Subgroups — C₁₃×#61284 #15747623

Order 3328.

1882 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×#3506	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3355	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3354	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3339	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3334	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3096	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3058	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2913	C₂	1	2	yes	maximal, complemented
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₁₃×#559	—	2	4	no	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#555	C₂²	1	4	yes	complemented
19	C₁₃×#553	C₂²	1	8	yes	complemented
20	C₁₃×#550	—	2	2	no	—
21	C₁₃×#547	C₂²	1	4	yes	complemented
22	C₁₃×#538	—	2	4	no	—
23	C₁₃×#535	C₂²	1	4	yes	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#525	—	2	4	no	—
27	C₁₃×#520	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#499	C₂²	1	2	yes	complemented
32	C₁₃×#499	C₂²	1	2	yes	complemented
33	C₁₃×#498	C₂²	1	2	yes	complemented
34	C₁₃×#482	C₂²	1	8	yes	complemented
35	C₁₃×#482	C₂²	1	8	yes	complemented
36	C₁₃×#481	C₂²	1	8	yes	complemented
37	C₁₃×#480	C₂²	1	8	yes	complemented
38	C₁₃×#478	C₂²	1	8	yes	complemented
39	C₁₃×#476	C₂²	1	4	yes	complemented
40	C₁₃×#474	C₂²	1	4	yes	complemented
41	C₁₃×#469	C₂²	1	8	yes	—
42	C₁₃×#466	C₂²	1	4	yes	—
43	C₁₃×#466	C₂²	1	4	yes	—
44	C₄×C₁₃×D₈	C₂²	1	2	yes	—
45	C₄×C₁₃×D₈	C₂²	1	2	yes	—
46	C₄×C₁₃×D₈	C₂²	1	2	yes	—
47	C₄×C₁₃×D₈	C₂²	1	2	yes	—
48	C₁₃×#436	C₂²	1	2	yes	complemented
49	C₁₃×#436	C₂²	1	2	yes	complemented
50	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
51	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
52	C₁₃×#428	C₂²	1	4	yes	—
53	C₁₃×#428	C₂²	1	8	yes	complemented
54	C₁₃×#427	C₂²	1	2	yes	—
55	C₁₃×#427	C₂²	1	2	yes	—
56	C₁₃×#427	C₂²	1	4	yes	complemented
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#107	C₂²	1	4	yes	complemented
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#418	C₂²	1	4	yes	—
61	C₂×C₁₃×#102	C₂²	1	2	yes	—
62	C₁₃×#408	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#41	—	2	4	no	—
65	C₂×C₁₃×#41	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₂×C₁₃×D₈	—	2	4	no	—
69	C₂×C₁₃×D₈	C₂³	1	2	yes	—
70	C₂×C₁₃×D₈	C₂³	1	2	yes	—
71	C₁₃×#131	—	2	8	no	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₃×#127	—	2	4	no	—
81	C₁₃×#127	D₄	1	1	yes	characteristic
82	C₁₃×#126	—	2	8	no	—
83	C₁₃×#125	C₂³	1	4	yes	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	—	2	8	no	—
86	C₁₃×#124	D₄	1	2	yes	—
87	C₁₃×#123	—	2	8	no	—
88	C₁₃×#123	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	4	no	—
92	C₁₃×#121	—	2	4	no	—
93	C₁₃×#121	—	2	8	no	—
94	C₁₃×#121	D₄	1	2	yes	—
95	C₁₃×#121	D₄	1	2	yes	—
96	C₁₃×#121	C₂³	1	8	yes	—
97	C₁₃×#121	C₂³	1	8	yes	—
98	C₁₃×#120	—	2	8	no	—
99	C₄×Q₈×C₁₃	—	2	4	no	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	8	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	C₂³	1	4	yes	—
108	C₄×D₄×C₁₃	C₂³	1	4	yes	—
109	C₄×D₄×C₁₃	C₂³	1	2	yes	—
110	C₄×D₄×C₁₃	C₂³	1	2	yes	—
111	C₁₃×#117	—	2	4	no	—
112	C₁₃×#117	C₂³	1	4	yes	—
113	C₁₃×#117	C₂³	1	8	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	C₂³	1	2	yes	—
119	C₁₃×#107	C₂³	1	2	yes	—
120	C₁₃×#107	C₂³	1	2	yes	—
121	C₁₃×#107	C₂³	1	8	yes	—
122	C₁₃×#107	C₂³	1	2	yes	—
123	C₁₃×#107	C₂³	1	2	yes	—
124	C₁₃×#107	C₂³	1	2	yes	—
125	C₁₃×#106	C₂³	1	4	yes	—
126	C₁₃×#106	C₂³	1	4	yes	—
127	C₁₃×#106	C₂³	1	8	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
130	C₁₃×#102	C₂³	1	4	yes	—
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×#102	C₂³	1	8	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
