Subgroups — C₁₉×#62913 #18068872

Order 4864.

6974 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3554	C₂	1	6	yes	maximal, complemented
2	C₁₉×#3552	C₂	1	6	yes	maximal, complemented
3	C₁₉×#3550	C₂	1	6	yes	maximal, complemented
4	C₁₉×#3547	C₂	1	6	yes	maximal, complemented
5	C₁₉×#3541	C₂	1	12	yes	maximal, complemented
6	C₁₉×#3523	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3518	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3511	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3506	C₂	1	3	yes	maximal, complemented
10	C₁₉×#3503	C₂	1	3	yes	maximal, complemented
11	C₁₉×#3499	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3497	C₂	1	2	yes	maximal, complemented
13	C₁₉×#3486	C₂	1	4	yes	maximal, complemented
14	C₁₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#3460	C₂	1	3	yes	maximal, complemented
18	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	complemented
19	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#563	C₂²	1	24	yes	complemented
21	C₁₉×#562	C₂²	1	24	yes	complemented
22	C₁₉×#559	C₂²	1	12	yes	—
23	C₁₉×#559	C₂²	1	3	yes	complemented
24	Q₈²×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	Q₈²×C₁₉	C₂²	1	6	yes	complemented
26	C₁₉×#557	C₂²	1	3	yes	complemented
27	C₁₉×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#557	C₂²	1	6	yes	complemented
29	C₁₉×#556	C₂²	1	6	yes	—
30	C₁₉×#556	C₂²	1	3	yes	complemented
31	C₁₉×#556	C₂²	1	6	yes	complemented
32	C₁₉×#556	C₂²	1	12	yes	complemented
33	C₁₉×#555	C₂²	1	6	yes	—
34	C₁₉×#555	C₂²	1	6	yes	complemented
35	C₁₉×#554	C₂²	1	6	yes	—
36	C₁₉×#554	C₂²	1	12	yes	—
37	C₁₉×#554	C₂²	1	3	yes	complemented
38	C₁₉×#554	C₂²	1	6	yes	complemented
39	C₁₉×#554	C₂²	1	6	yes	complemented
40	C₁₉×#553	C₂²	1	6	yes	—
41	C₁₉×#553	C₂²	1	12	yes	—
42	C₁₉×#553	C₂²	1	12	yes	—
43	C₁₉×#552	C₂²	1	12	yes	complemented
44	C₁₉×#550	C₂²	1	6	yes	—
45	C₁₉×#550	C₂²	1	1	yes	characteristic, complemented
46	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
47	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
48	D₄×Q₈×C₁₉	C₂²	1	6	yes	—
49	D₄×Q₈×C₁₉	C₂²	1	6	yes	—
50	D₄×Q₈×C₁₉	C₂²	1	2	yes	—
51	D₄×Q₈×C₁₉	C₂²	1	12	yes	—
52	D₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
53	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
54	D₄×Q₈×C₁₉	C₂²	1	12	yes	complemented
55	D₄×Q₈×C₁₉	C₂²	1	6	yes	complemented
56	C₁₉×#548	C₂²	1	2	yes	—
57	C₁₉×#548	C₂²	1	12	yes	—
58	C₁₉×#548	C₂²	1	4	yes	complemented
59	C₁₉×#548	C₂²	1	12	yes	complemented
60	C₁₉×#548	C₂²	1	12	yes	complemented
61	C₁₉×#547	C₂²	1	6	yes	—
62	C₁₉×#547	C₂²	1	6	yes	complemented
63	C₁₉×#547	C₂²	1	12	yes	complemented
64	C₁₉×#544	C₂²	1	3	yes	—
65	C₁₉×#544	C₂²	1	12	yes	complemented
66	C₁₉×#542	C₂²	1	6	yes	—
67	C₁₉×#542	C₂²	1	6	yes	—
68	C₁₉×#542	C₂²	1	12	yes	complemented
69	C₁₉×#542	C₂²	1	12	yes	complemented
70	C₁₉×#542	C₂²	1	24	yes	complemented
71	C₁₉×#541	C₂²	1	12	yes	complemented
72	C₁₉×#540	C₂²	1	6	yes	—
73	C₁₉×#540	C₂²	1	6	yes	—
74	C₁₉×#539	C₂²	1	24	yes	complemented
75	C₁₉×#538	C₂²	1	12	yes	—
76	C₁₉×#538	C₂²	1	12	yes	—
77	C₁₉×#537	C₂²	1	3	yes	—
78	C₁₉×#537	C₂²	1	12	yes	complemented
79	C₁₉×#536	C₂²	1	12	yes	complemented
80	C₁₉×#536	C₂²	1	12	yes	complemented
81	C₁₉×#536	C₂²	1	12	yes	complemented
82	C₁₉×#535	C₂²	1	1	yes	characteristic
83	C₁₉×#535	C₂²	1	3	yes	—
84	C₁₉×#533	C₂²	1	3	yes	—
85	C₁₉×#533	C₂²	1	6	yes	complemented
86	C₁₉×#533	C₂²	1	6	yes	complemented
87	C₁₉×#533	C₂²	1	6	yes	complemented
88	C₁₉×#532	C₂²	1	6	yes	—
89	C₁₉×#532	C₂²	1	6	yes	—
90	C₁₉×#532	C₂²	1	3	yes	—
91	C₁₉×#532	C₂²	1	6	yes	complemented
92	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
93	C₂×C₁₉×C₄⋊Q₈	C₂²	1	6	yes	complemented
94	C₁₉×#529	C₂²	1	6	yes	—
95	C₁₉×#529	C₂²	1	6	yes	—
96	C₁₉×#529	C₂²	1	6	yes	complemented
97	C₁₉×#525	C₂²	1	12	yes	—
98	C₁₉×#525	C₂²	1	12	yes	—
99	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
100	C₁₉×#520	C₂²	1	6	yes	—
101	C₁₉×#519	C₂²	1	4	yes	complemented
102	C₄×#41×C₁₉	C₂²	1	3	yes	—
103	C₄×#41×C₁₉	C₂²	1	3	yes	—
104	C₄×#41×C₁₉	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
106	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
108	C₁₉×2₋¹⁺⁴	—	4	16	no	—
109	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×#41×C₁₉	C₂³	1	3	yes	—
111	C₂×#41×C₁₉	C₂³	1	2	yes	—
112	C₂×#41×C₁₉	C₂³	1	12	yes	—
113	C₂×#41×C₁₉	C₂³	1	12	yes	—
114	C₂×#41×C₁₉	C₂³	1	12	yes	—
115	C₂²×Q₈×C₁₉	—	4	8	no	—
116	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
118	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
119	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
120	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
121	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
122	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
124	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
125	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
126	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
127	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
