Subgroups — C₁₃×#8470 #15694809

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#556	—	2	1	no	—
9	C₁₃×#555	—	2	1	no	—
10	C₁₃×#554	—	2	1	no	—
11	C₁₃×#553	—	2	2	no	—
12	C₁₃×#548	—	2	2	no	—
13	C₁₃×#547	—	2	1	no	—
14	C₁₃×#542	—	2	2	no	—
15	C₁₃×#537	C₄	1	2	yes	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#532	—	2	1	no	—
18	C₁₃×#532	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₄	1	2	yes	—
21	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₁₃×#423	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#101	—	2	2	no	—
25	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#343	—	2	2	no	—
28	C₁₃×#333	—	2	1	no	—
29	C₁₃×#331	—	2	1	no	—
30	C₁₃×#329	—	2	2	no	—
31	C₁₃×Q₈⋊C₈	—	2	1	no	—
32	C₁₃×Q₈⋊C₈	—	2	1	no	—
33	C₁₃×D₄⋊C₈	—	2	1	no	—
34	C₁₃×D₄⋊C₈	—	2	1	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
38	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
39	C₂×C₁₃×M₁₆	—	2	1	no	—
40	C₂×C₁₃×M₁₆	—	2	1	no	—
41	C₂×C₁₃×M₁₆	—	2	1	no	—
42	C₂×C₁₃×M₁₆	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
48	C₁₃×#127	D₄	1	1	yes	characteristic
49	C₁₃×#126	—	2	4	no	—
50	C₁₃×#125	—	2	2	no	—
51	C₁₃×#124	—	2	2	no	—
52	C₁₃×#124	—	2	4	no	—
53	C₁₃×#124	D₄	1	2	yes	—
54	C₁₃×#123	—	2	4	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	—	2	2	no	—
59	C₁₃×#121	—	2	2	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	4	no	—
63	C₁₃×#121	—	2	1	no	—
64	C₁₃×#121	—	2	1	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	4	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	—	2	1	no	—
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
77	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
78	C₁₃×#117	—	2	2	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	2	1	no	—
81	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	—	2	1	no	—
90	C₁₃×C₄⋊C₈	—	2	1	no	—
91	C₁₃×#101	—	4	4	no	—
92	C₁₃×#97	—	2	1	no	—
93	C₁₃×#97	—	2	1	no	—
94	C₄×C₈×C₁₃	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	#8470	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₃×#41	—	4	2	no	—
98	C₁₃×#41	—	4	4	no	—
99	C₁₃×#41	—	8	2	no	—
100	C₁₃×#41	—	8	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	4	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₁₃×M₁₆	—	2	2	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	4	1	no	—
126	C₁₃×M₁₆	—	4	1	no	—
127	C₁₃×M₁₆	—	4	2	no	—
128	C₁₃×M₁₆	—	4	2	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₂×C₈×C₁₃	—	4	1	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	2	4	no	—
148	C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₄²×C₁₃	—	2	4	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
161	#3511	C₂×C₁₃	1	1	yes	characteristic
162	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1560	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1489	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1489	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	8	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	4	no	—
180	D₄×C₁₃	—	4	1	no	—
181	D₄×C₁₃	—	4	1	no	—
182	D₄×C₁₃	—	4	1	no	—
183	D₄×C₁₃	—	4	1	no	—
184	D₄×C₁₃	—	8	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
208	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	—	8	1	no	—
212	C₈×C₁₃	—	8	1	no	—
213	#556	—	2	1	no	—
214	#555	—	2	1	no	—
215	#554	—	2	1	no	—
216	#553	—	2	2	no	—
217	#548	—	2	2	no	—
218	#547	—	2	1	no	—
219	#542	—	2	2	no	—
220	#537	C₄×C₁₃	1	2	yes	—
221	#533	—	2	1	no	—
222	#532	—	2	1	no	—
223	#532	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	#520	C₄×C₁₃	1	2	yes	—
226	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
227	#423	C₂²×C₁₃	1	1	yes	characteristic
