Subgroups — C₁₃×#18692 #15705031

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1644	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1643	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1642	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1641	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1560	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#562	—	2	2	no	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#554	C₂²	1	2	yes	—
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	C₂²	1	2	yes	—
17	C₁₃×#547	—	2	1	no	—
18	C₁₃×#547	—	2	1	no	—
19	C₁₃×#540	—	2	2	no	—
20	C₁₃×#537	—	2	2	no	—
21	C₁₃×#537	—	2	2	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#488	—	2	2	no	—
27	C₁₃×#487	C₂²	1	1	yes	characteristic
28	C₁₃×#487	C₂²	1	1	yes	characteristic
29	C₁₃×#486	C₂²	1	1	yes	characteristic
30	C₁₃×#486	C₂²	1	1	yes	characteristic
31	C₁₃×#477	—	2	1	no	—
32	C₁₃×#475	—	2	1	no	—
33	C₁₃×#475	C₂²	1	2	yes	—
34	C₁₃×#474	C₂²	1	2	yes	—
35	C₁₃×#470	—	2	2	no	—
36	C₁₃×#468	—	2	2	no	—
37	C₁₃×#462	—	2	1	no	—
38	C₁₃×#462	C₂²	1	2	yes	—
39	C₁₃×#461	C₂²	1	2	yes	—
40	C₁₃×#460	—	2	1	no	—
41	C₁₃×#423	C₂²	1	1	yes	characteristic
42	C₁₃×#423	C₂²	1	1	yes	characteristic
43	C₁₃×#416	—	2	2	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#333	C₂²	1	2	yes	—
46	C₁₃×#331	C₂²	1	2	yes	—
47	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
50	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	—	2	2	no	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	D₄	1	2	yes	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₃×#127	—	2	2	no	—
67	C₁₃×#127	D₄	1	1	yes	characteristic
68	C₁₃×#127	C₂³	1	1	yes	characteristic
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	1	no	—
71	C₁₃×#125	—	2	1	no	—
72	C₁₃×#124	—	2	1	no	—
73	C₁₃×#124	D₄	1	2	yes	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	—	2	4	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	4	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	D₄	1	2	yes	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	2	yes	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	—	2	2	no	—
110	C₁₃×#106	—	2	2	no	—
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₄×C₈×C₁₃	—	2	1	no	—
124	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	#18692	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	8	1	no	—
129	C₁₃×#41	—	8	1	no	—
130	C₁₃×#41	—	8	2	no	—
131	C₁₃×#41	—	8	2	no	—
132	C₁₃×#41	—	8	4	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
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	C₁₃×Q₁₆	—	8	2	no	—
157	C₁₃×SD₁₆	—	8	2	no	—
158	C₁₃×M₁₆	—	8	1	no	—
159	C₁₃×M₁₆	—	8	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	4	1	no	—
180	C₁₃×C₄⋊C₄	—	4	1	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	4	1	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	—	4	1	no	—
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	#3548	C₂×C₁₃	1	1	yes	characteristic
198	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1644	C₂×C₁₃	1	2	yes	complemented
202	#1643	C₂×C₁₃	1	2	yes	complemented
203	#1642	C₂×C₁₃	1	2	yes	complemented
204	#1641	C₂×C₁₃	1	2	yes	complemented
205	#1560	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	#120	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	4	2	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	1	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	1	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	8	1	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	8	1	no	—
229	D₄×C₁₃	—	8	2	no	—
230	D₄×C₁₃	—	8	2	no	—
231	D₄×C₁₃	—	8	4	no	—
232	D₄×C₁₃	—	8	4	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	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	8	4	no	—
248	C₂×C₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₁₃	—	4	1	no	—
256	C₈×C₁₃	—	4	1	no	—
257	C₈×C₁₃	—	4	2	no	—
258	C₈×C₁₃	—	4	2	no	—
259	#562	—	2	2	no	—
260	#554	—	2	1	no	—
261	#554	C₂²×C₁₃	1	2	yes	—
262	#550	—	2	1	no	—
263	#550	C₂²×C₁₃	1	2	yes	—
264	#547	—	2	1	no	—
265	#547	—	2	1	no	—
266	#540	—	2	2	no	—
267	#537	—	2	2	no	—
268	#537	—	2	2	no	—
269	#533	C₂²×C₁₃	1	1	yes	characteristic
270	#533	C₂²×C₁₃	1	1	yes	characteristic
271	#532	C₂²×C₁₃	1	1	yes	characteristic
272	#532	C₂²×C₁₃	1	1	yes	characteristic
273	#488	—	2	2	no	—
274	#487	C₂²×C₁₃	1	1	yes	characteristic
275	#487	C₂²×C₁₃	1	1	yes	characteristic
276	#486	C₂²×C₁₃	1	1	yes	characteristic
277	#486	C₂²×C₁₃	1	1	yes	characteristic