128	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
129	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
130	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	—
131	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	—
132	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
133	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
134	C₁₉×C₄⋊Q₈	C₂³	1	3	yes	—
135	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
136	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	—
137	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
138	C₁₉×#127	C₂³	1	2	yes	—
139	C₁₉×#127	C₂³	1	3	yes	—
140	C₁₉×#127	C₂³	1	6	yes	—
141	C₁₉×#126	C₂³	1	12	yes	—
142	C₁₉×#126	C₂³	1	12	yes	—
143	C₁₉×#126	C₂³	1	12	yes	—
144	C₁₉×#126	C₂³	1	24	yes	—
145	C₁₉×#126	C₂³	1	24	yes	—
146	C₁₉×#125	C₂³	1	6	yes	—
147	C₁₉×#125	C₂³	1	6	yes	—
148	C₁₉×#125	C₂³	1	6	yes	—
149	C₁₉×#125	C₂³	1	6	yes	—
150	C₁₉×#125	C₂³	1	12	yes	—
151	C₁₉×#125	C₂³	1	12	yes	—
152	C₁₉×#125	C₂³	1	24	yes	—
153	C₁₉×#124	C₂³	1	2	yes	—
154	C₁₉×#124	C₂³	1	6	yes	—
155	C₁₉×#124	C₂³	1	6	yes	—
156	C₁₉×#124	C₂³	1	12	yes	—
157	C₁₉×#124	C₂³	1	12	yes	—
158	C₁₉×#124	C₂³	1	6	yes	—
159	C₁₉×#124	C₂³	1	12	yes	—
160	C₁₉×#124	C₂³	1	24	yes	—
161	C₁₉×#124	C₂³	1	24	yes	—
162	C₁₉×#123	C₂³	1	12	yes	—
163	C₁₉×#123	C₂³	1	12	yes	—
164	C₁₉×#123	C₂³	1	24	yes	—
165	C₁₉×#123	C₂³	1	12	yes	—
166	C₁₉×#123	C₂³	1	12	yes	—
167	C₁₉×#123	C₂³	1	12	yes	—
168	C₁₉×#123	C₂³	1	24	yes	—
169	C₁₉×#123	C₂³	1	24	yes	—
170	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
171	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
172	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
173	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
174	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
180	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
181	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
183	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
185	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
190	C₁₉×#121	C₂³	1	6	yes	—
191	C₁₉×#121	C₂³	1	12	yes	—
192	C₁₉×#121	C₂³	1	12	yes	—
193	C₁₉×#121	C₂³	1	12	yes	—
194	C₁₉×#121	C₂³	1	2	yes	—
195	C₁₉×#121	C₂³	1	6	yes	—
196	C₁₉×#121	C₂³	1	6	yes	—
197	C₁₉×#121	C₂³	1	2	yes	—
198	C₁₉×#121	C₂³	1	6	yes	—
199	C₁₉×#121	C₂³	1	6	yes	—
200	C₁₉×#121	C₂³	1	6	yes	—
201	C₁₉×#121	C₂³	1	12	yes	—
202	C₁₉×#121	C₂³	1	6	yes	—
203	C₁₉×#121	C₂³	1	12	yes	—
204	C₁₉×#121	C₂³	1	12	yes	—
205	C₁₉×#121	C₂³	1	24	yes	—
206	C₁₉×#120	C₂³	1	4	yes	—
207	C₁₉×#120	C₂³	1	12	yes	—
208	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
211	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
212	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
214	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
215	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
216	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
217	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
218	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
219	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
221	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
222	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
223	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
224	C₄×Q₈×C₁₉	C₂³	1	12	yes	—
225	C₄×D₄×C₁₉	C₂³	1	6	yes	—
226	C₄×D₄×C₁₉	C₂³	1	6	yes	—
227	C₄×D₄×C₁₉	C₂³	1	6	yes	—
228	C₄×D₄×C₁₉	C₂³	1	6	yes	—
229	C₄×D₄×C₁₉	C₂³	1	6	yes	—
230	C₄×D₄×C₁₉	C₂³	1	6	yes	—
231	C₄×D₄×C₁₉	C₂³	1	3	yes	—
232	C₄×D₄×C₁₉	C₂³	1	3	yes	—
233	C₄×D₄×C₁₉	C₂³	1	6	yes	—
234	C₄×D₄×C₁₉	C₂³	1	6	yes	—
235	C₄×D₄×C₁₉	C₂³	1	3	yes	—
236	C₄×D₄×C₁₉	C₂³	1	3	yes	—
237	C₄×D₄×C₁₉	C₂³	1	6	yes	—
238	C₄×D₄×C₁₉	C₂³	1	6	yes	—
239	C₄×D₄×C₁₉	C₂³	1	24	yes	—
240	C₄×D₄×C₁₉	C₂³	1	12	yes	—
241	C₄×D₄×C₁₉	C₂³	1	12	yes	—
242	C₄×D₄×C₁₉	C₂³	1	12	yes	—
243	C₄×D₄×C₁₉	C₂³	1	24	yes	—
244	C₄×D₄×C₁₉	C₂³	1	6	yes	—
245	C₄×D₄×C₁₉	C₂³	1	12	yes	—
246	C₁₉×#117	C₂³	1	1	yes	characteristic
247	C₁₉×#117	C₂³	1	3	yes	—
248	C₁₉×#117	C₂³	1	6	yes	—
249	C₁₉×#117	C₂³	1	6	yes	—
250	C₁₉×#117	C₂³	1	6	yes	—
251	C₁₉×#117	C₂³	1	12	yes	—
252	C₁₉×#117	C₂³	1	12	yes	—
253	C₁₉×#117	C₂³	1	12	yes	—
254	C₁₉×#117	C₂³	1	12	yes	—
255	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
256	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
257	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
258	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
259	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
260	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
261	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
262	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
263	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
264	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
265	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
266	#41×C₁₉	—	2	8	no	—
267	#41×C₁₉	—	2	4	no	—
268	#41×C₁₉	—	2	12	no	—
269	#41×C₁₉	—	4	24	no	—
270	#41×C₁₉	—	4	24	no	—
271	#41×C₁₉	—	4	24	no	—
272	C₂×Q₈×C₁₉	—	2	4	no	—
273	C₂×Q₈×C₁₉	—	2	16	no	—
