Subgroups — C₁₃×#19823 #15706162

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#555	C₂²	1	1	yes	characteristic
18	C₁₃×#554	C₂²	1	1	yes	characteristic
19	D₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#488	—	2	1	no	—
23	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#486	C₂²	1	1	yes	characteristic
25	C₁₃×#486	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#482	—	2	1	no	—
29	C₁₃×#482	—	2	1	no	—
30	C₁₃×#481	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#476	C₂²	1	1	yes	characteristic
34	C₁₃×#476	C₂²	1	1	yes	characteristic
35	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#474	C₂²	1	1	yes	characteristic
37	C₁₃×#469	—	2	1	no	—
38	C₁₃×#465	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#463	—	2	1	no	—
41	C₁₃×#461	C₂²	1	1	yes	characteristic
42	C₁₃×#460	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#450	—	2	1	no	—
45	C₁₃×#447	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₄×C₁₃×SD₁₆	—	2	1	no	—
48	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
50	C₁₃×#436	C₂²	1	1	yes	characteristic
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#427	—	2	1	no	—
54	C₁₃×#418	—	2	1	no	—
55	C₂×C₁₃×#102	—	2	1	no	—
56	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	4	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×#127	C₂³	1	1	yes	characteristic
82	C₁₃×#126	—	4	1	no	—
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#124	—	4	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	4	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#120	—	4	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#117	—	2	1	no	—
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	D₄	1	1	yes	characteristic
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	D₄	1	1	yes	characteristic
123	C₁₃×#102	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	4	1	no	—
134	C₁₃×#102	D₄	1	1	yes	characteristic
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19823	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	4	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	—	4	1	no	—
155	C₂×D₄×C₁₃	—	4	2	no	—
156	C₂×D₄×C₁₃	—	4	2	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	—	8	1	no	—
159	C₂×D₄×C₁₃	—	8	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₁₃×Q₁₆	—	8	2	no	—
168	C₁₃×SD₁₆	—	4	1	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×D₈	—	2	2	no	—
172	C₁₃×D₈	—	8	1	no	—
173	C₁₃×M₁₆	—	8	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	4	2	no	—
180	C₂×C₈×C₁₃	—	8	1	no	—
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	—	4	1	no	—
211	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
212	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3325	C₂×C₁₃	1	1	yes	characteristic
215	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1720	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1703	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1677	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1671	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1639	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1634	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1632	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	8	2	no	—
232	C₂³×C₁₃	—	8	2	no	—
233	C₂³×C₁₃	—	16	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	8	1	no	—
239	Q₈×C₁₃	—	8	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	8	1	no	—
250	D₄×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	8	2	no	—
252	D₄×C₁₃	—	16	1	no	—
253	D₄×C₁₃	#135	1	2	yes	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	16	1	no	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	#555	C₂²×C₁₃	1	1	yes	characteristic
283	#554	C₂²×C₁₃	1	1	yes	characteristic
284	D₄²	C₂²×C₁₃	1	1	yes	characteristic
285	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#488	—	2	1	no	—
288	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
289	#486	C₂²×C₁₃	1	1	yes	characteristic
290	#486	C₂²×C₁₃	1	1	yes	characteristic
291	#486	C₂²×C₁₃	1	1	yes	characteristic
292	#485	—	2	1	no	—
293	#482	—	2	1	no	—
294	#482	—	2	1	no	—
295	#481	—	2	1	no	—
296	#479	—	2	1	no	—
297	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	#476	C₂²×C₁₃	1	1	yes	characteristic
299	#476	C₂²×C₁₃	1	1	yes	characteristic
300	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
301	#474	C₂²×C₁₃	1	1	yes	characteristic
302	#469	—	2	1	no	—
303	#465	—	2	1	no	—
304	#465	—	2	1	no	—
305	#463	—	2	1	no	—
306	#461	C₂²×C₁₃	1	1	yes	characteristic
307	#460	C₂²×C₁₃	1	1	yes	characteristic
308	#459	C₂²×C₁₃	1	1	yes	characteristic
309	#450	—	2	1	no	—
310	#447	—	2	1	no	—
311	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₄×SD₁₆	—	2	1	no	—
313	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
315	#436	C₂²×C₁₃	1	1	yes	characteristic
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	#427	—	2	1	no	—
319	#418	—	2	1	no	—
320	C₂×#102	—	2	1	no	—
321	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
