Subgroups — C₁₃×#34604 #15720943

Order 3328.

1536 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2666	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2664	C₂	1	2	yes	maximal
3	C₁₃×#2655	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2655	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2654	C₂	1	2	yes	maximal
6	C₁₃×#2650	C₂	1	2	yes	maximal
7	C₁₃×#2637	C₂	1	2	yes	maximal
8	C₁₃×#2634	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2402	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2401	C₂	1	2	yes	maximal
12	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#126	C₂	1	2	yes	maximal
17	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#401	C₂²	1	2	yes	—
27	C₁₃×#400	C₂²	1	2	yes	—
28	C₁₃×#400	C₂²	1	2	yes	—
29	C₁₃×#400	C₂²	1	2	yes	—
30	C₁₃×#400	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	—
33	C₁₃×#400	C₂²	1	1	yes	characteristic
34	C₁₃×#400	C₂²	1	1	yes	characteristic
35	C₁₃×#400	C₂²	1	2	yes	—
36	C₁₃×#400	C₂²	1	2	yes	—
37	C₁₃×#400	C₂²	1	2	yes	—
38	C₁₃×#399	C₂²	1	1	yes	characteristic
39	C₁₃×#399	C₂²	1	1	yes	characteristic
40	C₁₃×#398	C₂²	1	2	yes	—
41	C₁₃×#398	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	—
48	C₁₃×#398	C₂²	1	2	yes	—
49	C₁₃×#398	C₂²	1	2	yes	—
50	C₁₃×#397	C₂²	1	2	yes	—
51	C₁₃×#397	C₂²	1	2	yes	—
52	C₁₃×#397	C₂²	1	2	yes	—
53	C₁₃×#396	C₂²	1	2	yes	—
54	C₁₃×#396	C₂²	1	2	yes	—
55	C₁₃×#396	C₂²	1	2	yes	—
56	C₁₃×#395	C₂²	1	1	yes	characteristic
57	C₁₃×#395	C₂²	1	2	yes	—
58	C₁₃×#395	C₂²	1	2	yes	—
59	C₁₃×#395	C₂²	1	1	yes	characteristic
60	C₁₃×#393	C₂²	1	1	yes	characteristic
61	C₁₃×#393	C₂²	1	1	yes	characteristic
62	C₁₃×#391	C₂²	1	2	yes	—
63	C₁₃×#389	C₂²	1	2	yes	—
64	C₁₃×#389	C₂²	1	2	yes	—
65	C₁₃×#389	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#383	C₂²	1	2	yes	—
83	C₁₃×#382	C₂²	1	2	yes	—
84	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
85	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	1	yes	characteristic
105	C₄³×C₁₃	C₂²	1	1	yes	characteristic
106	C₄³×C₁₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#126	—	2	8	no	—
111	C₁₃×#125	—	2	8	no	—
112	C₄×Q₈×C₁₃	—	2	4	no	—
113	C₄×Q₈×C₁₃	—	2	4	no	—
114	C₄×Q₈×C₁₃	—	2	8	no	—
115	C₁₃×#117	—	2	4	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₁₃×#95	C₂³	1	2	yes	—
167	C₁₃×#95	C₂³	1	2	yes	—
168	C₁₃×#95	C₂³	1	2	yes	—
169	C₁₃×#95	C₂³	1	2	yes	—
170	C₁₃×#95	C₂³	1	2	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	1	yes	characteristic
173	C₁₃×#95	C₂³	1	1	yes	characteristic
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	1	yes	characteristic
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	1	yes	characteristic
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	#34604	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	2	4	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	4	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	—	4	2	no	—