136	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	#61284	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	2	no	—
142	C₁₃×#41	—	2	4	no	—
143	C₁₃×#41	—	2	4	no	—
144	C₁₃×#41	—	8	8	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₁₃	—	2	8	no	—
149	C₂×D₄×C₁₃	—	2	8	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	8	4	no	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×D₈	—	2	4	no	—
168	C₁₃×D₈	—	2	4	no	—
169	C₁₃×M₁₆	—	2	4	no	—
170	C₁₃×M₁₆	—	2	8	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	8	no	—
173	C₂×C₈×C₁₃	#41	1	4	yes	complemented
174	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
177	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
197	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
198	C₄²×C₁₃	—	2	8	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
204	#3506	C₂×C₁₃	1	2	yes	complemented
205	#3355	C₂×C₁₃	1	4	yes	complemented
206	#3354	C₂×C₁₃	1	4	yes	complemented
207	#3341	C₂×C₁₃	1	2	yes	complemented
208	#3339	C₂×C₁₃	1	4	yes	complemented
209	#3334	C₂×C₁₃	1	2	yes	complemented
210	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3096	C₂×C₁₃	1	4	yes	complemented
212	#3077	C₂×C₁₃	1	2	yes	complemented
213	#3058	C₂×C₁₃	1	2	yes	complemented
214	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2913	C₂×C₁₃	1	2	yes	complemented
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	4	4	no	—
219	C₂³×C₁₃	—	8	2	no	—
220	C₂³×C₁₃	—	8	2	no	—
221	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
222	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₃	—	2	4	no	—
224	Q₈×C₁₃	—	4	4	no	—
225	Q₈×C₁₃	—	8	2	no	—
226	D₄×C₁₃	—	2	8	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	8	8	no	—
234	D₄×C₁₃	—	8	8	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	8	4	no	—
244	C₂×C₄×C₁₃	—	8	2	no	—
245	C₂×C₄×C₁₃	—	8	8	no	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	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	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
253	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
255	C₈×C₁₃	—	2	4	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	C₂×#41	1	2	yes	—
259	C₈×C₁₃	C₂×#41	1	2	yes	—
260	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#131	C₂²×C₁₃	1	2	yes	—
262	#559	—	2	4	no	—
263	#556	—	2	2	no	—
264	#555	C₂²×C₁₃	1	4	yes	complemented
265	#553	C₂²×C₁₃	1	8	yes	complemented
266	#550	—	2	2	no	—
267	#547	C₂²×C₁₃	1	4	yes	complemented
268	#538	—	2	4	no	—
269	#535	C₂²×C₁₃	1	4	yes	—
270	#533	C₂²×C₁₃	1	2	yes	—
271	#532	C₂²×C₁₃	1	1	yes	characteristic
272	#525	—	2	4	no	—
273	#520	C₂²×C₁₃	1	4	yes	—
274	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
275	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	#499	C₂²×C₁₃	1	2	yes	complemented
278	#499	C₂²×C₁₃	1	2	yes	complemented
279	#498	C₂²×C₁₃	1	2	yes	complemented
280	#482	C₂²×C₁₃	1	8	yes	complemented
281	#482	C₂²×C₁₃	1	8	yes	complemented
282	#481	C₂²×C₁₃	1	8	yes	complemented
283	#480	C₂²×C₁₃	1	8	yes	complemented
284	#478	C₂²×C₁₃	1	8	yes	complemented
285	#476	C₂²×C₁₃	1	4	yes	complemented
286	#474	C₂²×C₁₃	1	4	yes	complemented
287	#469	C₂²×C₁₃	1	8	yes	—
288	#466	C₂²×C₁₃	1	4	yes	—
289	#466	C₂²×C₁₃	1	4	yes	—
290	C₄×D₈	C₂²×C₁₃	1	2	yes	—
291	C₄×D₈	C₂²×C₁₃	1	2	yes	—
292	C₄×D₈	C₂²×C₁₃	1	2	yes	—
293	C₄×D₈	C₂²×C₁₃	1	2	yes	—
294	#436	C₂²×C₁₃	1	2	yes	complemented
295	#436	C₂²×C₁₃	1	2	yes	complemented
296	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
297	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
298	#428	C₂²×C₁₃	1	4	yes	—
299	#428	C₂²×C₁₃	1	8	yes	complemented
300	#427	C₂²×C₁₃	1	2	yes	—
301	#427	C₂²×C₁₃	1	2	yes	—
302	#427	C₂²×C₁₃	1	4	yes	complemented
303	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#107	C₂²×C₁₃	1	4	yes	complemented
305	#423	C₂²×C₁₃	1	1	yes	characteristic
306	#418	C₂²×C₁₃	1	4	yes	—
