Subgroups — C₁₃×#24807 #15711146

Order 3328.

844 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3056	C₂	1	2	yes	maximal
3	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2052	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1901	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#525	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₁₃×#473	—	2	4	no	—
20	C₁₃×#470	—	2	2	no	—
21	C₁₃×#470	—	2	2	no	—
22	C₁₃×#470	—	2	2	no	—
23	C₁₃×#468	—	2	2	no	—
24	C₁₃×#467	—	2	2	no	—
25	C₁₃×#465	—	2	2	no	—
26	C₁₃×#436	—	2	2	no	—
27	C₁₃×#435	—	2	2	no	—
28	C₁₃×#430	—	2	4	no	—
29	C₂×C₁₃×#108	C₂²	1	2	yes	—
30	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
32	C₁₃×#428	C₂²	1	2	yes	—
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₁₃×#424	C₂²	1	1	yes	characteristic
35	C₁₃×#419	C₂²	1	2	yes	—
36	C₁₃×#417	C₂²	1	2	yes	—
37	C₂×C₁₃×#103	C₂²	1	2	yes	—
38	C₂×C₁₃×#101	C₂²	1	2	yes	—
39	C₂×C₁₃×#101	C₂²	1	2	yes	—
40	C₁₃×#408	C₂²	1	1	yes	characteristic
41	C₁₃×#407	C₂²	1	1	yes	characteristic
42	C₁₃×#405	C₂²	1	1	yes	characteristic
43	C₁₃×#343	C₂²	1	2	yes	—
44	C₁₃×#343	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#137	—	2	4	no	—
49	C₁₃×#137	—	4	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₁₃×#131	—	2	2	no	—
57	C₁₃×#131	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	4	no	—
63	C₂×C₁₃×M₁₆	—	4	2	no	—
64	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#123	—	2	1	no	—
75	C₁₃×C₂²⋊Q₈	—	2	2	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
80	C₁₃×#121	D₄	1	2	yes	—
81	C₁₃×#120	—	2	1	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₁₃×#117	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₁₃×#108	—	2	4	no	—
88	C₁₃×#108	—	2	2	no	—
89	C₁₃×#108	D₄	1	4	yes	complemented
90	C₁₃×#107	—	2	2	no	—
91	C₁₃×#106	—	2	1	no	—
92	C₁₃×#106	—	2	1	no	—
93	C₁₃×#106	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#103	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#102	—	2	2	no	—
100	C₁₃×#101	—	2	4	no	—
101	C₁₃×#101	—	4	2	no	—
102	C₁₃×C₂²⋊C₈	—	2	2	no	—
103	C₁₃×C₂²⋊C₈	—	2	2	no	—
104	C₁₃×#97	—	2	1	no	—
105	C₄×C₈×C₁₃	—	2	1	no	—
106	#24807	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	#41	1	1	yes	characteristic
108	C₁₃×#41	—	2	1	no	—
109	C₁₃×#41	—	2	1	no	—
110	C₁₃×#41	—	2	1	no	—
111	C₁₃×#41	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	4	4	no	—
134	C₁₃×Q₁₆	—	4	2	no	—
135	C₁₃×Q₁₆	—	4	2	no	—
136	C₁₃×SD₁₆	—	4	4	no	—
137	C₁₃×M₁₆	—	2	2	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	1	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	1	no	—
143	C₁₃×M₁₆	—	2	1	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	1	no	—
146	C₁₃×M₁₆	—	4	4	no	—
147	C₁₃×M₁₆	—	4	2	no	—
148	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	4	4	no	—
156	C₂×C₈×C₁₃	—	4	2	no	—
157	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₁₃	#41	1	2	yes	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	2	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#3056	C₂×C₁₃	1	2	yes	—
176	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2930	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2064	C₂×C₁₃	1	2	yes	complemented
180	#2052	C₂×C₁₃	1	2	yes	complemented
181	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1901	C₂×C₁₃	1	2	yes	complemented
184	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	#121	1	2	yes	—
190	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	1	no	—
192	Q₈×C₁₃	—	2	1	no	—
193	Q₈×C₁₃	—	4	2	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	Q₈×C₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	2	1	no	—
198	D₄×C₁₃	—	2	1	no	—
199	D₄×C₁₃	—	4	1	no	—
200	D₄×C₁₃	—	4	1	no	—
201	D₄×C₁₃	—	8	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	2	no	—
217	C₂×C₄×C₁₃	#121	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₃	—	2	2	no	—
225	C₈×C₁₃	—	2	4	no	—
226	C₈×C₁₃	—	4	1	no	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₈×C₁₃	#121	1	2	yes	—
230	C₈×C₁₃	#121	1	2	yes	—
231	C₂×#137	C₂²×C₁₃	1	2	yes	—
232	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
236	#525	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
238	#473	—	2	4	no	—
239	#470	—	2	2	no	—
240	#470	—	2	2	no	—
241	#470	—	2	2	no	—
242	#468	—	2	2	no	—
243	#467	—	2	2	no	—
244	#465	—	2	2	no	—
245	#436	—	2	2	no	—
246	#435	—	2	2	no	—
247	#430	—	2	4	no	—
248	C₂×#108	C₂²×C₁₃	1	2	yes	—
249	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
251	#428	C₂²×C₁₃	1	2	yes	—
252	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
253	#424	C₂²×C₁₃	1	1	yes	characteristic
254	#419	C₂²×C₁₃	1	2	yes	—