323	#333	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	#333	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	#332	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	#331	C₂²×C₁₃	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	16	4	no	—
345	C₂²×C₁₃	D₄²	1	1	yes	characteristic
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
356	C₄×C₁₃	#575	1	1	yes	characteristic
357	C₄×C₁₃	#577	1	1	yes	characteristic
358	C₄×C₁₃	#577	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂×Q₁₆	—	4	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
367	C₂×M₁₆	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	#127	C₂³×C₁₃	1	1	yes	characteristic
374	#126	—	4	1	no	—
375	#125	—	2	1	no	—
376	#124	—	2	1	no	—
377	#124	—	4	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	4	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#120	—	4	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	#107	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	D₄×C₁₃	1	1	yes	characteristic
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	#106	D₄×C₁₃	1	1	yes	characteristic
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	D₄×C₁₃	1	1	yes	characteristic
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	4	1	no	—
426	#102	D₄×C₁₃	1	1	yes	characteristic
427	#102	D₄×C₁₃	1	1	yes	characteristic
428	#102	D₄×C₁₃	1	1	yes	characteristic
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	8	1	no	—
438	C₂×C₁₃	—	8	1	no	—
439	C₂×C₁₃	—	16	1	no	—
440	C₂×C₁₃	#3267	1	1	yes	characteristic
441	C₂×C₁₃	#3282	1	1	yes	characteristic
442	C₂×C₁₃	#3288	1	1	yes	characteristic
443	C₂⁴	—	4	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	8	1	no	—
457	C₂×D₄	—	8	1	no	—
458	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	Q₁₆	—	8	2	no	—
466	SD₁₆	—	4	1	no	—
467	SD₁₆	—	4	2	no	—
468	SD₁₆	—	8	1	no	—
469	D₈	—	2	2	no	—
470	D₈	—	8	1	no	—
471	M₁₆	—	8	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	4	2	no	—
478	C₂×C₈	—	8	1	no	—
479	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	4	1	no	—
508	C₄²	—	4	1	no	—
509	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
510	C₁₃	#19823	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	8	2	no	—
516	C₂³	—	8	2	no	—
517	C₂³	—	16	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	8	1	no	—
523	Q₈	—	8	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	2	no	—
536	D₄	—	16	1	no	—
537	D₄	C₁₃×#135	1	2	yes	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	16	1	no	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	16	4	no	—
578	C₂²	D₄²×C₁₃	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
589	C₄	C₁₃×#575	1	1	yes	characteristic
590	C₄	C₁₃×#577	1	1	yes	characteristic
591	C₄	C₁₃×#577	1	1	yes	characteristic
592	C₂	—	4	2	no	—
593	C₂	—	8	1	no	—
594	C₂	—	8	1	no	—
595	C₂	—	16	1	no	—
596	C₂	C₁₃×#3267	1	1	yes	characteristic
597	C₂	C₁₃×#3282	1	1	yes	characteristic
598	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3325	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3360	C₂	semidirect
2. C₁₃×#3340	C₂	semidirect
4. C₁₃×#3295	C₂	semidirect
5. C₁₃×#1720	C₂	semidirect
6. C₁₃×#1703	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
8. C₁₃×#1677	C₂	semidirect
9. C₁₃×#1671	C₂	semidirect
10. C₁₃×#1639	C₂	semidirect
11. C₁₃×#1634	C₂	semidirect
12. C₁₃×#1632	C₂	semidirect
13. C₁₃×#1628	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
16. C₁₃×#556	C₂²	semidirect
20. C₁₃×#498	C₂²	semidirect
21. C₁₃×#494	C₂²	semidirect
23. C₁₃×#487	C₂²	semidirect
32. C₁₃×#477	C₂²	semidirect
35. C₁₃×#476	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
52. C₈×D₄×C₁₃	C₂²	semidirect
56. C₁₃×#334	C₂²	semidirect
57. C₁₃×#334	C₂²	semidirect
58. C₁₃×#333	C₂²	semidirect
59. C₁₃×#333	C₂²	semidirect
60. C₁₃×#332	C₂²	semidirect
62. C₁₃×Q₈⋊C₈	C₂²	semidirect
65. C₁₃×D₄⋊C₈	C₂²	semidirect
66. C₁₃×#322	C₂²	semidirect
144. #19823	C₁₃	direct (N × H)
212. #3360	C₂×C₁₃	semidirect
213. #3340	C₂×C₁₃	semidirect
215. #3295	C₂×C₁₃	semidirect
216. #1720	C₂×C₁₃	semidirect
217. #1703	C₂×C₁₃	semidirect
218. #1678	C₂×C₁₃	semidirect
219. #1677	C₂×C₁₃	semidirect
220. #1671	C₂×C₁₃	semidirect
221. #1639	C₂×C₁₃	semidirect
222. #1634	C₂×C₁₃	semidirect
223. #1632	C₂×C₁₃	semidirect
224. #1628	C₂×C₁₃	semidirect
225. #1583	C₂×C₁₃	semidirect
226. #1580	C₂×C₁₃	semidirect
281. #556	C₂²×C₁₃	semidirect
285. #498	C₂²×C₁₃	semidirect
286. #494	C₂²×C₁₃	semidirect
288. #487	C₂²×C₁₃	semidirect
297. #477	C₂²×C₁₃	semidirect
300. #476	C₂²×C₁₃	semidirect
311. C₈×Q₈	C₂²×C₁₃	semidirect
317. C₈×D₄	C₂²×C₁₃	semidirect
321. #334	C₂²×C₁₃	semidirect
322. #334	C₂²×C₁₃	semidirect
323. #333	C₂²×C₁₃	semidirect
324. #333	C₂²×C₁₃	semidirect
325. #332	C₂²×C₁₃	semidirect
327. Q₈⋊C₈	C₂²×C₁₃	semidirect
330. D₄⋊C₈	C₂²×C₁₃	semidirect
331. #322	C₂²×C₁₃	semidirect
510. C₁₃	#19823	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×#3360	2
C₁₃×#3340	2
C₁₃×#3325	2
C₁₃×#3295	2
C₁₃×#1720	2
C₁₃×#1703	2
C₁₃×#1678	2
C₁₃×#1677	2
C₁₃×#1671	2
C₁₃×#1639	2
C₁₃×#1634	2
C₁₃×#1632	2
C₁₃×#1628	2
C₁₃×#1583	2
C₁₃×#1580	2
#19823	13

Subgroups — C13×#19823 #15706162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19823 #15706162