Subgroups — C₁₃×#17587 #15703926

Order 3328.

1466 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1516	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1511	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1510	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1504	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	—	2	1	no	—
11	C₁₃×#525	—	2	1	no	—
12	C₁₃×#525	—	2	1	no	—
13	C₁₃×#525	—	2	1	no	—
14	C₁₃×#525	—	2	1	no	—
15	C₁₃×#525	C₄	1	2	yes	complemented
16	C₁₃×#525	C₄	1	2	yes	complemented
17	C₁₃×#525	C₂²	1	2	yes	—
18	C₁₃×#525	C₂²	1	2	yes	—
19	C₂×C₁₃×#123	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#120	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₁₃×#117	C₄	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
29	C₁₃×#407	—	2	1	no	—
30	C₁₃×#407	—	2	1	no	—
31	C₁₃×#407	C₂²	1	2	yes	—
32	C₁₃×#407	C₂²	1	2	yes	complemented
33	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
35	C₁₃×#381	—	2	1	no	—
36	C₁₃×#381	—	2	1	no	—
37	C₁₃×#381	C₂²	1	2	yes	—
38	C₁₃×#381	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#95	—	2	1	no	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
41	C₁₃×#328	C₂²	1	8	yes	complemented
42	C₁₃×#327	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	—	4	4	no	—
57	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	2	2	no	—
73	C₂×C₁₃×M₁₆	—	4	4	no	—
74	C₂²×C₈×C₁₃	—	2	2	no	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	C₂×C₄	1	2	yes	—
92	C₁₃×#121	C₂×C₄	1	2	yes	complemented
93	C₁₃×#121	C₂×C₄	1	2	yes	complemented
94	C₁₃×#121	C₂³	1	2	yes	—
95	C₁₃×#120	—	2	2	no	—
96	C₁₃×#120	—	2	2	no	—
97	C₁₃×#120	—	2	2	no	—
98	C₁₃×#120	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₁₃×#117	—	2	1	no	—
109	C₁₃×#117	C₂×C₄	1	2	yes	—
110	C₁₃×#117	C₂×C₄	1	2	yes	complemented
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
114	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×C₂²⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
128	C₁₃×#95	—	2	2	no	—
129	C₁₃×#95	—	2	2	no	—
130	C₁₃×#95	—	2	2	no	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	#17587	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	—	2	4	no	—
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	—	4	2	no	—
136	C₂⁴×C₁₃	—	4	2	no	—
137	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
138	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₁₃×#41	—	4	4	no	—
147	C₁₃×#41	—	4	4	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	4	2	no	—
150	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	—	4	4	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	—	4	4	no	—
162	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	4	2	no	—
173	C₂²×C₄×C₁₃	—	4	2	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₃	—	4	4	no	—
184	C₂²×C₄×C₁₃	—	4	4	no	—
185	C₂²×C₄×C₁₃	—	4	4	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×M₁₆	—	4	4	no	—
216	C₁₃×M₁₆	—	4	4	no	—
217	C₂×C₈×C₁₃	—	2	4	no	—
218	C₂×C₈×C₁₃	—	4	4	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
226	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	2	2	no	—
229	C₁₃×C₂²⋊C₄	—	2	2	no	—
230	C₁₃×C₂²⋊C₄	—	2	2	no	—
231	C₁₃×C₂²⋊C₄	—	2	2	no	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₁₃×C₂²⋊C₄	—	2	2	no	—
237	C₁₃×C₂²⋊C₄	—	4	4	no	—
238	C₁₃×C₂²⋊C₄	—	4	4	no	—
239	C₄²×C₁₃	—	2	2	no	—
240	C₄²×C₁₃	—	2	2	no	—
241	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
242	C₂×#407	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1516	C₂×C₁₃	1	4	yes	complemented
245	#1511	C₂×C₁₃	1	2	yes	complemented
246	#1510	C₂×C₁₃	1	2	yes	complemented
247	#1504	C₂×C₁₃	1	4	yes	complemented
248	C₂³×C₁₃	—	2	2	no	—
249	C₂³×C₁₃	—	2	2	no	—
250	C₂³×C₁₃	—	2	2	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	16	no	—
270	C₂³×C₁₃	—	4	2	no	—
271	C₂³×C₁₃	—	4	2	no	—
272	C₂³×C₁₃	—	4	2	no	—
273	C₂³×C₁₃	#99	1	4	yes	—
274	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	Q₈×C₁₃	—	4	2	no	—
282	Q₈×C₁₃	—	4	2	no	—
283	D₄×C₁₃	—	4	2	no	—
284	D₄×C₁₃	—	4	2	no	—
285	D₄×C₁₃	—	4	4	no	—
286	D₄×C₁₃	—	4	4	no	—
287	D₄×C₁₃	—	4	4	no	—
288	D₄×C₁₃	—	4	4	no	—
289	D₄×C₁₃	—	4	4	no	—
290	D₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	4	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	4	2	no	—
325	C₂×C₄×C₁₃	—	4	2	no	—
326	C₂×C₄×C₁₃	—	4	2	no	—
327	C₂×C₄×C₁₃	—	4	4	no	—
328	C₂×C₄×C₁₃	—	4	4	no	—
329	C₂×C₄×C₁₃	—	4	4	no	—
330	C₂×C₄×C₁₃	—	8	8	no	—
331	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₈×C₁₃	—	4	4	no	—
340	C₂²×#41	C₄×C₁₃	1	1	yes	characteristic, complemented
341	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×M₁₆	—	2	1	no	—
343	#525	—	2	1	no	—
344	#525	—	2	1	no	—
345	#525	—	2	1	no	—
346	#525	—	2	1	no	—
347	#525	C₄×C₁₃	1	2	yes	complemented
348	#525	C₄×C₁₃	1	2	yes	complemented
349	#525	C₂²×C₁₃	1	2	yes	—
350	#525	C₂²×C₁₃	1	2	yes	—
