Subgroups — C₂×C₁₉×#3524 #18068751

Order 4864.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3524	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#559	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#555	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₉×#553	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₉×#552	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#542	C₂	1	3	yes	maximal, complemented
11	C₂×C₁₉×#540	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₉×#529	C₂	1	3	yes	maximal, complemented
13	C₂×C₁₉×#529	C₂	1	3	yes	maximal, complemented
14	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#559	C₂²	1	48	yes	complemented
21	C₁₉×#557	C₂²	1	16	yes	complemented
22	C₁₉×#555	C₂²	1	48	yes	complemented
23	C₁₉×#553	C₂²	1	48	yes	complemented
24	C₁₉×#552	C₂²	1	48	yes	complemented
25	C₁₉×#550	C₂²	1	16	yes	complemented
26	C₁₉×#548	C₂²	1	16	yes	complemented
27	C₁₉×#548	C₂²	1	16	yes	complemented
28	C₁₉×#542	C₂²	1	48	yes	complemented
29	C₁₉×#540	C₂²	1	48	yes	complemented
30	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
31	C₂×C₁₉×#127	C₂²	1	3	yes	—
32	C₁₉×#529	C₂²	1	48	yes	complemented
33	C₁₉×#529	C₂²	1	48	yes	complemented
34	C₂×C₁₉×#126	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#126	C₂²	1	3	yes	—
36	C₂×C₁₉×#126	C₂²	1	6	yes	—
37	C₂×C₁₉×#125	C₂²	1	3	yes	—
38	C₂×C₁₉×#125	C₂²	1	3	yes	—
39	C₂×C₁₉×#125	C₂²	1	3	yes	—
40	C₂×C₁₉×#124	C₂²	1	3	yes	—
41	C₂×C₁₉×#124	C₂²	1	3	yes	—
42	C₂×C₁₉×#124	C₂²	1	3	yes	—
43	C₂×C₁₉×#124	C₂²	1	6	yes	—
44	C₂×C₁₉×#123	C₂²	1	6	yes	—
45	C₂×C₁₉×#123	C₂²	1	3	yes	—
46	C₂×C₁₉×#123	C₂²	1	3	yes	—
47	C₂×C₁₉×#123	C₂²	1	6	yes	—
48	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
49	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
50	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
51	C₂×C₁₉×#121	C₂²	1	3	yes	—
52	C₂×C₁₉×#121	C₂²	1	3	yes	—
53	C₂×C₁₉×#121	C₂²	1	3	yes	—
54	C₂×C₁₉×#121	C₂²	1	3	yes	—
55	C₂×C₁₉×#121	C₂²	1	6	yes	—
56	C₂×C₁₉×#121	C₂²	1	3	yes	—
57	C₁₉×#520	C₂²	1	16	yes	complemented
58	C₁₉×#519	C₂²	1	16	yes	complemented
59	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
60	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
63	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
64	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
65	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
67	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
68	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
69	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
70	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
71	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
72	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
73	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
74	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
75	C₂×C₁₉×#117	C₂²	1	3	yes	—
76	C₂×C₁₉×#117	C₂²	1	3	yes	—
77	C₂×C₁₉×#117	C₂²	1	3	yes	—
78	C₂×C₁₉×#117	C₂²	1	3	yes	—
79	C₂×C₁₉×#117	C₂²	1	6	yes	—
80	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
81	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
82	C₂×#41×C₁₉	—	2	8	no	—
83	C₂×#41×C₁₉	—	2	8	no	—
84	C₂×#41×C₁₉	C₂³	1	8	yes	—
85	C₂×#41×C₁₉	C₂³	1	8	yes	—
86	C₂²×Q₈×C₁₉	—	2	8	no	—
87	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
88	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
89	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
90	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
92	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
93	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
94	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
95	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
96	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
97	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
98	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
99	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
100	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
101	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
102	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
