Subgroups — C₁₃×#62095 #15748434

Order 3328.

2238 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3334	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3294	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3245	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3226	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3100	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#474	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₁₃×#550	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₁₃	—	2	1	no	—
16	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
18	C₁₃×#548	—	2	1	no	—
19	C₁₃×#547	—	2	3	no	—
20	C₁₃×#547	C₂²	1	3	yes	—
21	C₁₃×#547	C₂²	1	6	yes	complemented
22	C₁₃×#546	—	2	3	no	—
23	D₄²×C₁₃	C₂²	1	3	yes	—
24	C₁₃×#536	—	2	3	no	—
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₁₃×#532	C₂²	1	3	yes	complemented
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
28	C₁₃×#525	—	2	3	no	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
31	C₁₃×#500	C₂²	1	6	yes	complemented
32	C₁₃×#486	C₂²	1	6	yes	complemented
33	C₁₃×#480	C₂²	1	12	yes	complemented
34	C₁₃×#480	C₂²	1	6	yes	complemented
35	C₁₃×#474	C₂²	1	6	yes	—
36	C₁₃×#474	C₂²	1	3	yes	—
37	C₁₃×#474	C₂²	1	6	yes	complemented
38	C₁₃×#474	C₂²	1	6	yes	complemented
39	C₁₃×#474	C₂²	1	6	yes	complemented
40	C₁₃×#474	C₂²	1	3	yes	complemented
41	C₁₃×#466	C₂²	1	12	yes	complemented
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	6	yes	complemented
44	C₁₃×#459	C₂²	1	3	yes	complemented
45	C₁₃×#447	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
47	C₄×C₁₃×D₈	C₂²	1	6	yes	—
48	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
49	C₈×D₄×C₁₃	C₂²	1	6	yes	complemented
50	C₁₃×#431	C₂²	1	3	yes	complemented
51	C₂×C₁₃×#107	C₂²	1	6	yes	complemented
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	complemented
53	C₂×C₁₃×#102	C₂²	1	6	yes	—
54	C₁₃×2₋¹⁺⁴	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	—	2	6	no	—
58	C₂×C₁₃×#41	—	2	3	no	—
59	C₂×C₁₃×#41	—	2	3	no	—
60	C₂×C₁₃×#41	—	4	8	no	—
61	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	—	2	1	no	—
63	C₂²×Q₈×C₁₃	—	2	2	no	—
64	C₂²×Q₈×C₁₃	—	2	3	no	—
65	C₂²×D₄×C₁₃	—	2	3	no	—
66	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
67	C₂³×C₄×C₁₃	—	2	3	no	—
68	C₂×C₁₃×D₈	C₂³	1	2	yes	—
69	C₂×C₁₃×D₈	C₂³	1	6	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
71	C₁₃×C₄⋊Q₈	—	2	3	no	—
72	C₁₃×C₄⋊Q₈	—	2	3	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
76	C₁₃×#127	C₂³	1	1	yes	characteristic
77	C₁₃×#127	C₂³	1	3	yes	—
78	C₁₃×#124	—	2	3	no	—
79	C₁₃×#124	—	2	3	no	—
80	C₁₃×#123	—	2	6	no	—
81	C₁₃×#123	—	2	12	no	—
82	C₁₃×C₂²⋊Q₈	—	2	3	no	—
83	C₁₃×C₂²⋊Q₈	—	2	3	no	—
84	C₁₃×C₂²⋊Q₈	—	2	6	no	—
85	C₁₃×C₂²⋊Q₈	—	2	6	no	—
86	C₁₃×#121	—	2	3	no	—
87	C₁₃×#121	—	2	3	no	—
88	C₁₃×#121	—	2	3	no	—
89	C₁₃×#121	—	2	3	no	—
90	C₁₃×#121	C₂³	1	6	yes	—
91	C₁₃×#121	C₂³	1	6	yes	—
