Subgroups — C₁₃×#25876 #15712215

Order 3328.

1222 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1793	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
11	D₄×Q₈×C₁₃	—	2	1	no	—
12	D₄×Q₈×C₁₃	—	2	1	no	—
13	C₁₃×#547	—	2	1	no	—
14	C₁₃×#547	—	2	1	no	—
15	C₁₃×#547	—	2	2	no	—
16	C₁₃×#547	—	2	2	no	—
17	C₁₃×#536	—	2	2	no	—
18	C₁₃×#536	C₂²	1	2	yes	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#489	—	2	2	no	—
26	C₁₃×#487	—	2	1	no	—
27	C₁₃×#486	—	2	1	no	—
28	C₁₃×#477	—	2	1	no	—
29	C₁₃×#476	—	2	1	no	—
30	C₁₃×#475	—	2	1	no	—
31	C₁₃×#474	—	2	1	no	—
32	C₁₃×#428	C₂²	1	2	yes	—
33	C₁₃×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#104	C₂²	1	2	yes	—
35	C₂×C₁₃×#104	C₂²	1	4	yes	—
36	C₁₃×#417	C₂²	1	4	yes	—
37	C₁₃×#417	C₂²	1	2	yes	—
38	C₂×C₁₃×#101	C₂²	1	4	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₁₃×#391	—	2	2	no	—
41	C₁₃×#391	C₂²	1	4	yes	—
42	C₁₃×#382	—	2	2	no	—
43	C₄³×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	2	yes	—
45	C₁₃×2₋¹⁺⁴	—	2	8	no	—
46	C₁₃×2₋¹⁺⁴	—	4	4	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	4	no	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₃×#127	D₄	1	1	yes	characteristic
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	D₄	1	2	yes	—
73	C₁₃×#123	—	2	4	no	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#106	—	2	2	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	—	2	1	no	—
111	C₁₃×#104	—	2	4	no	—
112	C₁₃×#104	—	4	4	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#103	—	2	4	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	4	no	—
117	C₁₃×#101	—	4	4	no	—
118	C₁₃×#97	—	2	1	no	—
119	C₄×C₈×C₁₃	—	2	1	no	—
120	C₁₃×#95	—	2	8	no	—
121	#25876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	4	no	—
124	C₁₃×#41	—	2	4	no	—
125	C₁₃×#41	—	4	8	no	—
126	C₁₃×#41	—	4	16	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	4	no	—
129	C₁₃×#41	#41	1	4	yes	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	4	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	4	8	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	—	4	4	no	—
138	C₂×Q₈×C₁₃	—	4	4	no	—
139	C₂×Q₈×C₁₃	—	4	1	no	—
140	C₂×Q₈×C₁₃	—	4	1	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	4	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	4	1	no	—
180	C₁₃×C₄⋊C₄	—	4	1	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	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	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₄²×C₁₃	—	2	4	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	2	no	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	—	4	2	no	—
197	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
201	#3499	C₂×C₁₃	1	1	yes	characteristic
202	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2862	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2038	C₂×C₁₃	1	4	yes	complemented
206	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1962	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1793	C₂×C₁₃	1	4	yes	complemented
209	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	1	no	—
214	Q₈×C₁₃	—	2	4	no	—
215	Q₈×C₁₃	—	4	8	no	—
216	Q₈×C₁₃	—	4	2	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	8	2	no	—
220	Q₈×C₁₃	—	8	2	no	—
221	Q₈×C₁₃	#124	1	2	yes	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	2	1	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	4	4	no	—
227	D₄×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	#124	1	2	yes	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
258	C₈×C₁₃	—	4	2	no	—
259	C₈×C₁₃	—	4	2	no	—
260	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
261	D₄×Q₈	—	2	1	no	—
262	D₄×Q₈	—	2	1	no	—
263	#547	—	2	1	no	—
264	#547	—	2	1	no	—
265	#547	—	2	2	no	—
266	#547	—	2	2	no	—
267	#536	—	2	2	no	—
268	#536	C₂²×C₁₃	1	2	yes	—
269	#532	—	2	1	no	—
270	#532	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	—	2	1	no	—
272	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
275	#489	—	2	2	no	—
276	#487	—	2	1	no	—
277	#486	—	2	1	no	—
278	#477	—	2	1	no	—
279	#476	—	2	1	no	—
280	#475	—	2	1	no	—
281	#474	—	2	1	no	—
282	#428	C₂²×C₁₃	1	2	yes	—
283	#423	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#104	C₂²×C₁₃	1	2	yes	—
285	C₂×#104	C₂²×C₁₃	1	4	yes	—
286	#417	C₂²×C₁₃	1	2	yes	—
287	#417	C₂²×C₁₃	1	4	yes	—
288	C₂×#101	C₂²×C₁₃	1	4	yes	—