103	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
104	C₁₉×#127	C₂³	1	24	yes	—
105	C₁₉×#126	C₂³	1	8	yes	—
106	C₁₉×#126	C₂³	1	24	yes	—
107	C₁₉×#126	C₂³	1	48	yes	—
108	C₁₉×#125	C₂³	1	24	yes	—
109	C₁₉×#125	C₂³	1	24	yes	—
110	C₁₉×#125	C₂³	1	24	yes	—
111	C₁₉×#124	C₂³	1	24	yes	—
112	C₁₉×#124	C₂³	1	24	yes	—
113	C₁₉×#124	C₂³	1	24	yes	—
114	C₁₉×#124	C₂³	1	48	yes	—
115	C₁₉×#123	C₂³	1	48	yes	—
116	C₁₉×#123	C₂³	1	24	yes	—
117	C₁₉×#123	C₂³	1	24	yes	—
118	C₁₉×#123	C₂³	1	48	yes	—
119	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
121	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
122	C₁₉×#121	C₂³	1	24	yes	—
123	C₁₉×#121	C₂³	1	24	yes	—
124	C₁₉×#121	C₂³	1	24	yes	—
125	C₁₉×#121	C₂³	1	24	yes	—
126	C₁₉×#121	C₂³	1	48	yes	—
127	C₁₉×#121	C₂³	1	24	yes	—
128	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
129	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
130	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
131	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
132	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
133	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
134	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
135	C₄×D₄×C₁₉	C₂³	1	24	yes	—
136	C₄×D₄×C₁₉	C₂³	1	24	yes	—
137	C₄×D₄×C₁₉	C₂³	1	24	yes	—
138	C₄×D₄×C₁₉	C₂³	1	24	yes	—
139	C₄×D₄×C₁₉	C₂³	1	24	yes	—
140	C₄×D₄×C₁₉	C₂³	1	24	yes	—
141	C₄×D₄×C₁₉	C₂³	1	24	yes	—
142	C₄×D₄×C₁₉	C₂³	1	48	yes	—
143	C₁₉×#117	C₂³	1	24	yes	—
144	C₁₉×#117	C₂³	1	24	yes	—
145	C₁₉×#117	C₂³	1	24	yes	—
146	C₁₉×#117	C₂³	1	24	yes	—
147	C₁₉×#117	C₂³	1	48	yes	—
148	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
149	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
150	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
151	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
152	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
154	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
155	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
157	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
158	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
159	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
161	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
162	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
164	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
166	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
167	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
168	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
169	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
170	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
171	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
173	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
175	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
176	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
177	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
179	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
180	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
181	C₂×C₄²×C₁₉	C₂³	1	24	yes	—
182	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
183	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
184	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
185	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
186	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
187	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
188	#41×C₁₉	—	2	32	no	—
189	#41×C₁₉	—	2	32	no	—
190	C₂×Q₈×C₁₉	—	2	32	no	—
191	C₂×Q₈×C₁₉	—	2	12	no	—
192	C₂×Q₈×C₁₉	—	4	6	no	—
193	C₂×Q₈×C₁₉	#41	1	8	yes	—
194	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
195	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
196	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
197	C₂×D₄×C₁₉	—	2	12	no	—
198	C₂×D₄×C₁₉	—	2	12	no	—
199	C₂×D₄×C₁₉	—	4	6	no	—
200	C₂×D₄×C₁₉	—	4	6	no	—
201	C₂×D₄×C₁₉	—	4	6	no	—
202	C₂×D₄×C₁₉	—	4	12	no	—
203	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
204	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
205	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