274	C₂×Q₈×C₁₉	—	2	8	no	—
275	C₂×Q₈×C₁₉	—	4	12	no	—
276	C₂×Q₈×C₁₉	—	4	24	no	—
277	C₂×Q₈×C₁₉	—	4	24	no	—
278	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
280	C₂×Q₈×C₁₉	C₂⁴	1	3	yes	—
281	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
282	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
283	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
284	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
285	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
286	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
287	C₂×D₄×C₁₉	—	2	4	no	—
288	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
289	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
290	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
291	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
292	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
293	C₂×D₄×C₁₉	C₂⁴	1	3	yes	—
294	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
295	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
296	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
297	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
298	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
299	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
300	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
301	C₂²×C₄×C₁₉	—	4	12	no	—
302	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
304	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
305	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
306	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
307	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
308	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
309	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
310	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
311	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
312	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
313	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
314	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
316	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
317	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
318	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
319	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
320	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
321	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
322	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
323	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
324	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
325	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
326	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
327	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
328	C₄⋊C₄×C₁₉	C₂⁴	1	3	yes	—
329	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
330	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
331	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
334	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
335	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
336	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
339	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
340	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
341	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
342	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
343	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
344	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
345	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
346	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
347	C₂²⋊C₄×C₁₉	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
349	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
350	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
351	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
352	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
353	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
354	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
355	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
356	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
357	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
358	C₄²×C₁₉	C₂⁴	1	2	yes	—
359	C₄²×C₁₉	C₂⁴	1	3	yes	—
360	C₄²×C₁₉	C₂⁴	1	3	yes	—
361	C₄²×C₁₉	C₂⁴	1	3	yes	—
362	C₄²×C₁₉	C₂⁴	1	6	yes	—
363	C₄²×C₁₉	C₂⁴	1	6	yes	—
364	C₄²×C₁₉	C₂⁴	1	3	yes	—
365	C₄²×C₁₉	C₂⁴	1	6	yes	—
366	C₄²×C₁₉	C₂⁴	1	6	yes	—
367	C₄²×C₁₉	C₂⁴	1	6	yes	—
368	C₄²×C₁₉	C₂⁴	1	24	yes	—
369	#62913	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂³×C₁₉	—	2	4	no	—
371	C₂³×C₁₉	—	4	2	no	—
372	C₂³×C₁₉	—	4	2	no	—
373	C₂³×C₁₉	C₂⁵	1	4	yes	—
374	C₂³×C₁₉	C₂⁵	1	2	yes	—
375	C₂³×C₁₉	C₂⁵	1	6	yes	—
376	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
377	Q₈×C₁₉	—	2	6	no	—
378	Q₈×C₁₉	—	2	24	no	—
379	Q₈×C₁₉	—	2	12	no	—
380	Q₈×C₁₉	—	2	2	no	—
381	Q₈×C₁₉	—	2	6	no	—
382	Q₈×C₁₉	—	4	12	no	—
383	Q₈×C₁₉	—	4	12	no	—
384	Q₈×C₁₉	—	4	6	no	—