92	C₁₃×#120	—	2	6	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	—	2	3	no	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	D₄	1	3	yes	—
100	C₄×D₄×C₁₃	C₂³	1	3	yes	—
101	C₄×D₄×C₁₃	C₂³	1	6	yes	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₄×D₄×C₁₃	C₂³	1	3	yes	—
106	C₁₃×#117	D₄	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
111	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
112	C₁₃×#107	C₂³	1	6	yes	—
113	C₁₃×#107	C₂³	1	12	yes	—
114	C₁₃×#107	C₂³	1	6	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#102	C₂³	1	6	yes	—
119	C₁₃×#102	C₂³	1	12	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	2	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
124	C₄×C₈×C₁₃	C₂³	1	6	yes	—
125	#62095	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	3	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	12	no	—
129	C₁₃×#41	—	4	24	no	—
130	C₁₃×#41	—	4	12	no	—
131	C₁₃×#41	—	4	12	no	—
132	C₁₃×#41	D₈	1	8	yes	complemented
133	C₂×Q₈×C₁₃	—	2	3	no	—
134	C₂×Q₈×C₁₃	—	2	6	no	—
135	C₂×Q₈×C₁₃	—	2	3	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	—	4	12	no	—
139	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	6	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	3	no	—
145	C₂×D₄×C₁₃	—	2	3	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	3	no	—
148	C₂×D₄×C₁₃	—	4	3	no	—
149	C₂×D₄×C₁₃	—	4	12	no	—
150	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	3	no	—
155	C₂²×C₄×C₁₃	—	2	6	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	3	no	—
158	C₂²×C₄×C₁₃	—	2	3	no	—
159	C₂²×C₄×C₁₃	—	2	3	no	—
160	C₂²×C₄×C₁₃	—	2	6	no	—
161	C₂²×C₄×C₁₃	—	4	12	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
165	C₁₃×D₈	—	2	4	no	—
166	C₁₃×D₈	—	4	6	no	—
167	C₂×C₈×C₁₃	—	4	6	no	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
170	C₁₃×C₄⋊C₄	—	2	3	no	—
171	C₁₃×C₄⋊C₄	—	2	6	no	—
172	C₁₃×C₄⋊C₄	—	2	3	no	—
173	C₁₃×C₄⋊C₄	—	2	6	no	—
174	C₁₃×C₄⋊C₄	—	2	3	no	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	3	no	—
182	C₁₃×C₂²⋊C₄	—	2	3	no	—
183	C₁₃×C₂²⋊C₄	—	2	3	no	—
184	C₁₃×C₂²⋊C₄	—	2	6	no	—
185	C₁₃×C₂²⋊C₄	—	2	6	no	—
186	C₁₃×C₂²⋊C₄	—	2	6	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
188	C₄²×C₁₃	C₂×D₄	1	3	yes	—
189	C₄²×C₁₃	C₂×D₄	1	3	yes	—
190	C₄²×C₁₃	C₂⁴	1	3	yes	—
191	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
192	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
193	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
194	Q₈×D₈	C₂×C₁₃	1	2	yes	complemented
195	#3358	C₂×C₁₃	1	2	yes	complemented
196	#3334	C₂×C₁₃	1	6	yes	complemented
197	#3294	C₂×C₁₃	1	6	yes	complemented
198	#3245	C₂×C₁₃	1	3	yes	complemented
199	#3226	C₂×C₁₃	1	3	yes	complemented
200	#3100	C₂×C₁₃	1	3	yes	complemented
201	C₂×#474	C₂×C₁₃	1	3	yes	complemented
202	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	3	no	—
206	C₂³×C₁₃	—	4	6	no	—
207	C₂³×C₁₃	—	4	6	no	—
208	C₂³×C₁₃	—	8	3	no	—