206	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
207	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
208	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
209	C₂²×C₄×C₁₉	—	2	12	no	—
210	C₂²×C₄×C₁₉	—	2	12	no	—
211	C₂²×C₄×C₁₉	—	2	12	no	—
212	C₂²×C₄×C₁₉	—	4	6	no	—
213	C₂²×C₄×C₁₉	—	4	12	no	—
214	C₂²×C₄×C₁₉	—	4	6	no	—
215	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
216	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
217	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
218	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
222	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
224	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
227	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
228	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
230	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
231	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
232	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
233	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
234	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
235	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
236	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
238	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
239	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
240	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
241	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
242	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
243	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
244	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
245	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
246	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
247	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
248	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
249	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
250	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
251	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
252	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
253	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
254	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
255	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
256	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
257	C₂²⋊C₄×C₁₉	C₂⁴	1	4	yes	—
258	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
259	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
260	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
261	C₄²×C₁₉	C₂⁴	1	4	yes	—
262	C₄²×C₁₉	C₂⁴	1	12	yes	—
263	C₄²×C₁₉	C₂⁴	1	12	yes	—
264	C₄²×C₁₉	C₂⁴	1	12	yes	—
265	C₄²×C₁₉	C₂⁴	1	24	yes	—
266	C₄²×C₁₉	C₂⁴	1	12	yes	—
267	C₄²×C₁₉	C₂⁴	1	12	yes	—
268	C₂×#3524	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	2	6	no	—
271	C₂³×C₁₉	—	2	6	no	—
272	C₂³×C₁₉	—	2	6	no	—
273	C₂³×C₁₉	—	2	6	no	—
274	C₂³×C₁₉	—	2	6	no	—
275	C₂³×C₁₉	—	2	2	no	—
276	C₂³×C₁₉	—	2	2	no	—
277	C₂³×C₁₉	—	2	6	no	—
278	C₂³×C₁₉	C₂⁵	1	2	yes	—
279	C₂³×C₁₉	C₂⁵	1	6	yes	—
280	C₂³×C₁₉	C₂⁵	1	6	yes	—
281	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
282	Q₈×C₁₉	—	2	24	no	—
283	Q₈×C₁₉	—	4	12	no	—
284	Q₈×C₁₉	C₂×#41	1	16	yes	—
285	D₄×C₁₉	—	2	24	no	—
286	D₄×C₁₉	—	2	24	no	—
287	D₄×C₁₉	—	4	12	no	—
288	D₄×C₁₉	—	4	12	no	—
289	D₄×C₁₉	—	4	12	no	—
290	D₄×C₁₉	—	4	24	no	—
291	C₂×C₄×C₁₉	—	2	2	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	6	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	6	no	—
296	C₂×C₄×C₁₉	—	2	2	no	—
297	C₂×C₄×C₁₉	—	2	6	no	—
298	C₂×C₄×C₁₉	—	2	6	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	6	no	—
301	C₂×C₄×C₁₉	—	2	2	no	—
302	C₂×C₄×C₁₉	—	2	24	no	—
303	C₂×C₄×C₁₉	—	2	24	no	—
304	C₂×C₄×C₁₉	—	2	24	no	—
305	C₂×C₄×C₁₉	—	4	12	no	—
306	C₂×C₄×C₁₉	—	4	24	no	—
307	C₂×C₄×C₁₉	—	4	12	no	—
308	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
309	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
310	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
311	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
312	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
313	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
