Subgroups — C₁₃×#24523 #15710862

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2046	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1977	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1930	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1784	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#482	—	2	1	no	—
18	C₁₃×#482	—	2	1	no	—
19	C₁₃×#481	—	2	1	no	—
20	C₁₃×#480	—	2	1	no	—
21	C₁₃×#448	—	2	1	no	—
22	C₁₃×#448	—	2	1	no	—
23	C₁₃×#448	—	2	2	no	—
24	C₁₃×#433	—	2	2	no	—
25	C₁₃×#432	—	2	1	no	—
26	C₁₃×#431	—	2	1	no	—
27	C₂×C₁₃×#108	C₂²	1	2	yes	—
28	C₁₃×#428	C₂²	1	1	yes	characteristic
29	C₁₃×#428	C₂²	1	1	yes	characteristic
30	C₁₃×#424	C₂²	1	2	yes	—
31	C₁₃×#419	—	2	1	no	—
32	C₁₃×#419	—	2	1	no	—
33	C₁₃×#419	C₂²	1	2	yes	—
34	C₁₃×#419	C₂²	1	2	yes	—
35	C₁₃×#418	C₂²	1	1	yes	characteristic
36	C₁₃×#418	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	—	2	1	no	—
38	C₂×C₁₃×#103	—	2	1	no	—
39	C₂×C₁₃×#103	C₂²	1	2	yes	—
40	C₂×C₁₃×#101	C₂²	1	2	yes	—
41	C₂×C₁₃×#101	C₂²	1	2	yes	—
42	C₂×C₁₃×#100	C₂²	1	2	yes	—
43	C₁₃×#407	C₂²	1	1	yes	characteristic
44	C₁₃×#407	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#405	C₂²	1	2	yes	—
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#341	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	1	no	—
52	C₂²×Q₈×C₁₃	—	2	1	no	—
53	C₂²×Q₈×C₁₃	—	2	1	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	—	4	2	no	—
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×SD₁₆	—	2	4	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	4	2	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	4	2	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	—	2	1	no	—
77	C₁₃×#117	—	2	1	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₁₃×#117	D₄	1	1	yes	characteristic
80	C₁₃×#117	D₄	1	1	yes	characteristic
81	C₁₃×#117	C₂³	1	1	yes	characteristic
82	C₁₃×#117	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₁₃×#108	—	4	2	no	—
90	C₁₃×#107	—	2	1	no	—
91	C₁₃×#107	—	2	1	no	—
92	C₁₃×#106	—	2	1	no	—
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×#103	—	2	2	no	—
97	C₁₃×#103	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#102	—	2	1	no	—
103	C₁₃×#102	—	2	1	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	C₁₃×#101	—	2	4	no	—
107	C₁₃×#101	—	4	2	no	—
108	C₁₃×#100	—	4	2	no	—
109	C₁₃×C₂²⋊C₈	—	2	1	no	—
110	C₁₃×C₂²⋊C₈	—	2	1	no	—
111	C₁₃×C₂²⋊C₈	—	2	1	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
114	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
115	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
116	C₁₃×#97	—	2	2	no	—
117	C₄×C₈×C₁₃	—	2	2	no	—
118	#24523	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	1	no	—
120	C₂⁴×C₁₃	#41	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	4	4	no	—
129	C₂×Q₈×C₁₃	—	4	4	no	—
130	C₂×Q₈×C₁₃	—	4	4	no	—
131	C₂×Q₈×C₁₃	—	4	2	no	—
132	C₂×Q₈×C₁₃	—	4	2	no	—
133	C₂×Q₈×C₁₃	—	4	1	no	—
134	C₂×Q₈×C₁₃	—	4	1	no	—
135	C₂×Q₈×C₁₃	#41	1	4	yes	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	4	1	no	—
141	C₂×D₄×C₁₃	—	4	1	no	—
142	C₂×D₄×C₁₃	—	8	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	1	no	—
151	C₂²×C₄×C₁₃	—	4	1	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₁₃×SD₁₆	—	4	4	no	—
159	C₁₃×SD₁₆	—	4	4	no	—
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	4	2	no	—
174	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₁₃×C₂²⋊C₄	—	4	1	no	—
189	C₁₃×C₂²⋊C₄	—	4	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	#3094	C₂×C₁₃	1	1	yes	characteristic
195	C₂×#448	C₂×C₁₃	1	1	yes	characteristic
196	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#2064	C₂×C₁₃	1	2	yes	complemented
199	#2046	C₂×C₁₃	1	2	yes	complemented
200	#1977	C₂×C₁₃	1	2	yes	complemented
201	#1930	C₂×C₁₃	1	2	yes	complemented
202	#1900	C₂×C₁₃	1	1	yes	characteristic
203	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1784	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	4	1	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	8	1	no	—
211	C₂³×C₁₃	—	8	1	no	—
212	C₂³×C₁₃	#121	1	1	yes	characteristic
213	C₂³×C₁₃	#121	1	1	yes	characteristic
214	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	4	4	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	1	no	—
222	D₄×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	4	2	no	—
224	D₄×C₁₃	—	8	2	no	—
225	D₄×C₁₃	—	8	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	8	1	no	—
245	C₂×C₄×C₁₃	—	8	1	no	—
246	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
251	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	—	2	2	no	—
254	C₈×C₁₃	—	4	1	no	—
255	C₈×C₁₃	—	4	2	no	—
256	C₈×C₁₃	—	4	1	no	—
257	C₈×C₁₃	—	4	2	no	—
258	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
260	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
263	#482	—	2	1	no	—
264	#482	—	2	1	no	—
265	#481	—	2	1	no	—
266	#480	—	2	1	no	—
267	#448	—	2	1	no	—
268	#448	—	2	1	no	—
269	#448	—	2	2	no	—
270	#433	—	2	2	no	—
271	#432	—	2	1	no	—
272	#431	—	2	1	no	—
273	C₂×#108	C₂²×C₁₃	1	2	yes	—
274	#428	C₂²×C₁₃	1	1	yes	characteristic
275	#428	C₂²×C₁₃	1	1	yes	characteristic