289	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	#391	—	2	2	no	—
291	#391	C₂²×C₁₃	1	4	yes	—
292	#382	—	2	2	no	—
293	C₄³	C₂²×C₁₃	1	1	yes	characteristic
294	#339	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
304	C₂²×C₁₃	#546	1	2	yes	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	4	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	1	no	—
312	C₄×C₁₃	—	4	1	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	#454	1	2	yes	—
315	C₄×C₁₃	#456	1	2	yes	—
316	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
317	C₄×C₁₃	#535	1	1	yes	characteristic
318	C₄×C₁₃	#546	1	2	yes	—
319	2₋¹⁺⁴	—	2	8	no	—
320	2₋¹⁺⁴	—	4	4	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	C₂³×C₁₃	1	2	yes	—
325	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
331	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
344	#127	D₄×C₁₃	1	1	yes	characteristic
345	#124	—	2	2	no	—
346	#124	D₄×C₁₃	1	2	yes	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	#123	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	1	no	—
357	#121	—	2	1	no	—
358	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
359	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
367	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
368	#117	—	2	1	no	—
369	#117	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
374	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	#107	—	2	2	no	—
382	#106	—	2	2	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	#104	—	2	4	no	—
386	#104	—	4	4	no	—
387	#103	—	2	2	no	—
388	#103	—	2	4	no	—
389	#102	—	2	2	no	—
390	#102	—	2	4	no	—
391	#101	—	4	4	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	#95	—	2	8	no	—
395	C₂×C₁₃	—	2	2	no	—
396	C₂×C₁₃	—	4	2	no	—
397	C₂×C₁₃	—	8	2	no	—
398	C₂×C₁₃	#2435	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
401	#41	—	2	2	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	4	8	no	—
405	#41	—	4	16	no	—
406	#41	—	4	4	no	—
407	#41	—	4	4	no	—
408	#41	C₁₃×#41	1	4	yes	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	4	8	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	—	4	4	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	4	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₄²	—	2	4	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	4	2	no	—
476	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₁₃	#25876	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	1	no	—
482	C₂³	—	2	2	no	—
483	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	Q₈	—	2	1	no	—
485	Q₈	—	2	4	no	—
486	Q₈	—	4	8	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	8	2	no	—
491	Q₈	—	8	2	no	—
492	Q₈	C₁₃×#124	1	2	yes	—
493	D₄	—	2	4	no	—
494	D₄	—	2	1	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	C₁₃×#124	1	2	yes	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
522	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
523	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
524	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
529	C₈	—	4	2	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
540	C₂²	C₁₃×#546	1	2	yes	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	2	no	—
550	C₄	C₁₃×#454	1	2	yes	—
551	C₄	C₁₃×#456	1	2	yes	—
552	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
553	C₄	C₁₃×#535	1	1	yes	characteristic
554	C₄	C₁₃×#546	1	2	yes	—
555	C₂	—	2	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₁₃×#2435	1	1	yes	characteristic
559	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
560	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3141	C₂	semidirect
3. C₁₃×#3079	C₂	semidirect
4. C₁₃×#2862	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#1966	C₂	semidirect
7. C₁₃×#1962	C₂	semidirect
8. C₁₃×#1793	C₂	semidirect
9. C₄×C₁₃×#104	C₂	semidirect
121. #25876	C₁₃	direct (N × H)
202. #3141	C₂×C₁₃	semidirect
203. #3079	C₂×C₁₃	semidirect
204. #2862	C₂×C₁₃	semidirect
205. #2038	C₂×C₁₃	semidirect
206. #1966	C₂×C₁₃	semidirect
207. #1962	C₂×C₁₃	semidirect
208. #1793	C₂×C₁₃	semidirect
209. C₄×#104	C₂×C₁₃	semidirect
480. C₁₃	#25876	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×#3499	2
C₁₃×#3141	2
C₁₃×#3079	2
C₁₃×#2862	2
C₁₃×#2038	2
C₁₃×#1966	2
C₁₃×#1962	2
C₁₃×#1793	2
C₄×C₁₃×#104	2
#25876	13

Subgroups — C13×#25876 #15712215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25876 #15712215