Subgroups — C₁₃×#61947 #15748286

Order 3328.

2458 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3294	C₂	1	6	yes	maximal, complemented
6	D₄×C₁₃×D₈	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3245	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3205	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3100	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#459	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×D₈	C₂²	1	6	yes	complemented
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	C₂²	1	2	yes	complemented
17	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#548	—	2	1	no	—
20	C₁₃×#547	C₂²	1	3	yes	complemented
21	C₁₃×#546	—	2	3	no	—
22	D₄²×C₁₃	—	2	3	no	—
23	D₄²×C₁₃	C₂²	1	3	yes	complemented
24	D₄²×C₁₃	C₂²	1	6	yes	complemented
25	C₁₃×#535	—	2	3	no	—
26	C₁₃×#532	C₂²	1	3	yes	complemented
27	C₁₃×#532	C₂²	1	3	yes	complemented
28	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
29	C₁₃×#525	—	2	3	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
32	C₁₃×#493	C₂²	1	6	yes	complemented
33	C₁₃×#486	C₂²	1	6	yes	complemented
34	C₁₃×#480	C₂²	1	6	yes	complemented
35	C₁₃×#474	C₂²	1	6	yes	complemented
36	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#474	C₂²	1	3	yes	complemented
38	C₁₃×#466	C₂²	1	12	yes	complemented
39	C₁₃×#459	C₂²	1	6	yes	complemented
40	C₁₃×#459	C₂²	1	6	yes	complemented
41	C₁₃×#459	C₂²	1	3	yes	complemented
42	C₁₃×#459	C₂²	1	6	yes	complemented
43	C₁₃×#459	C₂²	1	6	yes	complemented
44	C₁₃×#459	C₂²	1	3	yes	complemented
45	C₁₃×#447	C₂²	1	6	yes	complemented
46	C₁₃×#447	C₂²	1	12	yes	complemented
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
48	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
49	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
50	C₈×D₄×C₁₃	C₂²	1	6	yes	complemented
51	C₁₃×#431	C₂²	1	3	yes	complemented
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	complemented
53	C₂×C₁₃×#102	C₂²	1	6	yes	complemented
54	C₁₃×H(5,𝔽₂)	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	—	2	2	no	—
57	C₂×C₁₃×#41	—	2	3	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×D₄×C₁₃	—	2	6	no	—
64	C₂²×D₄×C₁₃	—	2	3	no	—
65	C₂²×D₄×C₁₃	—	2	3	no	—
66	C₂²×D₄×C₁₃	—	2	3	no	—
67	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
69	C₂³×C₄×C₁₃	—	2	3	no	—
70	C₂×C₁₃×D₈	—	4	12	no	—
71	C₂×C₁₃×D₈	C₂³	1	6	yes	—
72	C₂×C₁₃×D₈	C₂³	1	6	yes	—
73	C₂×C₁₃×D₈	C₂³	1	12	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
77	C₁₃×#127	—	2	3	no	—
78	C₁₃×#127	—	2	3	no	—
79	C₁₃×#127	C₂³	1	3	yes	—
80	C₁₃×#127	C₂³	1	6	yes	—
81	C₁₃×#127	C₂³	1	3	yes	—
82	C₁₃×#124	—	2	3	no	—
83	C₁₃×#124	—	2	3	no	—
84	C₁₃×#123	—	2	6	no	—
85	C₁₃×C₂²⋊Q₈	—	2	3	no	—
86	C₁₃×C₂²⋊Q₈	—	2	3	no	—
87	C₁₃×#121	—	2	3	no	—
88	C₁₃×#121	—	2	3	no	—
89	C₁₃×#121	—	2	3	no	—
90	C₁₃×#121	—	2	3	no	—
91	C₁₃×#121	—	2	6	no	—