314	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
315	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
316	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
317	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
318	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
319	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
320	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
321	#3524	C₂×C₁₉	1	32	yes	direct product factor
322	C₂×#559	C₂×C₁₉	1	3	yes	complemented
323	C₂×#557	C₂×C₁₉	1	1	yes	characteristic, complemented
324	C₂×#555	C₂×C₁₉	1	3	yes	complemented
325	C₂×#553	C₂×C₁₉	1	3	yes	complemented
326	C₂×#552	C₂×C₁₉	1	3	yes	complemented
327	C₂×#550	C₂×C₁₉	1	1	yes	characteristic, complemented
328	C₂×#548	C₂×C₁₉	1	1	yes	characteristic, complemented
329	C₂×#548	C₂×C₁₉	1	1	yes	characteristic, complemented
330	C₂×#542	C₂×C₁₉	1	3	yes	complemented
331	C₂×#540	C₂×C₁₉	1	3	yes	complemented
332	C₂×#529	C₂×C₁₉	1	3	yes	complemented
333	C₂×#529	C₂×C₁₉	1	3	yes	complemented
334	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
335	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
336	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	2	6	no	—
339	C₂²×C₁₉	—	2	6	no	—
340	C₂²×C₁₉	—	2	6	no	—
341	C₂²×C₁₉	—	2	6	no	—
342	C₂²×C₁₉	—	2	6	no	—
343	C₂²×C₁₉	—	2	2	no	—
344	C₂²×C₁₉	—	2	2	no	—
345	C₂²×C₁₉	—	2	6	no	—
346	C₂²×C₁₉	—	4	4	no	—
347	C₂²×C₁₉	—	4	12	no	—
348	C₂²×C₁₉	—	4	12	no	—
349	C₂²×C₁₉	C₂²×#41	1	2	yes	—
350	C₂²×C₁₉	#585	1	2	yes	—
351	C₂²×C₁₉	#585	1	2	yes	—
352	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
353	C₄×C₁₉	—	2	2	no	—
354	C₄×C₁₉	—	2	2	no	—
355	C₄×C₁₉	—	2	6	no	—
356	C₄×C₁₉	—	2	2	no	—
357	C₄×C₁₉	—	2	6	no	—
358	C₄×C₁₉	—	2	2	no	—
359	C₄×C₁₉	—	2	6	no	—
360	C₄×C₁₉	—	2	6	no	—
361	C₄×C₁₉	—	2	2	no	—
362	C₄×C₁₉	—	2	6	no	—
363	C₄×C₁₉	—	2	2	no	—
364	C₄×C₁₉	C₂²×#41	1	12	yes	—
365	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
366	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
367	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
368	#559	C₂²×C₁₉	1	48	yes	complemented
369	#557	C₂²×C₁₉	1	16	yes	complemented
370	#555	C₂²×C₁₉	1	48	yes	complemented
371	#553	C₂²×C₁₉	1	48	yes	complemented
372	#552	C₂²×C₁₉	1	48	yes	complemented
373	#550	C₂²×C₁₉	1	16	yes	complemented
374	#548	C₂²×C₁₉	1	16	yes	complemented
375	#548	C₂²×C₁₉	1	16	yes	complemented
376	#542	C₂²×C₁₉	1	48	yes	complemented
377	#540	C₂²×C₁₉	1	48	yes	complemented
378	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
379	C₂×#127	C₂²×C₁₉	1	3	yes	—
380	#529	C₂²×C₁₉	1	48	yes	complemented
381	#529	C₂²×C₁₉	1	48	yes	complemented
382	C₂×#126	C₂²×C₁₉	1	1	yes	characteristic
383	C₂×#126	C₂²×C₁₉	1	3	yes	—
384	C₂×#126	C₂²×C₁₉	1	6	yes	—
385	C₂×#125	C₂²×C₁₉	1	3	yes	—
386	C₂×#125	C₂²×C₁₉	1	3	yes	—
387	C₂×#125	C₂²×C₁₉	1	3	yes	—
388	C₂×#124	C₂²×C₁₉	1	3	yes	—
389	C₂×#124	C₂²×C₁₉	1	3	yes	—
390	C₂×#124	C₂²×C₁₉	1	3	yes	—
391	C₂×#124	C₂²×C₁₉	1	6	yes	—
392	C₂×#123	C₂²×C₁₉	1	6	yes	—
393	C₂×#123	C₂²×C₁₉	1	3	yes	—
394	C₂×#123	C₂²×C₁₉	1	3	yes	—
395	C₂×#123	C₂²×C₁₉	1	6	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
399	C₂×#121	C₂²×C₁₉	1	3	yes	—
400	C₂×#121	C₂²×C₁₉	1	3	yes	—
401	C₂×#121	C₂²×C₁₉	1	3	yes	—
402	C₂×#121	C₂²×C₁₉	1	3	yes	—
403	C₂×#121	C₂²×C₁₉	1	6	yes	—
404	C₂×#121	C₂²×C₁₉	1	3	yes	—
405	#520	C₂²×C₁₉	1	16	yes	complemented
406	#519	C₂²×C₁₉	1	16	yes	complemented
407	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
408	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
411	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
413	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
415	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
416	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
417	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
418	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
419	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
420	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
421	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
422	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