249	C₁₃×C₄⋊C₄	—	4	2	no	—
250	C₁₃×C₄⋊C₄	—	4	2	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×C₂²⋊C₄	—	2	2	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	4	2	no	—
259	C₁₃×C₂²⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	4	2	no	—
261	C₄²×C₁₃	—	2	2	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	4	no	—
265	C₄²×C₁₃	—	2	4	no	—
266	C₄²×C₁₃	—	2	2	no	—
267	C₄²×C₁₃	—	2	4	no	—
268	C₄²×C₁₃	—	2	2	no	—
269	C₄²×C₁₃	—	2	2	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	—	2	2	no	—
272	C₄²×C₁₃	—	4	2	no	—
273	C₄²×C₁₃	—	4	2	no	—
274	C₄²×C₁₃	—	4	2	no	—
275	C₄²×C₁₃	#41	1	4	yes	—
276	C₄²×C₁₃	#41	1	8	yes	—
277	#2666	C₂×C₁₃	1	2	yes	complemented
278	#2664	C₂×C₁₃	1	2	yes	—
279	#2655	C₂×C₁₃	1	2	yes	complemented
280	#2655	C₂×C₁₃	1	2	yes	complemented
281	#2654	C₂×C₁₃	1	2	yes	—
282	#2650	C₂×C₁₃	1	2	yes	—
283	#2637	C₂×C₁₃	1	2	yes	—
284	#2634	C₂×C₁₃	1	2	yes	complemented
285	#2402	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#2402	C₂×C₁₃	1	2	yes	complemented
287	#2401	C₂×C₁₃	1	2	yes	—
288	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#2396	C₂×C₁₃	1	1	yes	characteristic
290	#2396	C₂×C₁₃	1	1	yes	characteristic
291	C₄×#125	C₂×C₁₃	1	2	yes	complemented
292	C₄×#126	C₂×C₁₃	1	2	yes	—
293	#2298	C₂×C₁₃	1	1	yes	characteristic
294	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	1	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
302	Q₈×C₁₃	—	2	8	no	—
303	Q₈×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
348	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
350	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
354	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
355	C₂×#126	C₂²×C₁₃	1	2	yes	—
356	C₂×#125	C₂²×C₁₃	1	2	yes	—
357	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
358	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
361	#401	C₂²×C₁₃	1	2	yes	—
362	#400	C₂²×C₁₃	1	2	yes	—
363	#400	C₂²×C₁₃	1	2	yes	—
364	#400	C₂²×C₁₃	1	2	yes	—
365	#400	C₂²×C₁₃	1	2	yes	—
366	#400	C₂²×C₁₃	1	2	yes	—
367	#400	C₂²×C₁₃	1	2	yes	—
368	#400	C₂²×C₁₃	1	1	yes	characteristic
369	#400	C₂²×C₁₃	1	1	yes	characteristic
370	#400	C₂²×C₁₃	1	2	yes	—
371	#400	C₂²×C₁₃	1	2	yes	—
372	#400	C₂²×C₁₃	1	2	yes	—
373	#399	C₂²×C₁₃	1	1	yes	characteristic
374	#399	C₂²×C₁₃	1	1	yes	characteristic
375	#398	C₂²×C₁₃	1	2	yes	—
376	#398	C₂²×C₁₃	1	2	yes	—
377	#398	C₂²×C₁₃	1	2	yes	—
378	#398	C₂²×C₁₃	1	2	yes	—
379	#398	C₂²×C₁₃	1	2	yes	—
380	#398	C₂²×C₁₃	1	2	yes	—
381	#398	C₂²×C₁₃	1	2	yes	—
382	#398	C₂²×C₁₃	1	2	yes	—
383	#398	C₂²×C₁₃	1	2	yes	—
384	#398	C₂²×C₁₃	1	2	yes	—
385	#397	C₂²×C₁₃	1	2	yes	—
386	#397	C₂²×C₁₃	1	2	yes	—
387	#397	C₂²×C₁₃	1	2	yes	—
388	#396	C₂²×C₁₃	1	2	yes	—