92	C₁₃×#121	—	2	6	no	—
93	C₁₃×#121	C₂³	1	6	yes	—
94	C₁₃×#121	C₂³	1	6	yes	—
95	C₁₃×#120	—	2	6	no	—
96	C₁₃×#120	—	2	12	no	—
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	—	2	3	no	—
102	C₄×D₄×C₁₃	—	2	3	no	—
103	C₄×D₄×C₁₃	D₄	1	3	yes	—
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₄×D₄×C₁₃	C₂³	1	3	yes	—
106	C₄×D₄×C₁₃	C₂³	1	6	yes	—
107	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×D₄×C₁₃	C₂³	1	3	yes	—
109	C₄×D₄×C₁₃	C₂³	1	3	yes	—
110	C₁₃×#117	D₄	1	3	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
113	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
114	C₁₃×#107	C₂³	1	2	yes	—
115	C₁₃×#107	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	12	yes	—
121	C₁₃×#102	C₂³	1	2	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×#102	C₂³	1	6	yes	—
124	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
125	C₄×C₈×C₁₃	C₂³	1	6	yes	—
126	#61947	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	3	no	—
128	C₂⁴×C₁₃	—	2	6	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₁₃×#41	—	4	8	no	—
131	C₁₃×#41	—	4	12	no	—
132	C₁₃×#41	—	4	12	no	—
133	C₁₃×#41	—	4	12	no	—
134	C₁₃×#41	D₈	1	8	yes	complemented
135	C₂×Q₈×C₁₃	—	2	3	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	4	4	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	2	3	no	—
144	C₂×D₄×C₁₃	—	2	3	no	—
145	C₂×D₄×C₁₃	—	2	6	no	—
146	C₂×D₄×C₁₃	—	2	3	no	—
147	C₂×D₄×C₁₃	—	2	3	no	—
148	C₂×D₄×C₁₃	—	2	6	no	—
149	C₂×D₄×C₁₃	—	2	6	no	—
150	C₂×D₄×C₁₃	—	4	3	no	—
151	C₂×D₄×C₁₃	—	4	6	no	—
152	C₂×D₄×C₁₃	—	4	6	no	—
153	C₂×D₄×C₁₃	—	4	12	no	—
154	C₂×D₄×C₁₃	—	4	24	no	—
155	C₂×D₄×C₁₃	—	4	12	no	—
156	C₂×D₄×C₁₃	—	8	6	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	—	2	3	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	3	no	—
164	C₂²×C₄×C₁₃	—	2	6	no	—
165	C₂²×C₄×C₁₃	—	2	3	no	—
166	C₂²×C₄×C₁₃	—	2	3	no	—
167	C₂²×C₄×C₁₃	—	4	12	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
171	C₁₃×D₈	—	2	12	no	—
172	C₁₃×D₈	—	4	12	no	—
173	C₁₃×D₈	—	4	6	no	—
174	C₂×C₈×C₁₃	—	4	6	no	—
175	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
177	C₁₃×C₄⋊C₄	—	2	3	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	3	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	3	no	—
187	C₁₃×C₂²⋊C₄	—	2	3	no	—
188	C₁₃×C₂²⋊C₄	—	2	3	no	—
189	C₁₃×C₂²⋊C₄	—	2	6	no	—
190	C₁₃×C₂²⋊C₄	—	2	6	no	—
191	C₁₃×C₂²⋊C₄	—	2	6	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
193	C₄²×C₁₃	C₂×D₄	1	3	yes	—
194	C₄²×C₁₃	C₂×D₄	1	3	yes	—
195	C₄²×C₁₃	C₂⁴	1	3	yes	—
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
198	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#3391	C₂×C₁₃	1	2	yes	complemented
200	#3358	C₂×C₁₃	1	2	yes	complemented
201	#3294	C₂×C₁₃	1	6	yes	complemented
202	D₄×D₈	C₂×C₁₃	1	6	yes	complemented
203	#3245	C₂×C₁₃	1	3	yes	complemented
204	#3205	C₂×C₁₃	1	3	yes	complemented