423	C₂×#117	C₂²×C₁₉	1	3	yes	—
424	C₂×#117	C₂²×C₁₉	1	3	yes	—
425	C₂×#117	C₂²×C₁₉	1	3	yes	—
426	C₂×#117	C₂²×C₁₉	1	3	yes	—
427	C₂×#117	C₂²×C₁₉	1	6	yes	—
428	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
429	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
430	C₂×C₁₉	—	4	2	no	—
431	C₂×C₁₉	—	4	6	no	—
432	C₂×C₁₉	—	4	6	no	—
433	C₂×C₁₉	#3524	1	4	yes	direct product factor
434	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
435	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
436	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
437	C₂×#41	—	2	8	no	—
438	C₂×#41	—	2	8	no	—
439	C₂×#41	C₂³×C₁₉	1	8	yes	—
440	C₂×#41	C₂³×C₁₉	1	8	yes	—
441	C₂²×Q₈	—	2	8	no	—
442	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
443	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
444	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
445	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
447	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
448	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
449	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
450	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
451	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
452	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
453	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
454	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
455	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
456	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
457	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
458	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
459	#127	C₂³×C₁₉	1	24	yes	—
460	#126	C₂³×C₁₉	1	8	yes	—
461	#126	C₂³×C₁₉	1	24	yes	—
462	#126	C₂³×C₁₉	1	48	yes	—
463	#125	C₂³×C₁₉	1	24	yes	—
464	#125	C₂³×C₁₉	1	24	yes	—
465	#125	C₂³×C₁₉	1	24	yes	—
466	#124	C₂³×C₁₉	1	24	yes	—
467	#124	C₂³×C₁₉	1	24	yes	—
468	#124	C₂³×C₁₉	1	24	yes	—
469	#124	C₂³×C₁₉	1	48	yes	—
470	#123	C₂³×C₁₉	1	48	yes	—
471	#123	C₂³×C₁₉	1	24	yes	—
472	#123	C₂³×C₁₉	1	24	yes	—
473	#123	C₂³×C₁₉	1	48	yes	—
474	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
475	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
476	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
477	#121	C₂³×C₁₉	1	24	yes	—
478	#121	C₂³×C₁₉	1	24	yes	—
479	#121	C₂³×C₁₉	1	24	yes	—
480	#121	C₂³×C₁₉	1	24	yes	—
481	#121	C₂³×C₁₉	1	48	yes	—
482	#121	C₂³×C₁₉	1	24	yes	—
483	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
484	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
485	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
486	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
487	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
488	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
489	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
490	C₄×D₄	C₂³×C₁₉	1	24	yes	—
491	C₄×D₄	C₂³×C₁₉	1	24	yes	—
492	C₄×D₄	C₂³×C₁₉	1	24	yes	—
493	C₄×D₄	C₂³×C₁₉	1	24	yes	—
494	C₄×D₄	C₂³×C₁₉	1	24	yes	—
495	C₄×D₄	C₂³×C₁₉	1	24	yes	—
496	C₄×D₄	C₂³×C₁₉	1	24	yes	—
497	C₄×D₄	C₂³×C₁₉	1	48	yes	—
498	#117	C₂³×C₁₉	1	24	yes	—
499	#117	C₂³×C₁₉	1	24	yes	—
500	#117	C₂³×C₁₉	1	24	yes	—
501	#117	C₂³×C₁₉	1	24	yes	—
502	#117	C₂³×C₁₉	1	48	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
532	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
533	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
534	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
535	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
536	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
537	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
538	C₂×C₄²	C₂³×C₁₉	1	24	yes	—
539	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
540	C₁₉	C₂×#3524	1	1	yes	characteristic, direct product factor, Sylow
541	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
542	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
543	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
544	#41	—	2	32	no	—
545	#41	—	2	32	no	—
546	C₂×Q₈	—	2	32	no	—
547	C₂×Q₈	—	2	12	no	—
548	C₂×Q₈	—	4	6	no	—
549	C₂×Q₈	#41×C₁₉	1	8	yes	—
550	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