389	#396	C₂²×C₁₃	1	2	yes	—
390	#396	C₂²×C₁₃	1	2	yes	—
391	#395	C₂²×C₁₃	1	1	yes	characteristic
392	#395	C₂²×C₁₃	1	2	yes	—
393	#395	C₂²×C₁₃	1	2	yes	—
394	#395	C₂²×C₁₃	1	1	yes	characteristic
395	#393	C₂²×C₁₃	1	1	yes	characteristic
396	#393	C₂²×C₁₃	1	1	yes	characteristic
397	#391	C₂²×C₁₃	1	2	yes	—
398	#389	C₂²×C₁₃	1	2	yes	—
399	#389	C₂²×C₁₃	1	2	yes	—
400	#389	C₂²×C₁₃	1	2	yes	—
401	#388	C₂²×C₁₃	1	2	yes	—
402	#388	C₂²×C₁₃	1	2	yes	—
403	#388	C₂²×C₁₃	1	2	yes	—
404	#388	C₂²×C₁₃	1	2	yes	—
405	#388	C₂²×C₁₃	1	2	yes	—
406	#387	C₂²×C₁₃	1	2	yes	—
407	#387	C₂²×C₁₃	1	2	yes	—
408	#387	C₂²×C₁₃	1	2	yes	—
409	#387	C₂²×C₁₃	1	2	yes	—
410	#387	C₂²×C₁₃	1	2	yes	—
411	#387	C₂²×C₁₃	1	2	yes	—
412	#387	C₂²×C₁₃	1	2	yes	—
413	#387	C₂²×C₁₃	1	2	yes	—
414	#387	C₂²×C₁₃	1	2	yes	—
415	#387	C₂²×C₁₃	1	2	yes	—
416	#387	C₂²×C₁₃	1	2	yes	—
417	#383	C₂²×C₁₃	1	2	yes	—
418	#382	C₂²×C₁₃	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
425	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
438	#376	C₂²×C₁₃	1	1	yes	characteristic
439	#376	C₂²×C₁₃	1	2	yes	—
440	C₄³	C₂²×C₁₃	1	2	yes	—
441	C₄³	C₂²×C₁₃	1	1	yes	characteristic
442	C₂²×C₁₃	—	4	1	no	—
443	C₂²×C₁₃	—	4	1	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₁₃	C₂²×#41	1	2	yes	—
449	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂²×C₁₃	#585	1	2	yes	—
452	C₄×C₁₃	—	2	4	no	—
453	C₄×C₁₃	—	2	2	no	—
454	C₄×C₁₃	—	2	2	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	4	1	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	1	no	—
460	C₄×C₁₃	—	4	1	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	#541	1	4	yes	—
470	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	#126	—	2	8	no	—
474	#125	—	2	8	no	—
475	C₄×Q₈	—	2	4	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×Q₈	—	2	8	no	—
478	#117	—	2	4	no	—
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
529	#95	C₂³×C₁₃	1	2	yes	—
530	#95	C₂³×C₁₃	1	2	yes	—
531	#95	C₂³×C₁₃	1	2	yes	—
532	#95	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	2	yes	—
534	#95	C₂³×C₁₃	1	2	yes	—
535	#95	C₂³×C₁₃	1	2	yes	—
536	#95	C₂³×C₁₃	1	2	yes	—
537	#95	C₂³×C₁₃	1	2	yes	—
538	#95	C₂³×C₁₃	1	2	yes	—
539	#95	C₂³×C₁₃	1	2	yes	—
540	#95	C₂³×C₁₃	1	2	yes	—
541	#95	C₂³×C₁₃	1	1	yes	characteristic
542	#95	C₂³×C₁₃	1	1	yes	characteristic
543	#95	C₂³×C₁₃	1	2	yes	—
544	#95	C₂³×C₁₃	1	2	yes	—
545	#95	C₂³×C₁₃	1	2	yes	—
546	#95	C₂³×C₁₃	1	2	yes	—
547	#95	C₂³×C₁₃	1	2	yes	—
548	#95	C₂³×C₁₃	1	2	yes	—
549	#95	C₂³×C₁₃	1	2	yes	—
550	#95	C₂³×C₁₃	1	2	yes	—
551	#95	C₂³×C₁₃	1	2	yes	—
552	#95	C₂³×C₁₃	1	1	yes	characteristic
553	#95	C₂³×C₁₃	1	2	yes	—
554	#95	C₂³×C₁₃	1	1	yes	characteristic
555	#95	C₂³×C₁₃	1	2	yes	—
556	#95	C₂³×C₁₃	1	2	yes	—
557	#95	C₂³×C₁₃	1	2	yes	—
558	#95	C₂³×C₁₃	1	2	yes	—
559	#95	C₂³×C₁₃	1	2	yes	—
560	#95	C₂³×C₁₃	1	2	yes	—
561	#95	C₂³×C₁₃	1	2	yes	—