205	#3100	C₂×C₁₃	1	3	yes	complemented
206	C₂×#459	C₂×C₁₃	1	3	yes	complemented
207	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	1	no	—
209	C₂³×C₁₃	—	2	3	no	—
210	C₂³×C₁₃	—	2	6	no	—
211	C₂³×C₁₃	—	4	6	no	—
212	C₂³×C₁₃	—	4	6	no	—
213	C₂³×C₁₃	—	4	12	no	—
214	C₂³×C₁₃	—	8	3	no	—
215	C₂³×C₁₃	—	8	6	no	—
216	C₂³×C₁₃	—	8	6	no	—
217	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
218	Q₈×C₁₃	—	4	6	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	Q₈×C₁₃	C₂×D₈	1	4	yes	complemented
221	D₄×C₁₃	—	2	6	no	—
222	D₄×C₁₃	—	2	3	no	—
223	D₄×C₁₃	—	2	1	no	—
224	D₄×C₁₃	—	2	3	no	—
225	D₄×C₁₃	—	2	6	no	—
226	D₄×C₁₃	—	4	6	no	—
227	D₄×C₁₃	—	4	6	no	—
228	D₄×C₁₃	—	4	12	no	—
229	D₄×C₁₃	—	4	12	no	—
230	D₄×C₁₃	—	4	6	no	—
231	D₄×C₁₃	—	4	12	no	—
232	D₄×C₁₃	—	4	6	no	—
233	D₄×C₁₃	—	8	3	no	—
234	D₄×C₁₃	—	8	6	no	—
235	D₄×C₁₃	—	8	6	no	—
236	D₄×C₁₃	C₂×D₈	1	12	yes	complemented
237	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
238	C₂×C₄×C₁₃	—	2	3	no	—
239	C₂×C₄×C₁₃	—	2	3	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	3	no	—
243	C₂×C₄×C₁₃	—	4	3	no	—
244	C₂×C₄×C₁₃	—	4	6	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	6	no	—
247	C₂×C₄×C₁₃	—	4	6	no	—
248	C₂×C₄×C₁₃	—	4	6	no	—
249	C₂×C₄×C₁₃	—	4	12	no	—
250	C₂×C₄×C₁₃	C₂×D₈	1	12	yes	complemented
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
257	C₈×C₁₃	—	2	6	no	—
258	C₈×C₁₃	—	2	2	no	—
259	C₂×H(5,𝔽₂)	—	2	1	no	—
260	C₂²×#41	—	2	1	no	—
261	C₂²×D₈	C₂²×C₁₃	1	6	yes	complemented
262	#550	—	2	1	no	—
263	#550	C₂²×C₁₃	1	2	yes	complemented
264	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
265	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#548	—	2	1	no	—
267	#547	C₂²×C₁₃	1	3	yes	complemented
268	#546	—	2	3	no	—
269	D₄²	—	2	3	no	—
270	D₄²	C₂²×C₁₃	1	3	yes	complemented
271	D₄²	C₂²×C₁₃	1	6	yes	complemented
272	#535	—	2	3	no	—
273	#532	C₂²×C₁₃	1	3	yes	complemented
274	#532	C₂²×C₁₃	1	3	yes	complemented
275	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
276	#525	—	2	3	no	—
277	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
279	#493	C₂²×C₁₃	1	6	yes	complemented
280	#486	C₂²×C₁₃	1	6	yes	complemented
281	#480	C₂²×C₁₃	1	6	yes	complemented
282	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	#474	C₂²×C₁₃	1	3	yes	complemented
284	#474	C₂²×C₁₃	1	6	yes	complemented
285	#466	C₂²×C₁₃	1	12	yes	complemented
286	#459	C₂²×C₁₃	1	3	yes	complemented
287	#459	C₂²×C₁₃	1	3	yes	complemented
288	#459	C₂²×C₁₃	1	6	yes	complemented
289	#459	C₂²×C₁₃	1	6	yes	complemented
290	#459	C₂²×C₁₃	1	6	yes	complemented
291	#459	C₂²×C₁₃	1	6	yes	complemented
292	#447	C₂²×C₁₃	1	6	yes	complemented
293	#447	C₂²×C₁₃	1	12	yes	complemented
294	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
295	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
296	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