551	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
552	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
553	C₂×D₄	—	2	12	no	—
554	C₂×D₄	—	2	12	no	—
555	C₂×D₄	—	4	6	no	—
556	C₂×D₄	—	4	6	no	—
557	C₂×D₄	—	4	6	no	—
558	C₂×D₄	—	4	12	no	—
559	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
560	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
561	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
562	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
563	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
564	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
565	C₂²×C₄	—	2	12	no	—
566	C₂²×C₄	—	2	12	no	—
567	C₂²×C₄	—	2	12	no	—
568	C₂²×C₄	—	4	6	no	—
569	C₂²×C₄	—	4	12	no	—
570	C₂²×C₄	—	4	6	no	—
571	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
573	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
577	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
579	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
580	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
581	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
582	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
584	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
585	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
586	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
587	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
588	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
589	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
590	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
591	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
592	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
593	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
594	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
595	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
596	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
597	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
598	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
599	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
600	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
601	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
602	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
603	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
604	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
605	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
606	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
607	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
608	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
609	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
610	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
611	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
612	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
613	C₂²⋊C₄	C₂⁴×C₁₉	1	4	yes	—
614	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
615	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
616	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
617	C₄²	C₂⁴×C₁₉	1	4	yes	—
618	C₄²	C₂⁴×C₁₉	1	12	yes	—
619	C₄²	C₂⁴×C₁₉	1	12	yes	—
620	C₄²	C₂⁴×C₁₉	1	12	yes	—
621	C₄²	C₂⁴×C₁₉	1	24	yes	—
622	C₄²	C₂⁴×C₁₉	1	12	yes	—
623	C₄²	C₂⁴×C₁₉	1	12	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	6	no	—
626	C₂³	—	2	6	no	—
627	C₂³	—	2	6	no	—
628	C₂³	—	2	6	no	—
629	C₂³	—	2	6	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	6	no	—
633	C₂³	C₂⁵×C₁₉	1	2	yes	—
634	C₂³	C₂⁵×C₁₉	1	6	yes	—
635	C₂³	C₂⁵×C₁₉	1	6	yes	—
636	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
637	Q₈	—	2	24	no	—
638	Q₈	—	4	12	no	—
639	Q₈	C₂×#41×C₁₉	1	16	yes	—
640	D₄	—	2	24	no	—
641	D₄	—	2	24	no	—
642	D₄	—	4	12	no	—
643	D₄	—	4	12	no	—
644	D₄	—	4	12	no	—
645	D₄	—	4	24	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	6	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	6	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	6	no	—
653	C₂×C₄	—	2	6	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	6	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	24	no	—