385	Q₈×C₁₉	H(5,𝔽₂)	1	4	yes	—
386	D₄×C₁₉	—	2	4	no	—
387	D₄×C₁₉	—	2	12	no	—
388	D₄×C₁₉	—	2	12	no	—
389	D₄×C₁₉	—	2	4	no	—
390	D₄×C₁₉	—	2	4	no	—
391	D₄×C₁₉	—	2	2	no	—
392	D₄×C₁₉	—	2	6	no	—
393	D₄×C₁₉	—	4	4	no	—
394	D₄×C₁₉	—	4	6	no	—
395	D₄×C₁₉	—	4	12	no	—
396	D₄×C₁₉	—	4	4	no	—
397	D₄×C₁₉	—	4	12	no	—
398	D₄×C₁₉	—	4	12	no	—
399	C₂×C₄×C₁₉	—	2	6	no	—
400	C₂×C₄×C₁₉	—	2	24	no	—
401	C₂×C₄×C₁₉	—	2	12	no	—
402	C₂×C₄×C₁₉	—	2	12	no	—
403	C₂×C₄×C₁₉	—	2	12	no	—
404	C₂×C₄×C₁₉	—	2	4	no	—
405	C₂×C₄×C₁₉	—	4	6	no	—
406	C₂×C₄×C₁₉	—	4	12	no	—
407	C₂×C₄×C₁₉	—	4	3	no	—
408	C₂×C₄×C₁₉	—	4	6	no	—
409	C₂×C₄×C₁₉	—	4	6	no	—
410	C₂×C₄×C₁₉	—	4	24	no	—
411	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	complemented
412	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
413	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
414	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
415	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
416	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
418	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
419	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
420	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
421	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
422	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
423	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
424	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
425	#3554	C₂×C₁₉	1	6	yes	complemented
426	#3552	C₂×C₁₉	1	6	yes	complemented
427	#3550	C₂×C₁₉	1	6	yes	complemented
428	#3547	C₂×C₁₉	1	6	yes	complemented
429	#3541	C₂×C₁₉	1	12	yes	complemented
430	#3523	C₂×C₁₉	1	2	yes	complemented
431	#3518	C₂×C₁₉	1	2	yes	complemented
432	#3511	C₂×C₁₉	1	3	yes	complemented
433	#3506	C₂×C₁₉	1	3	yes	complemented
434	#3503	C₂×C₁₉	1	3	yes	complemented
435	#3499	C₂×C₁₉	1	2	yes	complemented
436	#3497	C₂×C₁₉	1	2	yes	complemented
437	#3486	C₂×C₁₉	1	4	yes	complemented
438	#3480	C₂×C₁₉	1	1	yes	characteristic, complemented
439	Q₈×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
440	C₂×D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
441	#3460	C₂×C₁₉	1	3	yes	complemented
442	C₂²×C₁₉	—	2	1	no	—
443	C₂²×C₁₉	—	2	1	no	—
444	C₂²×C₁₉	—	2	4	no	—
445	C₂²×C₁₉	—	2	2	no	—
446	C₂²×C₁₉	—	2	6	no	—
447	C₂²×C₁₉	—	2	2	no	—
448	C₂²×C₁₉	—	2	6	no	—
449	C₂²×C₁₉	—	2	4	no	—
450	C₂²×C₁₉	—	2	2	no	—
451	C₂²×C₁₉	—	2	6	no	—
452	C₂²×C₁₉	—	2	4	no	—
453	C₂²×C₁₉	—	4	8	no	—
454	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
455	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
456	C₄×C₁₉	—	2	2	no	—
457	C₄×C₁₉	—	2	6	no	—
458	C₄×C₁₉	—	2	12	no	—
459	C₄×C₁₉	—	2	3	no	—
460	C₄×C₁₉	—	2	6	no	—
461	C₄×C₁₉	—	2	2	no	—
462	C₄×C₁₉	—	2	3	no	—
463	C₄×C₁₉	—	2	2	no	—
464	C₄×C₁₉	—	2	3	no	—
465	C₄×C₁₉	—	2	6	no	—
466	C₄×C₁₉	C₂×H(5,𝔽₂)	1	6	yes	—
467	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
468	C₄×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
469	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	complemented
470	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
471	#563	C₂²×C₁₉	1	24	yes	complemented
472	#562	C₂²×C₁₉	1	24	yes	complemented
473	#559	C₂²×C₁₉	1	12	yes	—
474	#559	C₂²×C₁₉	1	3	yes	complemented
475	Q₈²	C₂²×C₁₉	1	1	yes	characteristic, complemented
476	Q₈²	C₂²×C₁₉	1	6	yes	complemented
477	#557	C₂²×C₁₉	1	3	yes	complemented
478	#557	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	#557	C₂²×C₁₉	1	6	yes	complemented
480	#556	C₂²×C₁₉	1	6	yes	—
481	#556	C₂²×C₁₉	1	3	yes	complemented
482	#556	C₂²×C₁₉	1	6	yes	complemented
483	#556	C₂²×C₁₉	1	12	yes	complemented
484	#555	C₂²×C₁₉	1	6	yes	—
485	#555	C₂²×C₁₉	1	6	yes	complemented
486	#554	C₂²×C₁₉	1	6	yes	—
487	#554	C₂²×C₁₉	1	12	yes	—
488	#554	C₂²×C₁₉	1	3	yes	complemented
489	#554	C₂²×C₁₉	1	6	yes	complemented
490	#554	C₂²×C₁₉	1	6	yes	complemented
491	#553	C₂²×C₁₉	1	6	yes	—
492	#553	C₂²×C₁₉	1	12	yes	—
493	#553	C₂²×C₁₉	1	12	yes	—
494	#552	C₂²×C₁₉	1	12	yes	complemented
495	#550	C₂²×C₁₉	1	6	yes	—
496	#550	C₂²×C₁₉	1	1	yes	characteristic, complemented
497	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
498	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
499	D₄×Q₈	C₂²×C₁₉	1	6	yes	—
500	D₄×Q₈	C₂²×C₁₉	1	6	yes	—
501	D₄×Q₈	C₂²×C₁₉	1	2	yes	—
502	D₄×Q₈	C₂²×C₁₉	1	12	yes	—
503	D₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
504	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
505	D₄×Q₈	C₂²×C₁₉	1	12	yes	complemented
506	D₄×Q₈	C₂²×C₁₉	1	6	yes	complemented
507	#548	C₂²×C₁₉	1	2	yes	—
508	#548	C₂²×C₁₉	1	12	yes	—
509	#548	C₂²×C₁₉	1	4	yes	complemented
510	#548	C₂²×C₁₉	1	12	yes	complemented
511	#548	C₂²×C₁₉	1	12	yes	complemented
512	#547	C₂²×C₁₉	1	6	yes	—
513	#547	C₂²×C₁₉	1	6	yes	complemented
514	#547	C₂²×C₁₉	1	12	yes	complemented
515	#544	C₂²×C₁₉	1	3	yes	—
516	#544	C₂²×C₁₉	1	12	yes	complemented
517	#542	C₂²×C₁₉	1	6	yes	—
518	#542	C₂²×C₁₉	1	6	yes	—
519	#542	C₂²×C₁₉	1	12	yes	complemented
520	#542	C₂²×C₁₉	1	12	yes	complemented