297	C₈×D₄	C₂²×C₁₃	1	6	yes	complemented
298	#431	C₂²×C₁₃	1	3	yes	complemented
299	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	complemented
300	C₂×#102	C₂²×C₁₃	1	6	yes	complemented
301	C₂²×C₁₃	—	2	3	no	—
302	C₂²×C₁₃	—	2	3	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	—	4	6	no	—
307	C₂²×C₁₃	—	4	3	no	—
308	C₂²×C₁₃	—	4	3	no	—
309	C₂²×C₁₃	—	4	6	no	—
310	C₂²×C₁₃	—	4	3	no	—
311	C₂²×C₁₃	—	4	6	no	—
312	C₂²×C₁₃	—	8	12	no	—
313	C₂²×C₁₃	—	16	12	no	—
314	C₂²×C₁₃	C₂²×D₈	1	6	yes	—
315	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
316	C₄×C₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	3	no	—
318	C₄×C₁₃	—	2	3	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	4	3	no	—
322	C₄×C₁₃	C₂²×D₈	1	2	yes	—
323	C₄×C₁₃	C₂²×D₈	1	6	yes	—
324	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₄×C₁₃	#585	1	1	yes	characteristic
326	H(5,𝔽₂)	—	4	8	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	3	no	—
330	C₂×#41	—	2	3	no	—
331	C₂×#41	—	2	3	no	—
332	C₂×#41	—	4	8	no	—
333	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×D₄	—	2	6	no	—
336	C₂²×D₄	—	2	3	no	—
337	C₂²×D₄	—	2	3	no	—
338	C₂²×D₄	—	2	3	no	—
339	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
341	C₂³×C₄	—	2	3	no	—
342	C₂×D₈	—	4	12	no	—
343	C₂×D₈	C₂³×C₁₃	1	6	yes	—
344	C₂×D₈	C₂³×C₁₃	1	12	yes	—
345	C₂×D₈	C₂³×C₁₃	1	6	yes	—
346	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
347	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
349	#127	—	2	3	no	—
350	#127	—	2	3	no	—
351	#127	C₂³×C₁₃	1	3	yes	—
352	#127	C₂³×C₁₃	1	6	yes	—
353	#127	C₂³×C₁₃	1	3	yes	—
354	#124	—	2	3	no	—
355	#124	—	2	3	no	—
356	#123	—	2	6	no	—
357	C₂²⋊Q₈	—	2	3	no	—
358	C₂²⋊Q₈	—	2	3	no	—
359	#121	—	2	3	no	—
360	#121	—	2	3	no	—
361	#121	—	2	3	no	—
362	#121	—	2	3	no	—
363	#121	—	2	6	no	—
364	#121	—	2	6	no	—
365	#121	C₂³×C₁₃	1	6	yes	—
366	#121	C₂³×C₁₃	1	6	yes	—
367	#120	—	2	6	no	—
368	#120	—	2	12	no	—
369	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₄×D₄	—	2	3	no	—
372	C₄×D₄	—	2	3	no	—
373	C₄×D₄	—	2	3	no	—
374	C₄×D₄	—	2	3	no	—
375	C₄×D₄	D₄×C₁₃	1	3	yes	—
376	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₄×D₄	C₂³×C₁₃	1	3	yes	—
378	C₄×D₄	C₂³×C₁₃	1	3	yes	—
379	C₄×D₄	C₂³×C₁₃	1	3	yes	—
380	C₄×D₄	C₂³×C₁₃	1	6	yes	—
381	C₄×D₄	C₂³×C₁₃	1	3	yes	—
382	#117	D₄×C₁₃	1	3	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
384	C₂×C₂²⋊C₄	—	2	3	no	—
385	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
386	#107	C₂³×C₁₃	1	2	yes	—
387	#107	C₂³×C₁₃	1	6	yes	—
388	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
389	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
390	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
391	#102	C₂³×C₁₃	1	6	yes	—
392	#102	C₂³×C₁₃	1	12	yes	—
393	#102	C₂³×C₁₃	1	2	yes	—
394	#102	C₂³×C₁₃	1	6	yes	—
395	#102	C₂³×C₁₃	1	6	yes	—