307	C₂×#102	C₂²×C₁₃	1	2	yes	—
308	#408	C₂²×C₁₃	1	2	yes	—
309	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	4	no	—
313	C₂²×C₁₃	—	2	4	no	—
314	C₂²×C₁₃	—	2	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	8	8	no	—
319	C₂²×C₁₃	#547	1	2	yes	—
320	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	4	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	—	4	4	no	—
328	C₄×C₁₃	#547	1	2	yes	—
329	C₄×C₁₃	#576	1	2	yes	—
330	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
331	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
332	C₂×#41	—	2	4	no	—
333	C₂×#41	C₂³×C₁₃	1	2	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
335	C₂³×C₄	—	2	2	no	—
336	C₂×D₈	—	2	4	no	—
337	C₂×D₈	C₂³×C₁₃	1	2	yes	—
338	C₂×D₈	C₂³×C₁₃	1	2	yes	—
339	#131	—	2	8	no	—
340	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
341	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
342	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
343	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
347	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
348	#127	—	2	4	no	—
349	#127	D₄×C₁₃	1	1	yes	characteristic
350	#126	—	2	8	no	—
351	#125	C₂³×C₁₃	1	4	yes	—
352	#124	—	2	4	no	—
353	#124	—	2	8	no	—
354	#124	D₄×C₁₃	1	2	yes	—
355	#123	—	2	8	no	—
356	#123	—	2	8	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	#121	—	2	4	no	—
361	#121	—	2	8	no	—
362	#121	D₄×C₁₃	1	2	yes	—
363	#121	D₄×C₁₃	1	2	yes	—
364	#121	C₂³×C₁₃	1	8	yes	—
365	#121	C₂³×C₁₃	1	8	yes	—
366	#120	—	2	8	no	—
367	C₄×Q₈	—	2	4	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×D₄	—	2	8	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	8	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	C₂³×C₁₃	1	4	yes	—
376	C₄×D₄	C₂³×C₁₃	1	4	yes	—
377	C₄×D₄	C₂³×C₁₃	1	2	yes	—
378	C₄×D₄	C₂³×C₁₃	1	2	yes	—
379	#117	—	2	4	no	—
380	#117	C₂³×C₁₃	1	4	yes	—
381	#117	C₂³×C₁₃	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	#107	C₂³×C₁₃	1	2	yes	—
387	#107	C₂³×C₁₃	1	2	yes	—
388	#107	C₂³×C₁₃	1	2	yes	—
389	#107	C₂³×C₁₃	1	8	yes	—
390	#107	C₂³×C₁₃	1	2	yes	—
391	#107	C₂³×C₁₃	1	2	yes	—
392	#107	C₂³×C₁₃	1	2	yes	—
393	#106	C₂³×C₁₃	1	4	yes	—
394	#106	C₂³×C₁₃	1	4	yes	—
395	#106	C₂³×C₁₃	1	8	yes	—
396	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
397	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
398	#102	C₂³×C₁₃	1	4	yes	—
399	#102	C₂³×C₁₃	1	4	yes	—
400	#102	C₂³×C₁₃	1	8	yes	—
401	#102	C₂³×C₁₃	1	8	yes	—
402	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
403	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
404	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₁₃	—	2	2	no	—
409	C₂×C₁₃	—	4	4	no	—
410	C₂×C₁₃	—	8	4	no	—
411	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
413	C₂×C₁₃	#3584	1	1	yes	characteristic
414	C₂⁴	—	2	2	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	#41	—	8	8	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	8	4	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	D₈	—	2	4	no	—
441	D₈	—	2	4	no	—
442	M₁₆	—	2	4	no	—
443	M₁₆	—	2	8	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	8	no	—
446	C₂×C₈	C₁₃×#41	1	4	yes	complemented
447	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
448	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
450	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
470	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
471	C₄²	—	2	8	no	—
472	C₄²	—	2	4	no	—
473	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
476	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
477	C₁₃	#61284	1	1	yes	characteristic, direct product factor, Sylow
478	C₂³	—	2	4	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	2	no	—
482	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
483	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	Q₈	—	2	4	no	—