521	#542	C₂²×C₁₉	1	24	yes	complemented
522	#541	C₂²×C₁₉	1	12	yes	complemented
523	#540	C₂²×C₁₉	1	6	yes	—
524	#540	C₂²×C₁₉	1	6	yes	—
525	#539	C₂²×C₁₉	1	24	yes	complemented
526	#538	C₂²×C₁₉	1	12	yes	—
527	#538	C₂²×C₁₉	1	12	yes	—
528	#537	C₂²×C₁₉	1	3	yes	—
529	#537	C₂²×C₁₉	1	12	yes	complemented
530	#536	C₂²×C₁₉	1	12	yes	complemented
531	#536	C₂²×C₁₉	1	12	yes	complemented
532	#536	C₂²×C₁₉	1	12	yes	complemented
533	#535	C₂²×C₁₉	1	1	yes	characteristic
534	#535	C₂²×C₁₉	1	3	yes	—
535	#533	C₂²×C₁₉	1	3	yes	—
536	#533	C₂²×C₁₉	1	6	yes	complemented
537	#533	C₂²×C₁₉	1	6	yes	complemented
538	#533	C₂²×C₁₉	1	6	yes	complemented
539	#532	C₂²×C₁₉	1	6	yes	—
540	#532	C₂²×C₁₉	1	6	yes	—
541	#532	C₂²×C₁₉	1	3	yes	—
542	#532	C₂²×C₁₉	1	6	yes	complemented
543	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
544	C₂×C₄⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
545	#529	C₂²×C₁₉	1	6	yes	—
546	#529	C₂²×C₁₉	1	6	yes	—
547	#529	C₂²×C₁₉	1	6	yes	complemented
548	#525	C₂²×C₁₉	1	12	yes	—
549	#525	C₂²×C₁₉	1	12	yes	—
550	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
551	#520	C₂²×C₁₉	1	6	yes	—
552	#519	C₂²×C₁₉	1	4	yes	complemented
553	C₄×#41	C₂²×C₁₉	1	3	yes	—
554	C₄×#41	C₂²×C₁₉	1	3	yes	—
555	C₄×#41	C₂²×C₁₉	1	2	yes	complemented
556	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
557	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
558	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
559	C₂×C₁₉	—	2	2	no	—
560	C₂×C₁₉	—	4	2	no	—
561	C₂×C₁₉	—	4	6	no	—
562	C₂×C₁₉	—	4	4	no	—
563	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
565	C₂×C₁₉	2₋¹⁺⁶	1	1	yes	characteristic
566	2₋¹⁺⁴	—	4	16	no	—
567	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
568	C₂×#41	C₂³×C₁₉	1	3	yes	—
569	C₂×#41	C₂³×C₁₉	1	2	yes	—
570	C₂×#41	C₂³×C₁₉	1	12	yes	—
571	C₂×#41	C₂³×C₁₉	1	12	yes	—
572	C₂×#41	C₂³×C₁₉	1	12	yes	—
573	C₂²×Q₈	—	4	8	no	—
574	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
575	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
576	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
577	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
578	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
579	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
580	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
582	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
583	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
584	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
585	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
586	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
587	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
588	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	—
589	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	—
590	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
591	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
592	C₄⋊Q₈	C₂³×C₁₉	1	3	yes	—
593	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
594	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	—
595	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
596	#127	C₂³×C₁₉	1	2	yes	—
597	#127	C₂³×C₁₉	1	3	yes	—
598	#127	C₂³×C₁₉	1	6	yes	—
599	#126	C₂³×C₁₉	1	12	yes	—
600	#126	C₂³×C₁₉	1	12	yes	—
601	#126	C₂³×C₁₉	1	12	yes	—
602	#126	C₂³×C₁₉	1	24	yes	—
603	#126	C₂³×C₁₉	1	24	yes	—
604	#125	C₂³×C₁₉	1	6	yes	—
605	#125	C₂³×C₁₉	1	6	yes	—
606	#125	C₂³×C₁₉	1	6	yes	—
607	#125	C₂³×C₁₉	1	6	yes	—
608	#125	C₂³×C₁₉	1	12	yes	—
609	#125	C₂³×C₁₉	1	12	yes	—
610	#125	C₂³×C₁₉	1	24	yes	—
611	#124	C₂³×C₁₉	1	2	yes	—
612	#124	C₂³×C₁₉	1	6	yes	—
613	#124	C₂³×C₁₉	1	6	yes	—
614	#124	C₂³×C₁₉	1	12	yes	—
615	#124	C₂³×C₁₉	1	12	yes	—
616	#124	C₂³×C₁₉	1	6	yes	—
617	#124	C₂³×C₁₉	1	12	yes	—
618	#124	C₂³×C₁₉	1	24	yes	—
619	#124	C₂³×C₁₉	1	24	yes	—
620	#123	C₂³×C₁₉	1	12	yes	—
621	#123	C₂³×C₁₉	1	12	yes	—
622	#123	C₂³×C₁₉	1	24	yes	—
623	#123	C₂³×C₁₉	1	12	yes	—
624	#123	C₂³×C₁₉	1	12	yes	—
625	#123	C₂³×C₁₉	1	12	yes	—
626	#123	C₂³×C₁₉	1	24	yes	—
627	#123	C₂³×C₁₉	1	24	yes	—
628	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
629	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
630	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
631	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
632	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
633	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
634	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
635	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
636	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
637	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
638	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
639	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
640	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
641	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
642	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
643	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
