Subgroups — C₁₃×#25982 #15712321

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2897	C₂	1	2	yes	maximal
3	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2027	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1866	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1859	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1816	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1792	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	C₂²	1	2	yes	—
12	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
13	C₁₃×#520	C₂²	1	2	yes	—
14	C₁₃×#479	—	2	2	no	—
15	C₁₃×#478	—	2	2	no	—
16	C₁₃×#477	—	2	2	no	—
17	C₁₃×#474	—	2	2	no	—
18	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
19	C₁₃×#428	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
21	C₁₃×#424	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#104	C₂²	1	2	yes	—
23	C₁₃×#418	—	2	2	no	—
24	C₁₃×#418	C₂²	1	2	yes	—
25	C₁₃×#417	—	2	2	no	—
26	C₁₃×#417	C₂²	1	2	yes	—
27	C₁₃×#417	C₂²	1	2	yes	—
28	C₁₃×#416	—	2	2	no	—
29	C₁₃×#416	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	—	2	2	no	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#343	C₂²	1	2	yes	complemented
37	C₁₃×#339	C₂²	1	2	yes	complemented
38	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×H(5,𝔽₂)	—	2	4	no	—
40	C₁₃×H(5,𝔽₂)	—	4	1	no	—
41	C₁₃×H(5,𝔽₂)	Q₈	1	4	yes	complemented
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	4	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×#131	—	2	4	no	—
48	C₁₃×#131	—	4	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	1	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	4	2	no	—
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#108	—	4	2	no	—
69	C₁₃×#107	—	2	2	no	—
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×#104	—	2	4	no	—
76	C₁₃×#103	—	2	2	no	—
77	C₁₃×#103	—	2	2	no	—
78	C₁₃×#103	D₄	1	2	yes	—
79	C₁₃×#103	D₄	1	2	yes	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	2	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	D₄	1	2	yes	—
87	C₁₃×#102	D₄	1	2	yes	—
88	C₁₃×#100	—	4	1	no	—
89	#25982	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	—	4	1	no	—
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	2	8	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₁₃×#41	C₂×Q₈	1	4	yes	—
97	C₁₃×#41	#41	1	4	yes	—
98	C₂×Q₈×C₁₃	—	4	1	no	—
99	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	8	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	4	4	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	4	4	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	8	2	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	8	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	#3083	C₂×C₁₃	1	2	yes	complemented
146	#2897	C₂×C₁₃	1	2	yes	—
147	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2063	C₂×C₁₃	1	2	yes	complemented
149	#2027	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1866	C₂×C₁₃	1	2	yes	complemented
151	#1859	C₂×C₁₃	1	2	yes	complemented
152	#1816	C₂×C₁₃	1	2	yes	complemented
153	#1792	C₂×C₁₃	1	1	yes	characteristic
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	8	1	no	—
160	C₂³×C₁₃	—	8	1	no	—
161	C₂³×C₁₃	—	16	1	no	—
162	C₂³×C₁₃	—	16	1	no	—
163	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	16	1	no	—
166	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	2	4	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	4	8	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	8	1	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	16	2	no	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#131	C₂²×C₁₃	1	2	yes	—
198	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
199	#520	C₂²×C₁₃	1	2	yes	—
200	#479	—	2	2	no	—
201	#478	—	2	2	no	—
202	#477	—	2	2	no	—
203	#474	—	2	2	no	—
204	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
205	#428	C₂²×C₁₃	1	2	yes	complemented
206	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
207	#424	C₂²×C₁₃	1	2	yes	complemented
208	C₂×#104	C₂²×C₁₃	1	2	yes	—
209	#418	—	2	2	no	—
210	#418	C₂²×C₁₃	1	2	yes	—
211	#417	—	2	2	no	—
212	#417	C₂²×C₁₃	1	2	yes	—
213	#417	C₂²×C₁₃	1	2	yes	—
214	#416	—	2	2	no	—
215	#416	C₂²×C₁₃	1	2	yes	—
216	C₂×#102	—	2	2	no	—
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
219	#390	C₂²×C₁₃	1	1	yes	characteristic
220	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
221	#343	C₂²×C₁₃	1	2	yes	complemented
222	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
223	#339	C₂²×C₁₃	1	2	yes	complemented
224	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	—	8	2	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	16	1	no	—