396	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
397	C₄×C₈	C₂³×C₁₃	1	6	yes	—
398	C₂×C₁₃	—	2	6	no	—
399	C₂×C₁₃	—	4	2	no	—
400	C₂×C₁₃	—	8	3	no	—
401	C₂×C₁₃	—	8	6	no	—
402	C₂×C₁₃	#3488	1	1	yes	characteristic
403	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
404	C₂×C₁₃	#3585	1	1	yes	characteristic
405	C₂⁴	—	2	3	no	—
406	C₂⁴	—	2	6	no	—
407	#41	—	4	4	no	—
408	#41	—	4	8	no	—
409	#41	—	4	12	no	—
410	#41	—	4	12	no	—
411	#41	—	4	12	no	—
412	#41	C₁₃×D₈	1	8	yes	complemented
413	C₂×Q₈	—	2	3	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂×D₄	—	2	6	no	—
418	C₂×D₄	—	2	6	no	—
419	C₂×D₄	—	2	6	no	—
420	C₂×D₄	—	2	3	no	—
421	C₂×D₄	—	2	3	no	—
422	C₂×D₄	—	2	3	no	—
423	C₂×D₄	—	2	6	no	—
424	C₂×D₄	—	2	3	no	—
425	C₂×D₄	—	2	3	no	—
426	C₂×D₄	—	2	6	no	—
427	C₂×D₄	—	2	6	no	—
428	C₂×D₄	—	4	3	no	—
429	C₂×D₄	—	4	6	no	—
430	C₂×D₄	—	4	6	no	—
431	C₂×D₄	—	4	12	no	—
432	C₂×D₄	—	4	24	no	—
433	C₂×D₄	—	4	12	no	—
434	C₂×D₄	—	8	6	no	—
435	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
436	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
437	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
438	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	—	2	3	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	3	no	—
442	C₂²×C₄	—	2	6	no	—
443	C₂²×C₄	—	2	3	no	—
444	C₂²×C₄	—	2	3	no	—
445	C₂²×C₄	—	4	12	no	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
449	D₈	—	2	12	no	—
450	D₈	—	4	12	no	—
451	D₈	—	4	6	no	—
452	C₂×C₈	—	4	6	no	—
453	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
454	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
455	C₄⋊C₄	—	2	3	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	3	no	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
460	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	3	no	—
465	C₂²⋊C₄	—	2	3	no	—
466	C₂²⋊C₄	—	2	3	no	—
467	C₂²⋊C₄	—	2	6	no	—
468	C₂²⋊C₄	—	2	6	no	—
469	C₂²⋊C₄	—	2	6	no	—
470	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
471	C₄²	C₂×D₄×C₁₃	1	3	yes	—
472	C₄²	C₂×D₄×C₁₃	1	3	yes	—
473	C₄²	C₂⁴×C₁₃	1	3	yes	—
474	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₁₃	#61947	1	1	yes	characteristic, direct product factor, Sylow
476	C₂³	—	2	1	no	—
477	C₂³	—	2	3	no	—
478	C₂³	—	2	6	no	—
479	C₂³	—	4	6	no	—
480	C₂³	—	4	6	no	—
481	C₂³	—	4	12	no	—
482	C₂³	—	8	3	no	—
483	C₂³	—	8	6	no	—
484	C₂³	—	8	6	no	—
485	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
486	Q₈	—	4	6	no	—
487	Q₈	—	4	2	no	—
488	Q₈	C₂×C₁₃×D₈	1	4	yes	complemented
489	D₄	—	2	6	no	—
490	D₄	—	2	3	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	3	no	—
493	D₄	—	2	6	no	—
494	D₄	—	4	6	no	—
495	D₄	—	4	6	no	—
496	D₄	—	4	12	no	—
497	D₄	—	4	12	no	—
498	D₄	—	4	6	no	—
499	D₄	—	4	12	no	—
500	D₄	—	4	6	no	—
501	D₄	—	8	6	no	—
502	D₄	—	8	6	no	—
503	D₄	—	8	3	no	—
504	D₄	C₂×C₁₃×D₈	1	12	yes	complemented