644	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
645	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
646	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
647	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
648	#121	C₂³×C₁₉	1	6	yes	—
649	#121	C₂³×C₁₉	1	12	yes	—
650	#121	C₂³×C₁₉	1	12	yes	—
651	#121	C₂³×C₁₉	1	12	yes	—
652	#121	C₂³×C₁₉	1	2	yes	—
653	#121	C₂³×C₁₉	1	6	yes	—
654	#121	C₂³×C₁₉	1	6	yes	—
655	#121	C₂³×C₁₉	1	2	yes	—
656	#121	C₂³×C₁₉	1	6	yes	—
657	#121	C₂³×C₁₉	1	6	yes	—
658	#121	C₂³×C₁₉	1	6	yes	—
659	#121	C₂³×C₁₉	1	12	yes	—
660	#121	C₂³×C₁₉	1	6	yes	—
661	#121	C₂³×C₁₉	1	12	yes	—
662	#121	C₂³×C₁₉	1	12	yes	—
663	#121	C₂³×C₁₉	1	24	yes	—
664	#120	C₂³×C₁₉	1	4	yes	—
665	#120	C₂³×C₁₉	1	12	yes	—
666	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
667	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
668	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
669	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
670	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
671	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
672	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
673	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
674	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
675	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
676	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
677	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
678	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
679	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
680	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
681	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
682	C₄×Q₈	C₂³×C₁₉	1	12	yes	—
683	C₄×D₄	C₂³×C₁₉	1	6	yes	—
684	C₄×D₄	C₂³×C₁₉	1	6	yes	—
685	C₄×D₄	C₂³×C₁₉	1	6	yes	—
686	C₄×D₄	C₂³×C₁₉	1	6	yes	—
687	C₄×D₄	C₂³×C₁₉	1	6	yes	—
688	C₄×D₄	C₂³×C₁₉	1	6	yes	—
689	C₄×D₄	C₂³×C₁₉	1	3	yes	—
690	C₄×D₄	C₂³×C₁₉	1	3	yes	—
691	C₄×D₄	C₂³×C₁₉	1	6	yes	—
692	C₄×D₄	C₂³×C₁₉	1	6	yes	—
693	C₄×D₄	C₂³×C₁₉	1	3	yes	—
694	C₄×D₄	C₂³×C₁₉	1	3	yes	—
695	C₄×D₄	C₂³×C₁₉	1	6	yes	—
696	C₄×D₄	C₂³×C₁₉	1	6	yes	—
697	C₄×D₄	C₂³×C₁₉	1	24	yes	—
698	C₄×D₄	C₂³×C₁₉	1	12	yes	—
699	C₄×D₄	C₂³×C₁₉	1	12	yes	—
700	C₄×D₄	C₂³×C₁₉	1	12	yes	—
701	C₄×D₄	C₂³×C₁₉	1	24	yes	—
702	C₄×D₄	C₂³×C₁₉	1	6	yes	—
703	C₄×D₄	C₂³×C₁₉	1	12	yes	—
704	#117	C₂³×C₁₉	1	1	yes	characteristic
705	#117	C₂³×C₁₉	1	3	yes	—
706	#117	C₂³×C₁₉	1	6	yes	—
707	#117	C₂³×C₁₉	1	6	yes	—
708	#117	C₂³×C₁₉	1	6	yes	—
709	#117	C₂³×C₁₉	1	12	yes	—
710	#117	C₂³×C₁₉	1	12	yes	—
711	#117	C₂³×C₁₉	1	12	yes	—
712	#117	C₂³×C₁₉	1	12	yes	—
713	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
714	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
715	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
716	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
718	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
720	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
721	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
722	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
723	C₁₉	#62913	1	1	yes	characteristic, direct product factor, Sylow
724	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
725	#41	—	2	8	no	—
726	#41	—	2	4	no	—
727	#41	—	2	12	no	—
728	#41	—	4	24	no	—
729	#41	—	4	24	no	—
730	#41	—	4	24	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	2	16	no	—
733	C₂×Q₈	—	2	8	no	—
734	C₂×Q₈	—	4	12	no	—
735	C₂×Q₈	—	4	24	no	—
736	C₂×Q₈	—	4	24	no	—
737	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
738	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
739	C₂×Q₈	C₂⁴×C₁₉	1	3	yes	—
740	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
741	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
742	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
743	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
744	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
745	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
748	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
749	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
750	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
752	C₂×D₄	C₂⁴×C₁₉	1	3	yes	—
753	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
754	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
755	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
756	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
757	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
758	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
759	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
760	C₂²×C₄	—	4	12	no	—
761	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
763	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
764	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
765	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
766	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
767	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