255	#417	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	2	yes	—
257	C₂×#101	C₂²×C₁₃	1	2	yes	—
258	C₂×#101	C₂²×C₁₃	1	2	yes	—
259	#408	C₂²×C₁₃	1	1	yes	characteristic
260	#407	C₂²×C₁₃	1	1	yes	characteristic
261	#405	C₂²×C₁₃	1	1	yes	characteristic
262	#343	C₂²×C₁₃	1	2	yes	—
263	#343	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	2	2	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
273	C₂²×C₁₃	#548	1	1	yes	characteristic
274	C₂²×C₁₃	#553	1	1	yes	characteristic
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
281	C₄×C₁₃	#537	1	1	yes	characteristic
282	C₄×C₁₃	D₄²	1	1	yes	characteristic
283	C₄×C₁₃	#547	1	1	yes	characteristic
284	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
287	#137	—	2	4	no	—
288	#137	—	4	2	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×Q₁₆	—	2	1	no	—
291	C₂×Q₁₆	—	2	1	no	—
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	#131	—	2	2	no	—
296	#131	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	4	no	—
302	C₂×M₁₆	—	4	2	no	—
303	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
304	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
306	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
313	#123	—	2	1	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
319	#121	D₄×C₁₃	1	2	yes	—
320	#120	—	2	1	no	—
321	C₄×D₄	—	2	2	no	—
322	#117	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	#108	—	2	4	no	—
327	#108	—	2	2	no	—
328	#108	D₄×C₁₃	1	4	yes	complemented
329	#107	—	2	2	no	—
330	#106	—	2	1	no	—
331	#106	—	2	1	no	—
332	#106	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	2	no	—
335	#103	—	2	4	no	—
336	#103	—	2	2	no	—
337	#103	—	2	2	no	—
338	#102	—	2	2	no	—
339	#101	—	2	4	no	—
340	#101	—	4	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	#97	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₂×C₁₃	—	2	1	no	—
346	C₂×C₁₃	—	2	1	no	—
347	C₂×C₁₃	—	4	2	no	—
348	C₂×C₁₃	—	8	1	no	—
349	C₂×C₁₃	#2416	1	1	yes	characteristic
350	C₂×C₁₃	#3069	1	2	yes	—
351	C₂⁴	C₁₃×#41	1	1	yes	characteristic
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	—	2	1	no	—
355	#41	—	2	1	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	Q₁₆	—	4	4	no	—
378	Q₁₆	—	4	2	no	—
379	Q₁₆	—	4	2	no	—
380	SD₁₆	—	4	4	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	4	4	no	—
391	M₁₆	—	4	2	no	—
392	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	4	no	—
400	C₂×C₈	—	4	2	no	—
401	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
405	C₂×C₈	C₁₃×#41	1	2	yes	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	—	2	1	no	—
418	C₁₃	#24807	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₁₃×#121	1	2	yes	—
424	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
425	Q₈	—	2	1	no	—
426	Q₈	—	2	1	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	8	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	C₁₃×#121	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
456	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	2	4	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	2	no	—
463	C₈	C₁₃×#121	1	2	yes	—
464	C₈	C₁₃×#121	1	2	yes	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
474	C₂²	C₁₃×#548	1	1	yes	characteristic
475	C₂²	C₁₃×#553	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	2	no	—
481	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
482	C₄	C₁₃×#537	1	1	yes	characteristic
483	C₄	D₄²×C₁₃	1	1	yes	characteristic
484	C₄	C₁₃×#547	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	4	2	no	—
488	C₂	—	8	1	no	—
489	C₂	C₁₃×#2416	1	1	yes	characteristic
490	C₂	C₁₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#473	C₂	semidirect
3. C₂×C₁₃×#470	C₂	semidirect
5. C₂×C₁₃×#430	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#2052	C₂	semidirect
8. C₁₃×#1979	C₂	semidirect
9. C₁₃×#1951	C₂	semidirect
10. C₁₃×#1901	C₂	semidirect
11. C₁₃×#1815	C₂	semidirect
89. C₁₃×#108	D₄	semidirect
106. #24807	C₁₃	direct (N × H)
174. C₂×#473	C₂×C₁₃	semidirect
176. C₂×#470	C₂×C₁₃	semidirect
178. C₂×#430	C₂×C₁₃	semidirect
179. #2064	C₂×C₁₃	semidirect
180. #2052	C₂×C₁₃	semidirect
181. #1979	C₂×C₁₃	semidirect
182. #1951	C₂×C₁₃	semidirect
183. #1901	C₂×C₁₃	semidirect
184. #1815	C₂×C₁₃	semidirect
328. #108	D₄×C₁₃	semidirect
418. C₁₃	#24807	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×#473	2
C₁₃×#3056	2
C₂×C₁₃×#470	2
C₁₃×#2930	2
C₂×C₁₃×#430	2
C₁₃×#2064	2
C₁₃×#2052	2
C₁₃×#1979	2
C₁₃×#1951	2
C₁₃×#1901	2
C₁₃×#1815	2
#24807	13

Subgroups — C13×#24807 #15711146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24807 #15711146