276	#424	C₂²×C₁₃	1	2	yes	—
277	#419	—	2	1	no	—
278	#419	—	2	1	no	—
279	#419	C₂²×C₁₃	1	2	yes	—
280	#419	C₂²×C₁₃	1	2	yes	—
281	#418	C₂²×C₁₃	1	1	yes	characteristic
282	#418	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#103	—	2	1	no	—
284	C₂×#103	—	2	1	no	—
285	C₂×#103	C₂²×C₁₃	1	2	yes	—
286	C₂×#101	C₂²×C₁₃	1	2	yes	—
287	C₂×#101	C₂²×C₁₃	1	2	yes	—
288	C₂×#100	C₂²×C₁₃	1	2	yes	—
289	#407	C₂²×C₁₃	1	1	yes	characteristic
290	#407	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
292	#405	C₂²×C₁₃	1	2	yes	—
293	#343	C₂²×C₁₃	1	2	yes	—
294	#341	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	8	1	no	—
306	C₂²×C₁₃	—	16	2	no	—
307	C₂²×C₁₃	#471	1	2	yes	—
308	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
309	C₂²×C₁₃	#551	1	2	yes	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	—	4	1	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	1	no	—
317	C₄×C₁₃	—	8	1	no	—
318	C₄×C₁₃	#525	1	1	yes	characteristic
319	C₄×C₁₃	#535	1	1	yes	characteristic
320	C₄×C₁₃	#546	1	2	yes	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	—	2	4	no	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	4	2	no	—
328	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×SD₁₆	—	2	4	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×SD₁₆	—	4	2	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	4	2	no	—
339	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
340	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
342	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	—	2	1	no	—
351	#117	D₄×C₁₃	1	1	yes	characteristic
352	#117	D₄×C₁₃	1	1	yes	characteristic
353	#117	C₂³×C₁₃	1	1	yes	characteristic
354	#117	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	#108	—	4	2	no	—
362	#107	—	2	1	no	—
363	#107	—	2	1	no	—
364	#106	—	2	1	no	—
365	#106	—	2	1	no	—
366	C₄⋊C₈	—	2	2	no	—
367	C₄⋊C₈	—	2	2	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	#103	—	2	2	no	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#102	—	2	1	no	—
375	#102	—	2	1	no	—
376	#102	—	2	1	no	—
377	#102	—	2	1	no	—
378	#101	—	2	4	no	—
379	#101	—	4	2	no	—
380	#100	—	4	2	no	—
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	1	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
386	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
387	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
388	#97	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	C₂×C₁₃	—	2	2	no	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	4	1	no	—
393	C₂×C₁₃	—	16	1	no	—
394	C₂×C₁₃	#2411	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
396	C₂×C₁₃	#3069	1	1	yes	characteristic
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₁₃×#41	1	1	yes	characteristic
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	1	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	C₁₃×#41	1	4	yes	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	8	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	SD₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	4	2	no	—
452	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₁₃	#24523	1	1	yes	characteristic, direct product factor, Sylow
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	8	1	no	—
479	C₂³	—	8	1	no	—
480	C₂³	C₁₃×#121	1	1	yes	characteristic
481	C₂³	C₁₃×#121	1	1	yes	characteristic
482	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	4	4	no	—
486	Q₈	—	4	4	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
515	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
519	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	2	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	16	2	no	—
538	C₂²	C₁₃×#471	1	2	yes	—
539	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
540	C₂²	C₁₃×#551	1	2	yes	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	4	no	—
548	C₄	—	8	1	no	—
549	C₄	C₁₃×#525	1	1	yes	characteristic
550	C₄	C₁₃×#535	1	1	yes	characteristic
551	C₄	C₁₃×#546	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	1	no	—
555	C₂	—	16	1	no	—
556	C₂	C₁₃×#2411	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
558	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	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
3. C₁₃×#2924	C₂	semidirect
4. C₂×C₁₃×#419	C₂	semidirect
5. C₁₃×#2064	C₂	semidirect
6. C₁₃×#2046	C₂	semidirect
7. C₁₃×#1977	C₂	semidirect
8. C₁₃×#1930	C₂	semidirect
10. C₁₃×#1855	C₂	semidirect
11. C₁₃×#1784	C₂	semidirect
118. #24523	C₁₃	direct (N × H)
196. #2924	C₂×C₁₃	semidirect
197. C₂×#419	C₂×C₁₃	semidirect
198. #2064	C₂×C₁₃	semidirect
199. #2046	C₂×C₁₃	semidirect
200. #1977	C₂×C₁₃	semidirect
201. #1930	C₂×C₁₃	semidirect
203. #1855	C₂×C₁₃	semidirect
204. #1784	C₂×C₁₃	semidirect
472. C₁₃	#24523	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×#3094	2
C₂×C₁₃×#448	2
C₁₃×#2924	2
C₂×C₁₃×#419	2
C₁₃×#2064	2
C₁₃×#2046	2
C₁₃×#1977	2
C₁₃×#1930	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1784	2
#24523	13

Subgroups — C13×#24523 #15710862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24523 #15710862