768	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
769	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
770	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
771	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
772	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
773	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
774	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
775	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
776	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
777	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
778	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
779	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
780	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
781	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
782	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
783	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
784	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
785	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
786	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
787	C₄⋊C₄	C₂⁴×C₁₉	1	3	yes	—
788	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
789	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
790	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
793	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
794	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
795	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
796	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
797	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
798	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
799	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
800	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
801	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
802	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
803	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
804	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
805	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
806	C₂²⋊C₄	C₂⁴×C₁₉	1	2	yes	—
807	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
808	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
809	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
810	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
811	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
812	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
813	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
814	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
815	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
816	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
817	C₄²	C₂⁴×C₁₉	1	2	yes	—
818	C₄²	C₂⁴×C₁₉	1	3	yes	—
819	C₄²	C₂⁴×C₁₉	1	3	yes	—
820	C₄²	C₂⁴×C₁₉	1	3	yes	—
821	C₄²	C₂⁴×C₁₉	1	6	yes	—
822	C₄²	C₂⁴×C₁₉	1	6	yes	—
823	C₄²	C₂⁴×C₁₉	1	3	yes	—
824	C₄²	C₂⁴×C₁₉	1	6	yes	—
825	C₄²	C₂⁴×C₁₉	1	6	yes	—
826	C₄²	C₂⁴×C₁₉	1	6	yes	—
827	C₄²	C₂⁴×C₁₉	1	24	yes	—
828	C₂³	—	2	4	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	2	no	—
831	C₂³	C₂⁵×C₁₉	1	4	yes	—
832	C₂³	C₂⁵×C₁₉	1	2	yes	—
833	C₂³	C₂⁵×C₁₉	1	6	yes	—
834	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
835	Q₈	—	2	6	no	—
836	Q₈	—	2	24	no	—
837	Q₈	—	2	12	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	6	no	—
840	Q₈	—	4	12	no	—
841	Q₈	—	4	12	no	—
842	Q₈	—	4	6	no	—
843	Q₈	C₁₉×H(5,𝔽₂)	1	4	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	12	no	—
846	D₄	—	2	12	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	6	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	12	no	—
853	D₄	—	4	12	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	6	no	—
856	D₄	—	4	12	no	—
857	C₂×C₄	—	2	6	no	—
858	C₂×C₄	—	2	24	no	—
859	C₂×C₄	—	2	12	no	—
860	C₂×C₄	—	2	12	no	—
861	C₂×C₄	—	2	12	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	4	6	no	—
864	C₂×C₄	—	4	12	no	—
865	C₂×C₄	—	4	24	no	—
866	C₂×C₄	—	4	3	no	—
867	C₂×C₄	—	4	6	no	—
868	C₂×C₄	—	4	6	no	—
869	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	complemented
870	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
871	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
872	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
873	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
874	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
875	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
876	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
877	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
878	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
879	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
880	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
881	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
882	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	6	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	6	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	6	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	8	no	—