658	C₂×C₄	—	2	24	no	—
659	C₂×C₄	—	2	24	no	—
660	C₂×C₄	—	4	12	no	—
661	C₂×C₄	—	4	24	no	—
662	C₂×C₄	—	4	12	no	—
663	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
664	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
665	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
666	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
667	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
668	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
669	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
670	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
671	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
672	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
673	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
674	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
675	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	6	no	—
678	C₂²	—	2	6	no	—
679	C₂²	—	2	6	no	—
680	C₂²	—	2	6	no	—
681	C₂²	—	2	6	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	6	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	4	12	no	—
687	C₂²	—	4	12	no	—
688	C₂²	C₂²×#41×C₁₉	1	2	yes	—
689	C₂²	C₁₉×#585	1	2	yes	—
690	C₂²	C₁₉×#585	1	2	yes	—
691	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	6	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	6	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	6	no	—
699	C₄	—	2	6	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	6	no	—
702	C₄	—	2	2	no	—
703	C₄	C₂²×#41×C₁₉	1	12	yes	—
704	C₂	—	4	2	no	—
705	C₂	—	4	6	no	—
706	C₂	—	4	6	no	—
707	C₂	C₁₉×#3524	1	4	yes	direct product factor
708	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
709	C₂	C₂×C₁₉×#585	1	1	yes	characteristic
710	C₂	C₂×C₁₉×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3524	C₂	direct (N × H)
2. C₂×C₁₉×#559	C₂	semidirect
3. C₂×C₁₉×#557	C₂	semidirect
4. C₂×C₁₉×#555	C₂	semidirect
5. C₂×C₁₉×#553	C₂	semidirect
6. C₂×C₁₉×#552	C₂	semidirect
7. C₂×C₁₉×#550	C₂	semidirect
8. C₂×C₁₉×#548	C₂	semidirect
9. C₂×C₁₉×#548	C₂	semidirect
10. C₂×C₁₉×#542	C₂	semidirect
11. C₂×C₁₉×#540	C₂	semidirect
12. C₂×C₁₉×#529	C₂	semidirect
13. C₂×C₁₉×#529	C₂	semidirect
14. C₂×C₁₉×#520	C₂	semidirect
15. C₂×C₁₉×#519	C₂	semidirect
16. C₂×C₄×#41×C₁₉	C₂	semidirect
20. C₁₉×#559	C₂²	semidirect
21. C₁₉×#557	C₂²	semidirect
22. C₁₉×#555	C₂²	semidirect
23. C₁₉×#553	C₂²	semidirect
24. C₁₉×#552	C₂²	semidirect
25. C₁₉×#550	C₂²	semidirect
26. C₁₉×#548	C₂²	semidirect
27. C₁₉×#548	C₂²	semidirect
28. C₁₉×#542	C₂²	semidirect
29. C₁₉×#540	C₂²	semidirect
32. C₁₉×#529	C₂²	semidirect
33. C₁₉×#529	C₂²	semidirect
57. C₁₉×#520	C₂²	semidirect
58. C₁₉×#519	C₂²	semidirect
59. C₄×#41×C₁₉	C₂²	semidirect
268. C₂×#3524	C₁₉	direct (N × H)
321. #3524	C₂×C₁₉	direct (N × H)
322. C₂×#559	C₂×C₁₉	semidirect
323. C₂×#557	C₂×C₁₉	semidirect
324. C₂×#555	C₂×C₁₉	semidirect
325. C₂×#553	C₂×C₁₉	semidirect
326. C₂×#552	C₂×C₁₉	semidirect
327. C₂×#550	C₂×C₁₉	semidirect
328. C₂×#548	C₂×C₁₉	semidirect
329. C₂×#548	C₂×C₁₉	semidirect
330. C₂×#542	C₂×C₁₉	semidirect
331. C₂×#540	C₂×C₁₉	semidirect
332. C₂×#529	C₂×C₁₉	semidirect
333. C₂×#529	C₂×C₁₉	semidirect
334. C₂×#520	C₂×C₁₉	semidirect
335. C₂×#519	C₂×C₁₉	semidirect
336. C₂×C₄×#41	C₂×C₁₉	semidirect
368. #559	C₂²×C₁₉	semidirect
369. #557	C₂²×C₁₉	semidirect
370. #555	C₂²×C₁₉	semidirect
371. #553	C₂²×C₁₉	semidirect
372. #552	C₂²×C₁₉	semidirect
373. #550	C₂²×C₁₉	semidirect
374. #548	C₂²×C₁₉	semidirect
375. #548	C₂²×C₁₉	semidirect
376. #542	C₂²×C₁₉	semidirect
377. #540	C₂²×C₁₉	semidirect
380. #529	C₂²×C₁₉	semidirect
381. #529	C₂²×C₁₉	semidirect
405. #520	C₂²×C₁₉	semidirect
406. #519	C₂²×C₁₉	semidirect
407. C₄×#41	C₂²×C₁₉	semidirect
433. C₂×C₁₉	#3524	direct (N × H)
540. C₁₉	C₂×#3524	direct (N × H)
707. C₂	C₁₉×#3524	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×#3524	2
C₂×C₁₉×#559	2
C₂×C₁₉×#557	2
C₂×C₁₉×#555	2
C₂×C₁₉×#553	2
C₂×C₁₉×#552	2
C₂×C₁₉×#550	2
C₂×C₁₉×#548	2
C₂×C₁₉×#542	2
C₂×C₁₉×#540	2
C₂×C₁₉×#529	2
C₂×C₁₉×#520	2
C₂×C₁₉×#519	2
C₂×C₄×#41×C₁₉	2
C₂×#3524	19

Subgroups — C2×C19×#3524 #18068751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3524 #18068751