235	C₂²×C₁₃	—	16	4	no	—
236	C₂²×C₁₃	#543	1	1	yes	characteristic
237	C₂²×C₁₃	D₄²	1	1	yes	characteristic
238	C₂²×C₁₃	#551	1	1	yes	characteristic
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	—	8	1	no	—
245	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
246	C₄×C₁₃	#546	1	2	yes	—
247	H(5,𝔽₂)	—	2	4	no	—
248	H(5,𝔽₂)	—	4	1	no	—
249	H(5,𝔽₂)	Q₈×C₁₃	1	4	yes	complemented
250	C₂×#41	—	2	2	no	—
251	C₂×#41	C₂³×C₁₃	1	2	yes	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	4	1	no	—
254	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
255	#131	—	2	4	no	—
256	#131	—	4	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
259	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
262	C₄⋊Q₈	—	2	2	no	—
263	#125	—	2	2	no	—
264	C₂²⋊Q₈	—	4	1	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	—	4	2	no	—
268	#117	—	2	2	no	—
269	#117	C₂³×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	4	1	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	4	1	no	—
275	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
276	#108	—	4	2	no	—
277	#107	—	2	2	no	—
278	#107	—	2	2	no	—
279	#107	—	2	2	no	—
280	#106	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	#104	—	2	4	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	D₄×C₁₃	1	2	yes	—
287	#103	D₄×C₁₃	1	2	yes	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	D₄×C₁₃	1	2	yes	—
295	#102	D₄×C₁₃	1	2	yes	—
296	#100	—	4	1	no	—
297	C₂×C₁₃	—	2	1	no	—
298	C₂×C₁₃	—	2	1	no	—
299	C₂×C₁₃	—	4	4	no	—
300	C₂×C₁₃	—	8	2	no	—
301	C₂×C₁₃	#2437	1	1	yes	characteristic
302	C₂×C₁₃	#3289	1	1	yes	characteristic
303	C₂×C₁₃	#3292	1	1	yes	characteristic
304	C₂⁴	—	2	1	no	—
305	C₂⁴	—	4	1	no	—
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	—	2	8	no	—
309	#41	—	4	4	no	—
310	#41	C₂×Q₈×C₁₃	1	4	yes	—
311	#41	C₁₃×#41	1	4	yes	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	4	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	4	4	no	—
342	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	8	2	no	—
351	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	8	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	4	2	no	—
359	C₁₃	#25982	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	8	1	no	—
367	C₂³	—	16	1	no	—
368	C₂³	—	16	1	no	—
369	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	16	1	no	—
372	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	8	no	—
378	D₄	—	4	2	no	—
379	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	16	2	no	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
395	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
397	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	16	1	no	—
412	C₂²	—	16	4	no	—
413	C₂²	C₁₃×#543	1	1	yes	characteristic
414	C₂²	D₄²×C₁₃	1	1	yes	characteristic
415	C₂²	C₁₃×#551	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
423	C₄	C₁₃×#546	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	4	4	no	—
427	C₂	—	8	2	no	—
428	C₂	C₁₃×#2437	1	1	yes	characteristic
429	C₂	C₁₃×#3289	1	1	yes	characteristic
430	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×H(5,𝔽₂)	C₂²
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×#3083	C₂	semidirect
3. C₁₃×#2093	C₂	semidirect
4. C₁₃×#2063	C₂	semidirect
5. C₁₃×#2027	C₂	semidirect
6. C₁₃×#1866	C₂	semidirect
7. C₁₃×#1859	C₂	semidirect
8. C₁₃×#1816	C₂	semidirect
12. C₁₃×#544	C₂²	semidirect
18. C₂×C₁₃×#108	C₂²	semidirect
19. C₁₃×#428	C₂²	semidirect
20. C₂×C₁₃×#107	C₂²	semidirect
21. C₁₃×#424	C₂²	semidirect
34. C₁₃×#384	C₂²	semidirect
35. C₁₃×#343	C₂²	semidirect
36. C₁₃×#343	C₂²	semidirect
37. C₁₃×#339	C₂²	semidirect
38. C₁₃×#336	C₂²	semidirect
41. C₁₃×H(5,𝔽₂)	Q₈	semidirect
89. #25982	C₁₃	direct (N × H)
145. #3083	C₂×C₁₃	semidirect
147. #2093	C₂×C₁₃	semidirect
148. #2063	C₂×C₁₃	semidirect
149. #2027	C₂×C₁₃	semidirect
150. #1866	C₂×C₁₃	semidirect
151. #1859	C₂×C₁₃	semidirect
152. #1816	C₂×C₁₃	semidirect
198. #544	C₂²×C₁₃	semidirect
204. C₂×#108	C₂²×C₁₃	semidirect
205. #428	C₂²×C₁₃	semidirect
206. C₂×#107	C₂²×C₁₃	semidirect
207. #424	C₂²×C₁₃	semidirect
220. #384	C₂²×C₁₃	semidirect
221. #343	C₂²×C₁₃	semidirect
222. #343	C₂²×C₁₃	semidirect
223. #339	C₂²×C₁₃	semidirect
224. #336	C₂²×C₁₃	semidirect
249. H(5,𝔽₂)	Q₈×C₁₃	semidirect
359. C₁₃	#25982	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×#3083	2
C₁₃×#2897	2
C₁₃×#2093	2
C₁₃×#2063	2
C₁₃×#2027	2
C₁₃×#1866	2
C₁₃×#1859	2
C₁₃×#1816	2
C₁₃×#1792	2
#25982	13

Subgroups — C13×#25982 #15712321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25982 #15712321