228	#423	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#101	—	2	2	no	—
230	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
231	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	#343	—	2	2	no	—
233	#333	—	2	1	no	—
234	#331	—	2	1	no	—
235	#329	—	2	2	no	—
236	Q₈⋊C₈	—	2	1	no	—
237	Q₈⋊C₈	—	2	1	no	—
238	D₄⋊C₈	—	2	1	no	—
239	D₄⋊C₈	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	#379	1	1	yes	characteristic
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	#413	1	2	yes	—
259	C₄×C₁₃	#453	1	1	yes	characteristic
260	C₄×C₁₃	#454	1	1	yes	characteristic
261	C₄×C₁₃	#455	1	1	yes	characteristic
262	C₄×C₁₃	#456	1	1	yes	characteristic
263	C₂×#41	—	2	2	no	—
264	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
265	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
266	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
276	#127	D₄×C₁₃	1	1	yes	characteristic
277	#126	—	2	4	no	—
278	#125	—	2	2	no	—
279	#124	—	2	2	no	—
280	#124	—	2	4	no	—
281	#124	D₄×C₁₃	1	2	yes	—
282	#123	—	2	4	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	#121	—	2	2	no	—
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	—	2	4	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
296	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
305	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	#117	—	2	1	no	—
309	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
312	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	#101	—	4	4	no	—
320	#97	—	2	1	no	—
321	#97	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₂×C₁₃	—	4	1	no	—
325	C₂×C₁₃	—	8	1	no	—
326	C₂×C₁₃	—	8	2	no	—
327	C₂×C₁₃	#1785	1	1	yes	characteristic
328	C₂×C₁₃	#1792	1	1	yes	characteristic
329	C₂×C₁₃	#1793	1	1	yes	characteristic
330	#41	—	4	2	no	—
331	#41	—	4	4	no	—
332	#41	—	8	2	no	—
333	#41	—	8	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	4	1	no	—
360	M₁₆	—	4	2	no	—
361	M₁₆	—	4	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₁₃	#8470	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	8	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	1	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	8	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	8	4	no	—
430	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
433	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
434	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
435	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	8	1	no	—
439	C₈	—	8	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	C₁₃×#379	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	1	no	—
458	C₄	C₁₃×#413	1	2	yes	—
459	C₄	C₁₃×#453	1	1	yes	characteristic
460	C₄	C₁₃×#454	1	1	yes	characteristic
461	C₄	C₁₃×#455	1	1	yes	characteristic
462	C₄	C₁₃×#456	1	1	yes	characteristic
463	C₂	—	4	1	no	—
464	C₂	—	8	1	no	—
465	C₂	—	8	2	no	—
466	C₂	C₁₃×#1785	1	1	yes	characteristic
467	C₂	C₁₃×#1792	1	1	yes	characteristic
468	C₂	C₁₃×#1793	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3511	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#1997	C₂	semidirect
3. C₁₃×#1966	C₂	semidirect
4. C₁₃×#1560	C₂	semidirect
5. C₁₃×#1525	C₂	semidirect
6. C₁₃×#1489	C₂	semidirect
7. C₁₃×#1489	C₂	semidirect
96. #8470	C₁₃	direct (N × H)
162. #1997	C₂×C₁₃	semidirect
163. #1966	C₂×C₁₃	semidirect
164. #1560	C₂×C₁₃	semidirect
165. #1525	C₂×C₁₃	semidirect
166. #1489	C₂×C₁₃	semidirect
167. #1489	C₂×C₁₃	semidirect
394. C₁₃	#8470	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×#3511	2
C₁₃×#1997	2
C₁₃×#1966	2
C₁₃×#1560	2
C₁₃×#1525	2
C₁₃×#1489	2
#8470	13

Subgroups — C13×#8470 #15694809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8470 #15694809