278	#477	—	2	1	no	—
279	#475	—	2	1	no	—
280	#475	C₂²×C₁₃	1	2	yes	—
281	#474	C₂²×C₁₃	1	2	yes	—
282	#470	—	2	2	no	—
283	#468	—	2	2	no	—
284	#462	—	2	1	no	—
285	#462	C₂²×C₁₃	1	2	yes	—
286	#461	C₂²×C₁₃	1	2	yes	—
287	#460	—	2	1	no	—
288	#423	C₂²×C₁₃	1	1	yes	characteristic
289	#423	C₂²×C₁₃	1	1	yes	characteristic
290	#416	—	2	2	no	—
291	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
292	#333	C₂²×C₁₃	1	2	yes	—
293	#331	C₂²×C₁₃	1	2	yes	—
294	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
295	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
296	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
297	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	8	1	no	—
316	C₄×C₁₃	—	8	1	no	—
317	C₄×C₁₃	#455	1	2	yes	—
318	C₄×C₁₃	#576	1	1	yes	characteristic
319	C₄×C₁₃	#577	1	1	yes	characteristic
320	C₄×C₁₃	#577	1	1	yes	characteristic
321	C₄×C₁₃	#578	1	1	yes	characteristic
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	D₄×C₁₃	1	2	yes	—
326	C₂×Q₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	2	2	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
337	#127	—	2	2	no	—
338	#127	D₄×C₁₃	1	1	yes	characteristic
339	#127	C₂³×C₁₃	1	1	yes	characteristic
340	#125	—	2	2	no	—
341	#125	—	2	1	no	—
342	#125	—	2	1	no	—
343	#124	—	2	1	no	—
344	#124	D₄×C₁₃	1	2	yes	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
355	#121	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	—	2	2	no	—
358	#121	—	2	4	no	—
359	#121	—	2	4	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	2	no	—
364	#121	D₄×C₁₃	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	C₂³×C₁₃	1	2	yes	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	#107	—	2	2	no	—
381	#106	—	2	2	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
385	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₁₃	—	4	1	no	—
398	C₂×C₁₃	—	8	2	no	—
399	C₂×C₁₃	—	8	2	no	—
400	C₂×C₁₃	#3012	1	1	yes	characteristic
401	C₂×C₁₃	#3013	1	1	yes	characteristic
402	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
403	#41	—	4	4	no	—
404	#41	—	8	1	no	—
405	#41	—	8	1	no	—
406	#41	—	8	2	no	—
407	#41	—	8	2	no	—
408	#41	—	8	4	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
414	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	Q₁₆	—	8	2	no	—
433	SD₁₆	—	8	2	no	—
434	M₁₆	—	8	1	no	—
435	M₁₆	—	8	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	4	1	no	—
469	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
473	C₁₃	#18692	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	C₁₃×#120	1	1	yes	characteristic
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	8	1	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	8	1	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	4	no	—
498	D₄	—	8	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	8	4	no	—
514	C₂×C₄	—	8	4	no	—
515	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
516	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
517	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	2	no	—
524	C₈	—	4	2	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	C₁₃×#455	1	2	yes	—
545	C₄	C₁₃×#576	1	1	yes	characteristic
546	C₄	C₁₃×#577	1	1	yes	characteristic
547	C₄	C₁₃×#577	1	1	yes	characteristic
548	C₄	C₁₃×#578	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₁₃×#3012	1	1	yes	characteristic
553	C₂	C₁₃×#3013	1	1	yes	characteristic
554	C₂	C₂×C₁₃×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3548	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3255	C₂	semidirect
3. C₁₃×#3254	C₂	semidirect
4. C₁₃×#3131	C₂	semidirect
5. C₁₃×#1644	C₂	semidirect
6. C₁₃×#1643	C₂	semidirect
7. C₁₃×#1642	C₂	semidirect
8. C₁₃×#1641	C₂	semidirect
9. C₁₃×#1560	C₂	semidirect
10. C₁₃×#1493	C₂	semidirect
11. C₁₃×#1492	C₂	semidirect
126. #18692	C₁₃	direct (N × H)
198. #3255	C₂×C₁₃	semidirect
199. #3254	C₂×C₁₃	semidirect
200. #3131	C₂×C₁₃	semidirect
201. #1644	C₂×C₁₃	semidirect
202. #1643	C₂×C₁₃	semidirect
203. #1642	C₂×C₁₃	semidirect
204. #1641	C₂×C₁₃	semidirect
205. #1560	C₂×C₁₃	semidirect
206. #1493	C₂×C₁₃	semidirect
207. #1492	C₂×C₁₃	semidirect
473. C₁₃	#18692	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×#3548	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3131	2
C₁₃×#1644	2
C₁₃×#1643	2
C₁₃×#1642	2
C₁₃×#1641	2
C₁₃×#1560	2
C₁₃×#1493	2
C₁₃×#1492	2
#18692	13

Subgroups — C13×#18692 #15705031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18692 #15705031