351	C₂×#123	—	2	1	no	—
352	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
353	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#121	C₄×C₁₃	1	1	yes	characteristic, complemented
355	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#120	—	2	1	no	—
357	C₂×C₄×D₄	—	2	1	no	—
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×#117	C₄×C₁₃	1	1	yes	characteristic, complemented
360	C₂²×C₂²⋊C₄	—	2	1	no	—
361	#407	—	2	1	no	—
362	#407	—	2	1	no	—
363	#407	C₂²×C₁₃	1	2	yes	—
364	#407	C₂²×C₁₃	1	2	yes	complemented
365	C₂×C₂²⋊C₈	—	2	1	no	—
366	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
367	#381	—	2	1	no	—
368	#381	—	2	1	no	—
369	#381	C₂²×C₁₃	1	2	yes	—
370	#381	C₂²×C₁₃	1	2	yes	complemented
371	C₂×#95	—	2	1	no	—
372	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
373	#328	C₂²×C₁₃	1	8	yes	complemented
374	#327	C₂²×C₁₃	1	8	yes	complemented
375	C₂²×C₁₃	—	2	8	no	—
376	C₂²×C₁₃	—	2	1	no	—
377	C₂²×C₁₃	—	2	1	no	—
378	C₂²×C₁₃	—	2	1	no	—
379	C₂²×C₁₃	—	2	1	no	—
380	C₂²×C₁₃	—	2	1	no	—
381	C₂²×C₁₃	—	2	1	no	—
382	C₂²×C₁₃	—	2	1	no	—
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	1	no	—
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	2	1	no	—
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	2	1	no	—
389	C₂²×C₁₃	—	2	1	no	—
390	C₂²×C₁₃	—	2	1	no	—
391	C₂²×C₁₃	—	2	1	no	—
392	C₂²×C₁₃	—	4	4	no	—
393	C₂²×C₁₃	—	4	4	no	—
394	C₂²×C₁₃	—	4	4	no	—
395	C₂²×C₁₃	—	4	4	no	—
396	C₂²×C₁₃	—	4	4	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	2	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	8	4	no	—
402	C₂²×C₁₃	C₂×#99	1	2	yes	—
403	C₂²×C₁₃	C₂×#99	1	2	yes	—
404	C₂²×C₁₃	C₂×#99	1	2	yes	—
405	C₂²×C₁₃	#421	1	2	yes	—
406	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₂²×C₁₃	#575	1	2	yes	—
408	C₄×C₁₃	—	2	1	no	—
409	C₄×C₁₃	—	2	1	no	—
410	C₄×C₁₃	—	2	1	no	—
411	C₄×C₁₃	—	2	1	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	1	no	—
415	C₄×C₁₃	—	2	1	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	—	8	4	no	—
420	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
421	C₂×#41	—	2	1	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	4	4	no	—
424	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
425	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
426	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	2	2	no	—
433	C₂³×C₄	—	4	4	no	—
434	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
435	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
436	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
437	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
439	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
441	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
442	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×M₁₆	—	2	2	no	—
449	C₂×M₁₆	—	2	2	no	—
450	C₂×M₁₆	—	4	4	no	—
451	C₂²×C₈	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	#123	—	2	2	no	—
455	#123	—	2	2	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
461	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
462	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
463	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
464	#121	—	2	1	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	1	no	—
468	#121	C₂×C₄×C₁₃	1	2	yes	—
469	#121	C₂×C₄×C₁₃	1	2	yes	complemented
470	#121	C₂×C₄×C₁₃	1	2	yes	complemented
471	#121	C₂³×C₁₃	1	2	yes	—
472	#120	—	2	2	no	—
473	#120	—	2	2	no	—
474	#120	—	2	2	no	—
475	#120	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	#117	—	2	1	no	—
485	#117	—	2	1	no	—
486	#117	C₂×C₄×C₁₃	1	2	yes	—
487	#117	C₂×C₄×C₁₃	1	2	yes	complemented
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
491	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₂²⋊C₄	—	2	2	no	—
499	C₂×C₂²⋊C₄	—	4	4	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂²⋊C₈	—	2	2	no	—
502	C₂²⋊C₈	—	2	2	no	—
503	C₂²⋊C₈	—	2	2	no	—
504	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
505	#95	—	2	2	no	—
506	#95	—	2	2	no	—
507	#95	—	2	2	no	—
508	#95	C₂³×C₁₃	1	4	yes	—
509	C₂×C₁₃	—	2	2	no	—
510	C₂×C₁₃	—	2	2	no	—
511	C₂×C₁₃	—	2	2	no	—
512	C₂×C₁₃	—	2	2	no	—
513	C₂×C₁₃	—	2	2	no	—
514	C₂×C₁₃	—	4	1	no	—
515	C₂×C₁₃	—	4	1	no	—
516	C₂×C₁₃	—	8	2	no	—
517	C₂×C₁₃	C₂²×#99	1	1	yes	characteristic
518	C₂×C₁₃	#2896	1	1	yes	characteristic
519	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	2	1	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
525	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
526	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
527	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
528	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
531	#41	—	4	4	no	—
532	#41	—	4	4	no	—
533	#41	—	4	4	no	—
534	#41	—	4	4	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
