Subgroups — C₁₃×#18697 #15705036

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1638	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1637	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1628	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1627	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1561	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×#563	—	2	2	no	—
13	C₁₃×#559	—	2	1	no	—
14	Q₈²×C₁₃	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#556	C₂²	1	2	yes	—
17	D₄×Q₈×C₁₃	—	2	1	no	—
18	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#542	—	2	2	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#536	—	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	C₂²	1	2	yes	—
32	C₁₃×#476	—	2	1	no	—
33	C₁₃×#476	C₂²	1	2	yes	—
34	C₁₃×#474	—	2	1	no	—
35	C₁₃×#469	—	2	2	no	—
36	C₁₃×#468	—	2	2	no	—
37	C₁₃×#461	—	2	1	no	—
38	C₁₃×#460	C₂²	1	2	yes	—
39	C₁₃×#459	—	2	1	no	—
40	C₁₃×#459	C₂²	1	2	yes	—
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×#332	C₂²	1	2	yes	—
46	C₁₃×#332	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	1	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₃×#127	D₄	1	1	yes	characteristic
69	C₁₃×#127	C₂³	1	1	yes	characteristic
70	C₁₃×#126	—	2	4	no	—
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#125	—	2	1	no	—
73	C₁₃×#125	D₄	1	2	yes	—
74	C₁₃×#124	—	2	4	no	—
75	C₁₃×#124	—	2	2	no	—
76	C₁₃×#124	—	2	2	no	—
77	C₁₃×#124	—	2	1	no	—
78	C₁₃×#124	—	2	1	no	—
79	C₁₃×#123	—	2	4	no	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	D₄	1	2	yes	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂³	1	2	yes	—
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	D₄	1	2	yes	—
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×#102	—	2	2	no	—
119	C₁₃×#102	—	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	#18697	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	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	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	—	8	2	no	—
137	C₂×Q₈×C₁₃	—	8	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	4	1	no	—
146	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	4	1	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₁₃×SD₁₆	—	8	2	no	—
154	C₁₃×D₈	—	8	2	no	—
155	C₁₃×M₁₆	—	8	1	no	—
156	C₁₃×M₁₆	—	8	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	4	1	no	—
188	C₁₃×C₂²⋊C₄	—	4	1	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
196	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3253	C₂×C₁₃	1	1	yes	characteristic
199	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#1638	C₂×C₁₃	1	2	yes	complemented
201	#1637	C₂×C₁₃	1	2	yes	complemented
202	#1628	C₂×C₁₃	1	2	yes	complemented
203	#1627	C₂×C₁₃	1	2	yes	complemented
204	#1561	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	#120	1	1	yes	characteristic
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	4	2	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	4	1	no	—
215	Q₈×C₁₃	—	4	1	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	8	1	no	—
219	Q₈×C₁₃	—	8	4	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	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	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	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	8	4	no	—
245	C₂×C₄×C₁₃	—	8	2	no	—
246	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₁₃	—	4	1	no	—
253	C₈×C₁₃	—	4	1	no	—
254	C₈×C₁₃	—	4	2	no	—
255	C₈×C₁₃	—	4	2	no	—
256	#563	—	2	2	no	—
257	#559	—	2	1	no	—
258	Q₈²	—	2	1	no	—
259	#556	—	2	1	no	—
260	#556	C₂²×C₁₃	1	2	yes	—
261	D₄×Q₈	—	2	1	no	—
262	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
263	#542	—	2	2	no	—
264	#542	—	2	2	no	—
265	#536	—	2	2	no	—
266	#533	C₂²×C₁₃	1	1	yes	characteristic
267	#533	C₂²×C₁₃	1	1	yes	characteristic
268	#532	C₂²×C₁₃	1	1	yes	characteristic
269	#532	C₂²×C₁₃	1	1	yes	characteristic
270	#488	—	2	2	no	—
271	#487	C₂²×C₁₃	1	1	yes	characteristic
272	#487	C₂²×C₁₃	1	1	yes	characteristic
273	#486	C₂²×C₁₃	1	1	yes	characteristic
274	#486	C₂²×C₁₃	1	1	yes	characteristic
275	#477	C₂²×C₁₃	1	2	yes	—
276	#476	—	2	1	no	—
277	#476	C₂²×C₁₃	1	2	yes	—
278	#474	—	2	1	no	—
279	#469	—	2	2	no	—
280	#468	—	2	2	no	—
281	#461	—	2	1	no	—
282	#460	C₂²×C₁₃	1	2	yes	—
283	#459	—	2	1	no	—
284	#459	C₂²×C₁₃	1	2	yes	—
285	#423	C₂²×C₁₃	1	1	yes	characteristic
286	#423	C₂²×C₁₃	1	1	yes	characteristic