895	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
896	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	6	no	—
899	C₄	—	2	12	no	—
900	C₄	—	2	3	no	—
901	C₄	—	2	6	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	3	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	3	no	—
906	C₄	—	2	6	no	—
907	C₄	C₂×C₁₉×H(5,𝔽₂)	1	6	yes	—
908	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
909	C₄	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	6	no	—
914	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₁₉×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3554	C₂	semidirect
2. C₁₉×#3552	C₂	semidirect
3. C₁₉×#3550	C₂	semidirect
4. C₁₉×#3547	C₂	semidirect
5. C₁₉×#3541	C₂	semidirect
6. C₁₉×#3523	C₂	semidirect
7. C₁₉×#3518	C₂	semidirect
8. C₁₉×#3511	C₂	semidirect
9. C₁₉×#3506	C₂	semidirect
10. C₁₉×#3503	C₂	semidirect
11. C₁₉×#3499	C₂	semidirect
12. C₁₉×#3497	C₂	semidirect
13. C₁₉×#3486	C₂	semidirect
14. C₁₉×#3480	C₂	semidirect
15. Q₈×#41×C₁₉	C₂	semidirect
16. C₂×D₄×Q₈×C₁₉	C₂	semidirect
17. C₁₉×#3460	C₂	semidirect
18. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
20. C₁₉×#563	C₂²	semidirect
21. C₁₉×#562	C₂²	semidirect
23. C₁₉×#559	C₂²	semidirect
24. Q₈²×C₁₉	C₂²	semidirect
25. Q₈²×C₁₉	C₂²	semidirect
26. C₁₉×#557	C₂²	semidirect
27. C₁₉×#557	C₂²	semidirect
28. C₁₉×#557	C₂²	semidirect
30. C₁₉×#556	C₂²	semidirect
31. C₁₉×#556	C₂²	semidirect
32. C₁₉×#556	C₂²	semidirect
34. C₁₉×#555	C₂²	semidirect
37. C₁₉×#554	C₂²	semidirect
38. C₁₉×#554	C₂²	semidirect
39. C₁₉×#554	C₂²	semidirect
43. C₁₉×#552	C₂²	semidirect
45. C₁₉×#550	C₂²	semidirect
52. D₄×Q₈×C₁₉	C₂²	semidirect
53. D₄×Q₈×C₁₉	C₂²	semidirect
54. D₄×Q₈×C₁₉	C₂²	semidirect
55. D₄×Q₈×C₁₉	C₂²	semidirect
58. C₁₉×#548	C₂²	semidirect
59. C₁₉×#548	C₂²	semidirect
60. C₁₉×#548	C₂²	semidirect
62. C₁₉×#547	C₂²	semidirect
63. C₁₉×#547	C₂²	semidirect
65. C₁₉×#544	C₂²	semidirect
68. C₁₉×#542	C₂²	semidirect
69. C₁₉×#542	C₂²	semidirect
70. C₁₉×#542	C₂²	semidirect
71. C₁₉×#541	C₂²	semidirect
74. C₁₉×#539	C₂²	semidirect
78. C₁₉×#537	C₂²	semidirect
79. C₁₉×#536	C₂²	semidirect
80. C₁₉×#536	C₂²	semidirect
81. C₁₉×#536	C₂²	semidirect
85. C₁₉×#533	C₂²	semidirect
86. C₁₉×#533	C₂²	semidirect
87. C₁₉×#533	C₂²	semidirect
91. C₁₉×#532	C₂²	semidirect
93. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
96. C₁₉×#529	C₂²	semidirect
101. C₁₉×#519	C₂²	semidirect
104. C₄×#41×C₁₉	C₂²	semidirect
106. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
369. #62913	C₁₉	direct (N × H)
411. C₂×C₄×C₁₉	2₋¹⁺⁴	semidirect
425. #3554	C₂×C₁₉	semidirect
426. #3552	C₂×C₁₉	semidirect
427. #3550	C₂×C₁₉	semidirect
428. #3547	C₂×C₁₉	semidirect
429. #3541	C₂×C₁₉	semidirect
430. #3523	C₂×C₁₉	semidirect
431. #3518	C₂×C₁₉	semidirect
432. #3511	C₂×C₁₉	semidirect
433. #3506	C₂×C₁₉	semidirect
434. #3503	C₂×C₁₉	semidirect
435. #3499	C₂×C₁₉	semidirect
436. #3497	C₂×C₁₉	semidirect
437. #3486	C₂×C₁₉	semidirect
438. #3480	C₂×C₁₉	semidirect
439. Q₈×#41	C₂×C₁₉	semidirect
440. C₂×D₄×Q₈	C₂×C₁₉	semidirect
441. #3460	C₂×C₁₉	semidirect
469. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
471. #563	C₂²×C₁₉	semidirect
472. #562	C₂²×C₁₉	semidirect
474. #559	C₂²×C₁₉	semidirect
475. Q₈²	C₂²×C₁₉	semidirect
476. Q₈²	C₂²×C₁₉	semidirect
477. #557	C₂²×C₁₉	semidirect
478. #557	C₂²×C₁₉	semidirect
479. #557	C₂²×C₁₉	semidirect
481. #556	C₂²×C₁₉	semidirect
482. #556	C₂²×C₁₉	semidirect
483. #556	C₂²×C₁₉	semidirect
485. #555	C₂²×C₁₉	semidirect
488. #554	C₂²×C₁₉	semidirect
489. #554	C₂²×C₁₉	semidirect
490. #554	C₂²×C₁₉	semidirect
494. #552	C₂²×C₁₉	semidirect
496. #550	C₂²×C₁₉	semidirect
503. D₄×Q₈	C₂²×C₁₉	semidirect
504. D₄×Q₈	C₂²×C₁₉	semidirect
505. D₄×Q₈	C₂²×C₁₉	semidirect
506. D₄×Q₈	C₂²×C₁₉	semidirect
509. #548	C₂²×C₁₉	semidirect
510. #548	C₂²×C₁₉	semidirect
511. #548	C₂²×C₁₉	semidirect
513. #547	C₂²×C₁₉	semidirect
514. #547	C₂²×C₁₉	semidirect
516. #544	C₂²×C₁₉	semidirect
519. #542	C₂²×C₁₉	semidirect
520. #542	C₂²×C₁₉	semidirect
521. #542	C₂²×C₁₉	semidirect
522. #541	C₂²×C₁₉	semidirect
525. #539	C₂²×C₁₉	semidirect
529. #537	C₂²×C₁₉	semidirect
530. #536	C₂²×C₁₉	semidirect
531. #536	C₂²×C₁₉	semidirect
532. #536	C₂²×C₁₉	semidirect
536. #533	C₂²×C₁₉	semidirect
537. #533	C₂²×C₁₉	semidirect
538. #533	C₂²×C₁₉	semidirect
542. #532	C₂²×C₁₉	semidirect
544. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
547. #529	C₂²×C₁₉	semidirect
552. #519	C₂²×C₁₉	semidirect
555. C₄×#41	C₂²×C₁₉	semidirect
557. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
723. C₁₉	#62913	direct (N × H)
869. C₂×C₄	C₁₉×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3554	2
C₁₉×#3552	2
C₁₉×#3550	2
C₁₉×#3547	2
C₁₉×#3541	2
C₁₉×#3523	2
C₁₉×#3518	2
C₁₉×#3511	2
C₁₉×#3506	2
C₁₉×#3503	2
C₁₉×#3499	2
C₁₉×#3497	2
C₁₉×#3486	2
C₁₉×#3480	2
Q₈×#41×C₁₉	2
C₂×D₄×Q₈×C₁₉	2
C₁₉×#3460	2
#62913	19

Subgroups — C19×#62913 #18068872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62913 #18068872