575	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
576	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
577	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
578	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
579	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
580	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
581	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
582	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
583	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
584	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
585	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	M₁₆	—	4	4	no	—
603	M₁₆	—	4	4	no	—
604	C₂×C₈	—	2	4	no	—
605	C₂×C₈	—	4	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
613	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	2	no	—
628	C₁₃	#17587	1	1	yes	characteristic, direct product factor, Sylow
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	16	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	C₁₃×#99	1	4	yes	—
655	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
656	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
657	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
658	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
659	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
660	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	8	8	no	—
712	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
713	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
714	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
715	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
716	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
717	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
718	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
720	C₈	—	4	4	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	8	4	no	—
748	C₂²	C₂×C₁₃×#99	1	2	yes	—
749	C₂²	C₂×C₁₃×#99	1	2	yes	—
750	C₂²	C₂×C₁₃×#99	1	2	yes	—
751	C₂²	C₁₃×#421	1	2	yes	—
752	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
753	C₂²	C₁₃×#575	1	2	yes	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	8	4	no	—
766	C₂	—	2	2	no	—
767	C₂	—	2	2	no	—
768	C₂	—	2	2	no	—
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	4	1	no	—
773	C₂	—	8	2	no	—
774	C₂	C₂²×C₁₃×#99	1	1	yes	characteristic
775	C₂	C₁₃×#2896	1	1	yes	characteristic
776	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#407	C₂	semidirect
3. C₂×C₁₃×#381	C₂	semidirect
4. C₁₃×#1516	C₂	semidirect
5. C₁₃×#1511	C₂	semidirect
6. C₁₃×#1510	C₂	semidirect
7. C₁₃×#1504	C₂	semidirect
8. C₂²×C₁₃×#41	C₄	semidirect
15. C₁₃×#525	C₄	semidirect
16. C₁₃×#525	C₄	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
22. C₂×C₁₃×#121	C₄	semidirect
27. C₂×C₁₃×#117	C₄	semidirect
32. C₁₃×#407	C₂²	semidirect
34. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
38. C₁₃×#381	C₂²	semidirect
40. C₂×C₁₃×#95	C₂²	semidirect
41. C₁₃×#328	C₂²	semidirect
42. C₁₃×#327	C₂²	semidirect
48. C₂×C₁₃×#41	C₂×C₄	semidirect
49. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
53. C₂²×D₄×C₁₃	C₂×C₄	semidirect
84. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
85. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₁₃×#121	C₂×C₄	semidirect
93. C₁₃×#121	C₂×C₄	semidirect
110. C₁₃×#117	C₂×C₄	semidirect
113. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
114. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
132. #17587	C₁₃	direct (N × H)
242. C₂×#407	C₂×C₁₃	semidirect
243. C₂×#381	C₂×C₁₃	semidirect
244. #1516	C₂×C₁₃	semidirect
245. #1511	C₂×C₁₃	semidirect
246. #1510	C₂×C₁₃	semidirect
247. #1504	C₂×C₁₃	semidirect
340. C₂²×#41	C₄×C₁₃	semidirect
347. #525	C₄×C₁₃	semidirect
348. #525	C₄×C₁₃	semidirect
352. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
354. C₂×#121	C₄×C₁₃	semidirect
359. C₂×#117	C₄×C₁₃	semidirect
364. #407	C₂²×C₁₃	semidirect
366. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
370. #381	C₂²×C₁₃	semidirect
372. C₂×#95	C₂²×C₁₃	semidirect
373. #328	C₂²×C₁₃	semidirect
374. #327	C₂²×C₁₃	semidirect
425. C₂×#41	C₂×C₄×C₁₃	semidirect
426. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
430. C₂²×D₄	C₂×C₄×C₁₃	semidirect
461. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
462. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
469. #121	C₂×C₄×C₁₃	semidirect
470. #121	C₂×C₄×C₁₃	semidirect
487. #117	C₂×C₄×C₁₃	semidirect
490. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
491. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
628. C₁₃	#17587	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂×C₁₃×#407	2
C₂×C₁₃×#381	2
C₁₃×#1516	2
C₁₃×#1511	2
C₁₃×#1510	2
C₁₃×#1504	2
#17587	13

Subgroups — C13×#17587 #15703926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17587 #15703926