209	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
210	Q₈×C₁₃	—	4	6	no	—
211	Q₈×C₁₃	—	4	12	no	—
212	Q₈×C₁₃	—	4	6	no	—
213	Q₈×C₁₃	C₂×D₈	1	4	yes	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	2	3	no	—
216	D₄×C₁₃	—	2	1	no	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	2	3	no	—
219	D₄×C₁₃	—	4	6	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	12	no	—
222	D₄×C₁₃	—	4	12	no	—
223	D₄×C₁₃	—	4	6	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	8	3	no	—
226	D₄×C₁₃	C₂×D₈	1	12	yes	—
227	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
228	C₂×C₄×C₁₃	—	2	3	no	—
229	C₂×C₄×C₁₃	—	2	3	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	3	no	—
232	C₂×C₄×C₁₃	—	2	6	no	—
233	C₂×C₄×C₁₃	—	4	3	no	—
234	C₂×C₄×C₁₃	—	4	6	no	—
235	C₂×C₄×C₁₃	—	4	12	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	6	no	—
238	C₂×C₄×C₁₃	—	4	6	no	—
239	C₂×C₄×C₁₃	—	4	6	no	—
240	C₂×C₄×C₁₃	—	4	12	no	—
241	C₂×C₄×C₁₃	C₂×D₈	1	12	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
248	C₈×C₁₃	—	2	2	no	—
249	C₈×C₁₃	—	2	6	no	—
250	C₂×2₋¹⁺⁴	—	2	1	no	—
251	C₂²×#41	—	2	1	no	—
252	#550	C₂²×C₁₃	1	1	yes	characteristic
253	D₄×Q₈	—	2	1	no	—
254	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
256	#548	—	2	1	no	—
257	#547	—	2	3	no	—
258	#547	C₂²×C₁₃	1	3	yes	—
259	#547	C₂²×C₁₃	1	6	yes	complemented
260	#546	—	2	3	no	—
261	D₄²	C₂²×C₁₃	1	3	yes	—
262	#536	—	2	3	no	—
263	#532	C₂²×C₁₃	1	3	yes	—
264	#532	C₂²×C₁₃	1	3	yes	complemented
265	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
266	#525	—	2	3	no	—
267	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
269	#500	C₂²×C₁₃	1	6	yes	complemented
270	#486	C₂²×C₁₃	1	6	yes	complemented
271	#480	C₂²×C₁₃	1	6	yes	complemented
272	#480	C₂²×C₁₃	1	12	yes	complemented
273	#474	C₂²×C₁₃	1	3	yes	—
274	#474	C₂²×C₁₃	1	6	yes	—
275	#474	C₂²×C₁₃	1	6	yes	complemented
276	#474	C₂²×C₁₃	1	6	yes	complemented
277	#474	C₂²×C₁₃	1	3	yes	complemented
278	#474	C₂²×C₁₃	1	6	yes	complemented
279	#466	C₂²×C₁₃	1	12	yes	complemented
280	#459	C₂²×C₁₃	1	1	yes	characteristic
281	#459	C₂²×C₁₃	1	3	yes	complemented
282	#459	C₂²×C₁₃	1	6	yes	complemented
283	#447	C₂²×C₁₃	1	6	yes	—
284	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
285	C₄×D₈	C₂²×C₁₃	1	6	yes	—
286	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
287	C₈×D₄	C₂²×C₁₃	1	6	yes	complemented
288	#431	C₂²×C₁₃	1	3	yes	complemented
289	C₂×#107	C₂²×C₁₃	1	6	yes	complemented
290	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	complemented
291	C₂×#102	C₂²×C₁₃	1	6	yes	—
292	C₂²×C₁₃	—	2	3	no	—
293	C₂²×C₁₃	—	2	3	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	4	1	no	—
296	C₂²×C₁₃	—	4	1	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	3	no	—
299	C₂²×C₁₃	—	4	3	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	3	no	—
303	C₂²×C₁₃	—	8	12	no	—
304	C₂²×C₁₃	C₂²×D₈	1	6	yes	—
305	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	3	no	—
