Subgroups — C₁₃×#25052 #15711391

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2079	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2040	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1974	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₁₃×#537	C₂²	1	2	yes	—
15	C₁₃×#520	C₂²	1	2	yes	—
16	C₁₃×#485	—	2	2	no	—
17	C₁₃×#483	—	2	2	no	—
18	C₁₃×#482	—	2	2	no	—
19	C₁₃×#481	—	2	2	no	—
20	C₁₃×#468	—	2	2	no	—
21	C₁₃×#467	—	2	1	no	—
22	C₁₃×#466	—	2	1	no	—
23	C₁₃×#440	—	2	2	no	—
24	C₄×C₁₃×Q₁₆	—	2	1	no	—
25	C₄×C₁₃×D₈	—	2	1	no	—
26	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
27	C₁₃×#428	C₂²	1	2	yes	—
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#417	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₁₃×#417	C₂²	1	2	yes	—
36	C₁₃×#416	C₂²	1	1	yes	characteristic
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#382	C₂²	1	2	yes	—
41	C₁₃×#343	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#341	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
51	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	2	no	—
63	C₁₃×#121	—	2	2	no	—
64	C₁₃×#121	—	2	2	no	—
65	C₁₃×#121	—	4	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	4	2	no	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#108	—	2	2	no	—
76	C₁₃×#107	—	2	1	no	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#107	—	2	1	no	—
79	C₁₃×#107	—	2	1	no	—
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#104	—	2	2	no	—
85	C₁₃×#104	—	2	4	no	—
86	C₁₃×#103	—	2	2	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	D₄	1	1	yes	characteristic
90	C₁₃×#103	D₄	1	1	yes	characteristic
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	D₄	1	1	yes	characteristic
95	C₁₃×#102	D₄	1	1	yes	characteristic
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	C₁₃×#97	—	2	1	no	—
99	C₄×C₈×C₁₃	—	2	1	no	—
100	C₄×C₈×C₁₃	—	2	2	no	—
101	C₁₃×#95	—	4	2	no	—
102	#25052	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	—	2	1	no	—
105	C₁₃×#41	—	2	1	no	—
106	C₁₃×#41	—	2	1	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×Q₁₆	—	2	2	no	—
126	C₁₃×SD₁₆	—	2	4	no	—
127	C₁₃×D₈	—	2	2	no	—
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	2	1	no	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₁₃×M₁₆	—	2	1	no	—
132	C₁₃×M₁₆	—	2	1	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	4	2	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	4	2	no	—
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	#41	1	2	yes	—
146	C₂×C₈×C₁₃	#41	1	2	yes	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
154	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	4	2	no	—
162	C₄²×C₁₃	#41	1	2	yes	—
163	#3099	C₂×C₁₃	1	2	yes	complemented
164	#3061	C₂×C₁₃	1	1	yes	characteristic
165	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#2079	C₂×C₁₃	1	2	yes	complemented
167	#2040	C₂×C₁₃	1	2	yes	complemented
168	#1974	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1860	C₂×C₁₃	1	2	yes	complemented
171	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1764	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	2	1	no	—
179	Q₈×C₁₃	—	2	1	no	—
180	Q₈×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	1	no	—
183	D₄×C₁₃	—	2	1	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	1	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	16	2	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	2	no	—
204	C₂×C₄×C₁₃	—	8	2	no	—
205	C₂×C₄×C₁₃	—	16	2	no	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₈×C₁₃	#123	1	2	yes	—
218	C₈×C₁₃	#123	1	2	yes	—
219	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
221	#537	C₂²×C₁₃	1	2	yes	—
222	#520	C₂²×C₁₃	1	2	yes	—
223	#485	—	2	2	no	—
224	#483	—	2	2	no	—
225	#482	—	2	2	no	—
226	#481	—	2	2	no	—
227	#468	—	2	2	no	—
228	#467	—	2	1	no	—
229	#466	—	2	1	no	—
230	#440	—	2	2	no	—
231	C₄×Q₁₆	—	2	1	no	—
232	C₄×D₈	—	2	1	no	—
233	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
234	#428	C₂²×C₁₃	1	2	yes	—
235	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₁₃	1	2	yes	—
238	C₂×#104	C₂²×C₁₃	1	2	yes	—
239	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
240	#417	C₂²×C₁₃	1	2	yes	—
241	#417	C₂²×C₁₃	1	2	yes	—
242	#417	C₂²×C₁₃	1	2	yes	—
243	#416	C₂²×C₁₃	1	1	yes	characteristic
244	#408	C₂²×C₁₃	1	2	yes	—
245	#405	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