485	Q₈	—	4	4	no	—
486	Q₈	—	8	2	no	—
487	D₄	—	2	8	no	—
488	D₄	—	2	4	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	4	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	4	no	—
494	D₄	—	8	8	no	—
495	D₄	—	8	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	8	4	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	8	no	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
513	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
514	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
515	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
516	C₈	—	2	4	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	C₂×C₁₃×#41	1	2	yes	—
520	C₈	C₂×C₁₃×#41	1	2	yes	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	8	no	—
530	C₂²	C₁₃×#547	1	2	yes	—
531	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	4	no	—
539	C₄	C₁₃×#547	1	2	yes	—
540	C₄	C₁₃×#576	1	2	yes	—
541	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
542	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
543	C₂	—	2	2	no	—
544	C₂	—	4	4	no	—
545	C₂	—	8	4	no	—
546	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
547	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
548	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₁₃×#3355	C₂	semidirect
3. C₁₃×#3354	C₂	semidirect
4. C₁₃×#3341	C₂	semidirect
5. C₁₃×#3339	C₂	semidirect
6. C₁₃×#3334	C₂	semidirect
7. C₁₃×#3160	C₂	semidirect
8. C₁₃×#3096	C₂	semidirect
9. C₁₃×#3077	C₂	semidirect
10. C₁₃×#3058	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
12. C₁₃×#2931	C₂	semidirect
13. C₁₃×#2913	C₂	semidirect
18. C₁₃×#555	C₂²	semidirect
19. C₁₃×#553	C₂²	semidirect
21. C₁₃×#547	C₂²	semidirect
29. C₁₃×#500	C₂²	semidirect
30. C₁₃×#500	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#499	C₂²	semidirect
33. C₁₃×#498	C₂²	semidirect
34. C₁₃×#482	C₂²	semidirect
35. C₁₃×#482	C₂²	semidirect
36. C₁₃×#481	C₂²	semidirect
37. C₁₃×#480	C₂²	semidirect
38. C₁₃×#478	C₂²	semidirect
39. C₁₃×#476	C₂²	semidirect
40. C₁₃×#474	C₂²	semidirect
48. C₁₃×#436	C₂²	semidirect
49. C₁₃×#436	C₂²	semidirect
50. C₈×D₄×C₁₃	C₂²	semidirect
51. C₈×D₄×C₁₃	C₂²	semidirect
53. C₁₃×#428	C₂²	semidirect
56. C₁₃×#427	C₂²	semidirect
58. C₂×C₁₃×#107	C₂²	semidirect
140. #61284	C₁₃	direct (N × H)
173. C₂×C₈×C₁₃	#41	semidirect
204. #3506	C₂×C₁₃	semidirect
205. #3355	C₂×C₁₃	semidirect
206. #3354	C₂×C₁₃	semidirect
207. #3341	C₂×C₁₃	semidirect
208. #3339	C₂×C₁₃	semidirect
209. #3334	C₂×C₁₃	semidirect
210. #3160	C₂×C₁₃	semidirect
211. #3096	C₂×C₁₃	semidirect
212. #3077	C₂×C₁₃	semidirect
213. #3058	C₂×C₁₃	semidirect
214. C₂×C₄×D₈	C₂×C₁₃	semidirect
215. #2931	C₂×C₁₃	semidirect
216. #2913	C₂×C₁₃	semidirect
264. #555	C₂²×C₁₃	semidirect
265. #553	C₂²×C₁₃	semidirect
267. #547	C₂²×C₁₃	semidirect
275. #500	C₂²×C₁₃	semidirect
276. #500	C₂²×C₁₃	semidirect
277. #499	C₂²×C₁₃	semidirect
278. #499	C₂²×C₁₃	semidirect
279. #498	C₂²×C₁₃	semidirect
280. #482	C₂²×C₁₃	semidirect
281. #482	C₂²×C₁₃	semidirect
282. #481	C₂²×C₁₃	semidirect
283. #480	C₂²×C₁₃	semidirect
284. #478	C₂²×C₁₃	semidirect
285. #476	C₂²×C₁₃	semidirect
286. #474	C₂²×C₁₃	semidirect
294. #436	C₂²×C₁₃	semidirect
295. #436	C₂²×C₁₃	semidirect
296. C₈×D₄	C₂²×C₁₃	semidirect
297. C₈×D₄	C₂²×C₁₃	semidirect
299. #428	C₂²×C₁₃	semidirect
302. #427	C₂²×C₁₃	semidirect
304. C₂×#107	C₂²×C₁₃	semidirect
446. C₂×C₈	C₁₃×#41	semidirect
477. C₁₃	#61284	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×#3506	2
C₁₃×#3355	2
C₁₃×#3354	2
C₁₃×#3341	2
C₁₃×#3339	2
C₁₃×#3334	2
C₁₃×#3160	2
C₁₃×#3096	2
C₁₃×#3077	2
C₁₃×#3058	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2931	2
C₁₃×#2913	2
#61284	13

Subgroups — C13×#61284 #15747623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61284 #15747623