287	#416	—	2	2	no	—
288	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
289	#332	C₂²×C₁₃	1	2	yes	—
290	#332	C₂²×C₁₃	1	2	yes	—
291	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
292	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
293	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
294	D₄⋊C₈	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	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	8	1	no	—
302	C₂²×C₁₃	—	8	1	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	8	1	no	—
314	C₄×C₁₃	#454	1	2	yes	—
315	C₄×C₁₃	#576	1	1	yes	characteristic
316	C₄×C₁₃	#577	1	1	yes	characteristic
317	C₄×C₁₃	#577	1	1	yes	characteristic
318	C₄×C₁₃	#578	1	1	yes	characteristic
319	C₂×#41	—	2	1	no	—
320	C₂×#41	—	2	1	no	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂×SD₁₆	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	4	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
331	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	#127	D₄×C₁₃	1	1	yes	characteristic
337	#127	C₂³×C₁₃	1	1	yes	characteristic
338	#126	—	2	4	no	—
339	#126	—	2	4	no	—
340	#125	—	2	1	no	—
341	#125	D₄×C₁₃	1	2	yes	—
342	#124	—	2	4	no	—
343	#124	—	2	2	no	—
344	#124	—	2	2	no	—
345	#124	—	2	1	no	—
346	#124	—	2	1	no	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	D₄×C₁₃	1	2	yes	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	C₂³×C₁₃	1	2	yes	—
373	#117	—	2	1	no	—
374	#117	—	2	2	no	—
375	#117	D₄×C₁₃	1	2	yes	—
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	#107	—	2	2	no	—
378	#106	—	2	2	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
382	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#103	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₁₃	—	4	1	no	—
395	C₂×C₁₃	—	8	2	no	—
396	C₂×C₁₃	—	16	1	no	—
397	C₂×C₁₃	#3012	1	1	yes	characteristic
398	C₂×C₁₃	#3013	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
400	#41	—	4	4	no	—
401	#41	—	8	1	no	—
402	#41	—	8	1	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	8	2	no	—
410	C₂×Q₈	—	8	2	no	—
411	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	SD₁₆	—	8	2	no	—
427	D₈	—	8	2	no	—
428	M₁₆	—	8	1	no	—
429	M₁₆	—	8	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	4	2	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
451	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
452	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₁₃	#18697	1	1	yes	characteristic, direct product factor, Sylow
470	C₂³	—	2	2	no	—
471	C₂³	—	4	1	no	—
472	C₂³	C₁₃×#120	1	1	yes	characteristic
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	4	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	8	1	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	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	8	4	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
510	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
511	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	—	8	1	no	—
538	C₄	C₁₃×#454	1	2	yes	—
539	C₄	C₁₃×#576	1	1	yes	characteristic
540	C₄	C₁₃×#577	1	1	yes	characteristic
541	C₄	C₁₃×#577	1	1	yes	characteristic
542	C₄	C₁₃×#578	1	1	yes	characteristic
543	C₂	—	4	1	no	—
544	C₂	—	8	2	no	—
545	C₂	—	16	1	no	—
546	C₂	C₁₃×#3012	1	1	yes	characteristic
547	C₂	C₁₃×#3013	1	1	yes	characteristic
548	C₂	C₂×C₁₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3253	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
1. C₁₃×#3550	C₂	semidirect
2. C₁₃×#3254	C₂	semidirect
4. C₁₃×#3131	C₂	semidirect
5. C₁₃×#1638	C₂	semidirect
6. C₁₃×#1637	C₂	semidirect
7. C₁₃×#1628	C₂	semidirect
8. C₁₃×#1627	C₂	semidirect
9. C₁₃×#1561	C₂	semidirect
10. C₁₃×#1493	C₂	semidirect
11. C₁₃×#1492	C₂	semidirect
126. #18697	C₁₃	direct (N × H)
196. #3550	C₂×C₁₃	semidirect
197. #3254	C₂×C₁₃	semidirect
199. #3131	C₂×C₁₃	semidirect
200. #1638	C₂×C₁₃	semidirect
201. #1637	C₂×C₁₃	semidirect
202. #1628	C₂×C₁₃	semidirect
203. #1627	C₂×C₁₃	semidirect
204. #1561	C₂×C₁₃	semidirect
205. #1493	C₂×C₁₃	semidirect
206. #1492	C₂×C₁₃	semidirect
469. C₁₃	#18697	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×#3550	2
C₁₃×#3254	2
C₁₃×#3253	2
C₁₃×#3131	2
C₁₃×#1638	2
C₁₃×#1637	2
C₁₃×#1628	2
C₁₃×#1627	2
C₁₃×#1561	2
C₁₃×#1493	2
C₁₃×#1492	2
#18697	13

Subgroups — C13×#18697 #15705036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18697 #15705036