562	#95	C₂³×C₁₃	1	2	yes	—
563	C₂×C₁₃	—	8	1	no	—
564	C₂×C₁₃	#3444	1	1	yes	characteristic
565	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
566	C₂×C₁₃	#3455	1	1	yes	characteristic
567	C₂×C₁₃	#3461	1	2	yes	—
568	C₂×C₁₃	#3461	1	2	yes	—
569	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	4	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	4	2	no	—
641	C₄²	—	4	2	no	—
642	C₄²	—	4	2	no	—
643	C₄²	C₁₃×#41	1	4	yes	—
644	C₄²	C₁₃×#41	1	8	yes	—
645	C₁₃	#34604	1	1	yes	characteristic, direct product factor, Sylow
646	C₂³	—	2	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
652	Q₈	—	2	8	no	—
653	Q₈	—	4	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	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	1	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	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
698	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
699	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
700	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
701	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
702	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
703	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
704	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
711	C₂²	C₂²×C₁₃×#41	1	2	yes	—
712	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
713	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
714	C₂²	C₁₃×#585	1	2	yes	—
715	C₄	—	2	4	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	C₁₃×#541	1	4	yes	—
733	C₂	—	8	1	no	—
734	C₂	C₁₃×#3444	1	1	yes	characteristic
735	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
736	C₂	C₁₃×#3455	1	1	yes	characteristic
737	C₂	C₁₃×#3461	1	2	yes	—
738	C₂	C₁₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2666	C₂	semidirect
3. C₁₃×#2655	C₂	semidirect
4. C₁₃×#2655	C₂	semidirect
8. C₁₃×#2634	C₂	semidirect
9. C₁₃×#2402	C₂	semidirect
10. C₁₃×#2402	C₂	semidirect
12. C₁₃×#2399	C₂	semidirect
15. C₄×C₁₃×#125	C₂	semidirect
18. C₁₃×#2295	C₂	semidirect
19. C₄²×Q₈×C₁₃	C₂	semidirect
200. #34604	C₁₃	direct (N × H)
277. #2666	C₂×C₁₃	semidirect
279. #2655	C₂×C₁₃	semidirect
280. #2655	C₂×C₁₃	semidirect
284. #2634	C₂×C₁₃	semidirect
285. #2402	C₂×C₁₃	semidirect
286. #2402	C₂×C₁₃	semidirect
288. #2399	C₂×C₁₃	semidirect
291. C₄×#125	C₂×C₁₃	semidirect
294. #2295	C₂×C₁₃	semidirect
295. C₄²×Q₈	C₂×C₁₃	semidirect
645. C₁₃	#34604	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2666	2
C₁₃×#2664	2
C₁₃×#2655	2
C₁₃×#2654	2
C₁₃×#2650	2
C₁₃×#2637	2
C₁₃×#2634	2
C₁₃×#2402	2
C₁₃×#2401	2
C₁₃×#2399	2
C₁₃×#2396	2
C₄×C₁₃×#125	2
C₄×C₁₃×#126	2
C₁₃×#2298	2
C₁₃×#2295	2
C₄²×Q₈×C₁₃	2
#34604	13

Subgroups — C13×#34604 #15720943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34604 #15720943