308	C₄×C₁₃	—	2	3	no	—
309	C₄×C₁₃	—	4	1	no	—
310	C₄×C₁₃	—	4	3	no	—
311	C₄×C₁₃	—	4	6	no	—
312	C₄×C₁₃	C₂²×D₈	1	2	yes	—
313	C₄×C₁₃	C₂²×D₈	1	6	yes	—
314	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₄×C₁₃	#585	1	1	yes	characteristic
316	2₋¹⁺⁴	—	4	8	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	3	no	—
319	C₂×#41	—	2	6	no	—
320	C₂×#41	—	2	3	no	—
321	C₂×#41	—	2	3	no	—
322	C₂×#41	—	4	8	no	—
323	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	3	no	—
327	C₂²×D₄	—	2	3	no	—
328	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
329	C₂³×C₄	—	2	3	no	—
330	C₂×D₈	C₂³×C₁₃	1	2	yes	—
331	C₂×D₈	C₂³×C₁₃	1	6	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
333	C₄⋊Q₈	—	2	3	no	—
334	C₄⋊Q₈	—	2	3	no	—
335	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
336	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
337	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
338	#127	C₂³×C₁₃	1	3	yes	—
339	#127	C₂³×C₁₃	1	1	yes	characteristic
340	#124	—	2	3	no	—
341	#124	—	2	3	no	—
342	#123	—	2	6	no	—
343	#123	—	2	12	no	—
344	C₂²⋊Q₈	—	2	3	no	—
345	C₂²⋊Q₈	—	2	3	no	—
346	C₂²⋊Q₈	—	2	6	no	—
347	C₂²⋊Q₈	—	2	6	no	—
348	#121	—	2	3	no	—
349	#121	—	2	3	no	—
350	#121	—	2	3	no	—
351	#121	—	2	3	no	—
352	#121	C₂³×C₁₃	1	6	yes	—
353	#121	C₂³×C₁₃	1	6	yes	—
354	#120	—	2	6	no	—
355	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
356	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₄×D₄	—	2	3	no	—
358	C₄×D₄	—	2	3	no	—
359	C₄×D₄	—	2	3	no	—
360	C₄×D₄	—	2	3	no	—
361	C₄×D₄	D₄×C₁₃	1	3	yes	—
362	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₄×D₄	C₂³×C₁₃	1	3	yes	—
364	C₄×D₄	C₂³×C₁₃	1	3	yes	—
365	C₄×D₄	C₂³×C₁₃	1	3	yes	—
366	C₄×D₄	C₂³×C₁₃	1	6	yes	—
367	C₄×D₄	C₂³×C₁₃	1	3	yes	—
368	#117	D₄×C₁₃	1	3	yes	—
369	C₂×C₄⋊C₄	—	2	3	no	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
372	C₂×C₂²⋊C₄	—	2	3	no	—
373	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
374	#107	C₂³×C₁₃	1	6	yes	—
375	#107	C₂³×C₁₃	1	12	yes	—
376	#107	C₂³×C₁₃	1	6	yes	—
377	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
378	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
380	#102	C₂³×C₁₃	1	6	yes	—
381	#102	C₂³×C₁₃	1	12	yes	—
382	#102	C₂³×C₁₃	1	6	yes	—
383	#102	C₂³×C₁₃	1	2	yes	—
384	#102	C₂³×C₁₃	1	6	yes	—
385	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
386	C₄×C₈	C₂³×C₁₃	1	6	yes	—
387	C₂×C₁₃	—	2	6	no	—
388	C₂×C₁₃	—	4	2	no	—
389	C₂×C₁₃	—	8	2	no	—
390	C₂×C₁₃	—	8	3	no	—
391	C₂×C₁₃	#3489	1	1	yes	characteristic
392	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
393	C₂×C₁₃	#3586	1	1	yes	characteristic
394	C₂⁴	—	2	3	no	—
395	#41	—	4	4	no	—
396	#41	—	4	12	no	—
397	#41	—	4	24	no	—
398	#41	—	4	12	no	—
399	#41	—	4	12	no	—
400	#41	C₁₃×D₈	1	8	yes	complemented
401	C₂×Q₈	—	2	3	no	—
402	C₂×Q₈	—	2	6	no	—
403	C₂×Q₈	—	2	3	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	—	4	12	no	—