247	#382	C₂²×C₁₃	1	2	yes	—
248	#343	C₂²×C₁₃	1	2	yes	—
249	#343	C₂²×C₁₃	1	2	yes	—
250	#341	C₂²×C₁₃	1	1	yes	characteristic
251	#339	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	1	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	#542	1	1	yes	characteristic
261	C₂²×C₁₃	D₄²	1	1	yes	characteristic
262	C₂²×C₁₃	#553	1	1	yes	characteristic
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	4	1	no	—
266	C₄×C₁₃	—	4	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
271	C₄×C₁₃	#532	1	1	yes	characteristic
272	C₄×C₁₃	#547	1	1	yes	characteristic
273	C₄×C₁₃	#547	1	1	yes	characteristic
274	C₂×#41	C₂³×C₁₃	1	2	yes	—
275	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
276	#135	—	2	2	no	—
277	#135	—	2	2	no	—
278	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
279	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
280	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
281	#131	—	2	2	no	—
282	#131	—	2	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	4	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	4	2	no	—
298	#117	—	2	2	no	—
299	#117	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	#108	—	2	2	no	—
305	#107	—	2	1	no	—
306	#107	—	2	1	no	—
307	#107	—	2	1	no	—
308	#107	—	2	1	no	—
309	#107	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	—	2	2	no	—
312	#106	—	2	2	no	—
313	#104	—	2	4	no	—
314	#104	—	2	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	—	2	2	no	—
318	#103	D₄×C₁₃	1	1	yes	characteristic
319	#103	D₄×C₁₃	1	1	yes	characteristic
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	D₄×C₁₃	1	1	yes	characteristic
324	#102	D₄×C₁₃	1	1	yes	characteristic
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	#97	—	2	1	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	2	2	no	—
330	#95	—	4	2	no	—
331	C₂×C₁₃	—	2	1	no	—
332	C₂×C₁₃	—	2	1	no	—
333	C₂×C₁₃	—	8	2	no	—
334	C₂×C₁₃	—	8	1	no	—
335	C₂×C₁₃	#2422	1	1	yes	characteristic
336	C₂×C₁₃	#3290	1	1	yes	characteristic
337	C₂×C₁₃	#3290	1	1	yes	characteristic
338	#41	—	2	2	no	—
339	#41	—	2	1	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	1	no	—
346	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
360	Q₁₆	—	2	2	no	—
361	SD₁₆	—	2	4	no	—
362	D₈	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₈	C₁₃×#41	1	2	yes	—
381	C₂×C₈	C₁₃×#41	1	2	yes	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	2	no	—
397	C₄²	C₁₃×#41	1	2	yes	—
398	C₁₃	#25052	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	1	no	—
404	Q₈	—	2	1	no	—
405	Q₈	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	16	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	16	2	no	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
436	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	C₁₃×#123	1	2	yes	—
443	C₈	C₁₃×#123	1	2	yes	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	C₁₃×#542	1	1	yes	characteristic
453	C₂²	D₄²×C₁₃	1	1	yes	characteristic
454	C₂²	C₁₃×#553	1	1	yes	characteristic
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
463	C₄	C₁₃×#532	1	1	yes	characteristic
464	C₄	C₁₃×#547	1	1	yes	characteristic
465	C₄	C₁₃×#547	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	8	2	no	—
469	C₂	—	8	1	no	—
470	C₂	C₁₃×#2422	1	1	yes	characteristic
471	C₂	C₁₃×#3290	1	1	yes	characteristic
472	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3061	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3099	C₂	semidirect
3. C₁₃×#2951	C₂	semidirect
4. C₁₃×#2079	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#1974	C₂	semidirect
7. C₁₃×#1952	C₂	semidirect
8. C₁₃×#1860	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
10. C₁₃×#1816	C₂	semidirect
11. C₁₃×#1764	C₂	semidirect
102. #25052	C₁₃	direct (N × H)
163. #3099	C₂×C₁₃	semidirect
165. #2951	C₂×C₁₃	semidirect
166. #2079	C₂×C₁₃	semidirect
167. #2040	C₂×C₁₃	semidirect
168. #1974	C₂×C₁₃	semidirect
169. #1952	C₂×C₁₃	semidirect
170. #1860	C₂×C₁₃	semidirect
171. #1846	C₂×C₁₃	semidirect
172. #1816	C₂×C₁₃	semidirect
173. #1764	C₂×C₁₃	semidirect
398. C₁₃	#25052	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×#3099	2
C₁₃×#3061	2
C₁₃×#2951	2
C₁₃×#2079	2
C₁₃×#2040	2
C₁₃×#1974	2
C₁₃×#1952	2
C₁₃×#1860	2
C₁₃×#1846	2
C₁₃×#1816	2
C₁₃×#1764	2
#25052	13

Subgroups — C13×#25052 #15711391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25052 #15711391