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	4	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	1	no	—
264	C₂×C₄×C₁₉	—	4	1	no	—
265	C₂×C₄×C₁₉	—	4	1	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	8	2	no	—
268	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#120	1	2	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
272	C₈×C₁₉	—	4	4	no	—
273	C₈×C₁₉	—	4	2	no	—
274	#3544	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#3020	C₂×C₁₉	1	2	yes	complemented
276	C₂×#456	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#2205	C₂×C₁₉	1	2	yes	complemented
278	#2204	C₂×C₁₉	1	2	yes	complemented
279	#2203	C₂×C₁₉	1	4	yes	complemented
280	#2133	C₂×C₁₉	1	2	yes	complemented
281	C₂×#356	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	2	no	—
284	C₂²×C₁₉	—	4	2	no	—
285	C₂²×C₁₉	—	4	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	8	2	no	—
288	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂²×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	4	2	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	2	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
304	#575	—	2	2	no	—
305	C₂×#137	—	2	1	no	—
306	#563	—	2	1	no	—
307	#563	C₂²×C₁₉	1	2	yes	complemented
308	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	#555	C₂²×C₁₉	1	1	yes	characteristic, complemented
310	#554	—	2	1	no	—
311	#552	—	2	2	no	—
312	#547	—	2	2	no	—
313	#544	—	2	2	no	—
314	#542	—	2	2	no	—
315	#536	—	2	1	no	—
316	#536	C₂²×C₁₉	1	2	yes	—
317	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	#529	—	2	1	no	—
319	#456	—	2	1	no	—
320	#456	—	2	1	no	—
321	#456	—	2	2	no	—
322	#456	C₂²×C₁₉	1	2	yes	—
323	#456	C₂²×C₁₉	1	4	yes	—
324	#456	C₂²×C₁₉	1	2	yes	—
325	#454	—	2	2	no	—
326	#454	C₂²×C₁₉	1	4	yes	—
327	#421	—	2	2	no	—
328	C₂×#104	—	2	1	no	—
329	C₂×#101	C₂²×C₁₉	1	2	yes	—
330	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
331	#356	C₂²×C₁₉	1	2	yes	complemented
332	#356	C₂²×C₁₉	1	2	yes	complemented
333	#356	C₂²×C₁₉	1	4	yes	complemented
334	#355	C₂²×C₁₉	1	4	yes	complemented
335	C₂×C₁₉	—	2	1	no	—
336	C₂×C₁₉	—	2	1	no	—
337	C₂×C₁₉	—	2	1	no	—
338	C₂×C₁₉	—	8	2	no	—
339	C₂×C₁₉	—	8	2	no	—
340	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
341	2₋¹⁺⁴	—	2	2	no	—
342	2₋¹⁺⁴	—	2	1	no	—
343	2₋¹⁺⁴	—	4	2	no	—
344	2₋¹⁺⁴	C₂³×C₁₉	1	2	yes	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	4	1	no	—
349	C₂×#41	D₄×C₁₉	1	2	yes	—
350	C₂²×Q₈	—	4	1	no	—
351	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
353	#137	—	2	2	no	—
354	#137	—	2	2	no	—
355	#137	—	2	4	no	—
356	#137	—	4	2	no	—
357	#137	—	4	2	no	—
358	AGL(1,ℤ/8)	—	2	4	no	—
359	AGL(1,ℤ/8)	—	4	2	no	—
360	#135	—	4	4	no	—
361	C₂×Q₁₆	—	4	1	no	—
362	C₂×SD₁₆	—	4	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	—	2	2	no	—
369	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
370	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
371	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
372	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
375	#126	—	2	2	no	—
376	#126	—	2	2	no	—
377	#126	—	2	2	no	—
378	#125	—	2	1	no	—
379	#125	—	2	2	no	—
380	#125	—	2	2	no	—
381	#125	—	2	2	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	D₄×C₁₉	1	2	yes	—
386	#124	C₂³×C₁₉	1	2	yes	—
387	#123	—	2	2	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	#121	—	2	1	no	—