407	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂×D₄	—	2	6	no	—
409	C₂×D₄	—	2	6	no	—
410	C₂×D₄	—	2	6	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	3	no	—
413	C₂×D₄	—	2	3	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	3	no	—
416	C₂×D₄	—	4	3	no	—
417	C₂×D₄	—	4	12	no	—
418	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
420	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
421	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	—	2	3	no	—
423	C₂²×C₄	—	2	6	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	3	no	—
426	C₂²×C₄	—	2	3	no	—
427	C₂²×C₄	—	2	3	no	—
428	C₂²×C₄	—	2	6	no	—
429	C₂²×C₄	—	4	12	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
433	D₈	—	2	4	no	—
434	D₈	—	4	6	no	—
435	C₂×C₈	—	4	6	no	—
436	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
437	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
438	C₄⋊C₄	—	2	3	no	—
439	C₄⋊C₄	—	2	6	no	—
440	C₄⋊C₄	—	2	3	no	—
441	C₄⋊C₄	—	2	6	no	—
442	C₄⋊C₄	—	2	3	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
445	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	2	3	no	—
450	C₂²⋊C₄	—	2	3	no	—
451	C₂²⋊C₄	—	2	3	no	—
452	C₂²⋊C₄	—	2	6	no	—
453	C₂²⋊C₄	—	2	6	no	—
454	C₂²⋊C₄	—	2	6	no	—
455	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
456	C₄²	C₂×D₄×C₁₃	1	3	yes	—
457	C₄²	C₂×D₄×C₁₃	1	3	yes	—
458	C₄²	C₂⁴×C₁₃	1	3	yes	—
459	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₁₃	#62095	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	3	no	—
464	C₂³	—	4	6	no	—
465	C₂³	—	4	6	no	—
466	C₂³	—	8	3	no	—
467	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
468	Q₈	—	4	6	no	—
469	Q₈	—	4	12	no	—
470	Q₈	—	4	6	no	—
471	Q₈	C₂×C₁₃×D₈	1	4	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	3	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	3	no	—
477	D₄	—	4	6	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	12	no	—
480	D₄	—	4	12	no	—
481	D₄	—	4	6	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	3	no	—
484	D₄	C₂×C₁₃×D₈	1	12	yes	—
485	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
486	C₂×C₄	—	2	3	no	—
487	C₂×C₄	—	2	3	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	3	no	—
490	C₂×C₄	—	2	6	no	—
491	C₂×C₄	—	4	3	no	—
492	C₂×C₄	—	4	6	no	—
493	C₂×C₄	—	4	12	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	6	no	—
496	C₂×C₄	—	4	6	no	—
497	C₂×C₄	—	4	6	no	—
498	C₂×C₄	—	4	12	no	—
499	C₂×C₄	C₂×C₁₃×D₈	1	12	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
505	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	6	no	—
508	C₂²	—	2	3	no	—
509	C₂²	—	2	3	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	3	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	3	no	—
517	C₂²	—	4	3	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	12	no	—
520	C₂²	C₂²×C₁₃×D₈	1	6	yes	—
521	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	3	no	—