401	#121	—	2	2	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	#117	—	2	2	no	—
408	#117	—	2	1	no	—
409	#117	—	2	2	no	—
410	#117	D₄×C₁₉	1	2	yes	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
414	#104	—	2	2	no	—
415	#104	—	2	2	no	—
416	#104	—	2	4	no	—
417	#104	—	2	4	no	—
418	#101	—	2	2	no	—
419	#101	—	2	1	no	—
420	#101	C₂³×C₁₉	1	2	yes	—
421	#101	C₂³×C₁₉	1	4	yes	—
422	C₁₉	#33569	1	1	yes	characteristic, direct product factor, Sylow
423	#41	—	2	4	no	—
424	#41	—	2	2	no	—
425	#41	—	2	4	no	—
426	#41	—	2	2	no	—
427	#41	—	4	2	no	—
428	#41	—	4	1	no	—
429	#41	—	4	2	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	4	no	—
433	#41	—	4	2	no	—
434	#41	—	4	1	no	—
435	#41	—	4	2	no	—
436	#41	—	8	1	no	—
437	#41	—	8	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	1	no	—
446	C₂×Q₈	—	4	1	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	4	4	no	—
449	C₂×Q₈	—	4	2	no	—
450	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
452	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
455	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	Q₁₆	—	4	2	no	—
473	Q₁₆	—	4	2	no	—
474	Q₁₆	—	4	4	no	—
475	SD₁₆	—	4	2	no	—
476	SD₁₆	—	4	2	no	—
477	SD₁₆	—	4	4	no	—
478	SD₁₆	—	4	4	no	—
479	D₈	—	4	4	no	—
480	M₁₆	—	2	4	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	4	2	no	—
483	M₁₆	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₁₉	1	2	yes	—
518	C₄²	C₂×D₄×C₁₉	1	2	yes	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	C₁₉×#120	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	4	2	no	—
533	Q₈	—	8	1	no	—
534	Q₈	—	8	1	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	8	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
569	C₂×C₄	C₁₉×#120	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
572	C₈	—	4	4	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	2	no	—
580	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²	C₁₉×B(4,𝔽₂)	1	1	yes	characteristic
582	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	8	2	no	—
599	C₂	—	8	2	no	—
600	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₉
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3544	C₂	semidirect
2. C₁₉×#3020	C₂	semidirect
3. C₂×C₁₉×#456	C₂	semidirect
4. C₁₉×#2205	C₂	semidirect
5. C₁₉×#2204	C₂	semidirect
6. C₁₉×#2203	C₂	semidirect
7. C₁₉×#2133	C₂	semidirect
8. C₂×C₁₉×#356	C₂	semidirect
13. C₁₉×#563	C₂²	semidirect
14. Q₈²×C₁₉	C₂²	semidirect
15. C₁₉×#555	C₂²	semidirect
37. C₁₉×#356	C₂²	semidirect
38. C₁₉×#356	C₂²	semidirect
39. C₁₉×#356	C₂²	semidirect
40. C₁₉×#355	C₂²	semidirect
218. #33569	C₁₉	direct (N × H)
274. #3544	C₂×C₁₉	semidirect
275. #3020	C₂×C₁₉	semidirect
276. C₂×#456	C₂×C₁₉	semidirect
277. #2205	C₂×C₁₉	semidirect
278. #2204	C₂×C₁₉	semidirect
279. #2203	C₂×C₁₉	semidirect
280. #2133	C₂×C₁₉	semidirect
281. C₂×#356	C₂×C₁₉	semidirect
307. #563	C₂²×C₁₉	semidirect
308. Q₈²	C₂²×C₁₉	semidirect
309. #555	C₂²×C₁₉	semidirect
331. #356	C₂²×C₁₉	semidirect
332. #356	C₂²×C₁₉	semidirect
333. #356	C₂²×C₁₉	semidirect
334. #355	C₂²×C₁₉	semidirect
422. C₁₉	#33569	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3544	2
C₁₉×#3020	2
C₂×C₁₉×#456	2
C₁₉×#2205	2
C₁₉×#2204	2
C₁₉×#2203	2
C₁₉×#2133	2
C₂×C₁₉×#356	2
#33569	19

Subgroups — C19×#33569 #18039528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33569 #18039528