524	C₄	—	2	3	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	3	no	—
527	C₄	—	4	6	no	—
528	C₄	C₂²×C₁₃×D₈	1	2	yes	—
529	C₄	C₂²×C₁₃×D₈	1	6	yes	—
530	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
531	C₄	C₁₃×#585	1	1	yes	characteristic
532	C₂	—	2	6	no	—
533	C₂	—	4	2	no	—
534	C₂	—	8	3	no	—
535	C₂	—	8	2	no	—
536	C₂	C₁₃×#3489	1	1	yes	characteristic
537	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
538	C₂	C₁₃×#3586	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3499	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. Q₈×C₁₃×D₈	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3334	C₂	semidirect
6. C₁₃×#3294	C₂	semidirect
7. C₁₃×#3245	C₂	semidirect
8. C₁₃×#3226	C₂	semidirect
9. C₁₃×#3100	C₂	semidirect
10. C₂×C₁₃×#474	C₂	semidirect
11. C₁₃×#2988	C₂	semidirect
17. D₄×Q₈×C₁₃	C₂²	semidirect
21. C₁₃×#547	C₂²	semidirect
26. C₁₃×#532	C₂²	semidirect
27. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×#500	C₂²	semidirect
32. C₁₃×#486	C₂²	semidirect
33. C₁₃×#480	C₂²	semidirect
34. C₁₃×#480	C₂²	semidirect
37. C₁₃×#474	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#474	C₂²	semidirect
40. C₁₃×#474	C₂²	semidirect
41. C₁₃×#466	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
48. C₄×C₁₃×D₈	C₂²	semidirect
49. C₈×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#431	C₂²	semidirect
51. C₂×C₁₃×#107	C₂²	semidirect
52. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
125. #62095	C₁₃	direct (N × H)
132. C₁₃×#41	D₈	semidirect
192. #3499	C₂×C₁₃	semidirect
193. D₄×#41	C₂×C₁₃	semidirect
194. Q₈×D₈	C₂×C₁₃	semidirect
195. #3358	C₂×C₁₃	semidirect
196. #3334	C₂×C₁₃	semidirect
197. #3294	C₂×C₁₃	semidirect
198. #3245	C₂×C₁₃	semidirect
199. #3226	C₂×C₁₃	semidirect
200. #3100	C₂×C₁₃	semidirect
201. C₂×#474	C₂×C₁₃	semidirect
202. #2988	C₂×C₁₃	semidirect
227. D₄×C₁₃	2₋¹⁺⁴	semidirect
255. D₄×Q₈	C₂²×C₁₃	semidirect
259. #547	C₂²×C₁₃	semidirect
264. #532	C₂²×C₁₃	semidirect
265. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
269. #500	C₂²×C₁₃	semidirect
270. #486	C₂²×C₁₃	semidirect
271. #480	C₂²×C₁₃	semidirect
272. #480	C₂²×C₁₃	semidirect
275. #474	C₂²×C₁₃	semidirect
276. #474	C₂²×C₁₃	semidirect
277. #474	C₂²×C₁₃	semidirect
278. #474	C₂²×C₁₃	semidirect
279. #466	C₂²×C₁₃	semidirect
281. #459	C₂²×C₁₃	semidirect
282. #459	C₂²×C₁₃	semidirect
284. C₈×Q₈	C₂²×C₁₃	semidirect
286. C₄×D₈	C₂²×C₁₃	semidirect
287. C₈×D₄	C₂²×C₁₃	semidirect
288. #431	C₂²×C₁₃	semidirect
289. C₂×#107	C₂²×C₁₃	semidirect
290. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
400. #41	C₁₃×D₈	semidirect
460. C₁₃	#62095	direct (N × H)
485. D₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3499	2
D₄×C₁₃×#41	2
Q₈×C₁₃×D₈	2
C₁₃×#3358	2
C₁₃×#3334	2
C₁₃×#3294	2
C₁₃×#3245	2
C₁₃×#3226	2
C₁₃×#3100	2
C₂×C₁₃×#474	2
C₁₃×#2988	2
#62095	13

Subgroups — C13×#62095 #15748434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62095 #15748434