505	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
506	C₂×C₄	—	2	3	no	—
507	C₂×C₄	—	2	3	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	3	no	—
511	C₂×C₄	—	4	3	no	—
512	C₂×C₄	—	4	6	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	6	no	—
515	C₂×C₄	—	4	6	no	—
516	C₂×C₄	—	4	6	no	—
517	C₂×C₄	—	4	12	no	—
518	C₂×C₄	C₂×C₁₃×D₈	1	12	yes	complemented
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
524	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
525	C₈	—	2	6	no	—
526	C₈	—	2	2	no	—
527	C₂²	—	2	3	no	—
528	C₂²	—	2	3	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	3	no	—
533	C₂²	—	4	6	no	—
534	C₂²	—	4	6	no	—
535	C₂²	—	4	3	no	—
536	C₂²	—	4	3	no	—
537	C₂²	—	4	6	no	—
538	C₂²	—	8	12	no	—
539	C₂²	—	16	12	no	—
540	C₂²	C₂²×C₁₃×D₈	1	6	yes	—
541	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
542	C₄	—	2	1	no	—
543	C₄	—	2	3	no	—
544	C₄	—	2	3	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	3	no	—
548	C₄	C₂²×C₁₃×D₈	1	2	yes	—
549	C₄	C₂²×C₁₃×D₈	1	6	yes	—
550	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
551	C₄	C₁₃×#585	1	1	yes	characteristic
552	C₂	—	2	6	no	—
553	C₂	—	4	2	no	—
554	C₂	—	8	3	no	—
555	C₂	—	8	6	no	—
556	C₂	C₁₃×#3488	1	1	yes	characteristic
557	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
558	C₂	C₁₃×#3585	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×#3498	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3391	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3294	C₂	semidirect
6. D₄×C₁₃×D₈	C₂	semidirect
7. C₁₃×#3245	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3100	C₂	semidirect
10. C₂×C₁₃×#459	C₂	semidirect
11. C₁₃×#2988	C₂	semidirect
14. C₂²×C₁₃×D₈	C₂²	semidirect
16. C₁₃×#550	C₂²	semidirect
17. C₁₃×#550	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
23. D₄²×C₁₃	C₂²	semidirect
24. D₄²×C₁₃	C₂²	semidirect
26. C₁₃×#532	C₂²	semidirect
27. C₁₃×#532	C₂²	semidirect
28. C₂×C₁₃×#127	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₁₃×#493	C₂²	semidirect
33. C₁₃×#486	C₂²	semidirect
34. C₁₃×#480	C₂²	semidirect
35. C₁₃×#474	C₂²	semidirect
36. C₁₃×#474	C₂²	semidirect
37. C₁₃×#474	C₂²	semidirect
38. C₁₃×#466	C₂²	semidirect
39. C₁₃×#459	C₂²	semidirect
40. C₁₃×#459	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#447	C₂²	semidirect
46. C₁₃×#447	C₂²	semidirect
47. C₈×Q₈×C₁₃	C₂²	semidirect
48. C₄×C₁₃×D₈	C₂²	semidirect
49. C₄×C₁₃×D₈	C₂²	semidirect
50. C₈×D₄×C₁₃	C₂²	semidirect
51. C₁₃×#431	C₂²	semidirect
52. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
53. C₂×C₁₃×#102	C₂²	semidirect
126. #61947	C₁₃	direct (N × H)
134. C₁₃×#41	D₈	semidirect
197. #3498	C₂×C₁₃	semidirect
198. D₄×#41	C₂×C₁₃	semidirect
199. #3391	C₂×C₁₃	semidirect
200. #3358	C₂×C₁₃	semidirect
201. #3294	C₂×C₁₃	semidirect
202. D₄×D₈	C₂×C₁₃	semidirect
203. #3245	C₂×C₁₃	semidirect
204. #3205	C₂×C₁₃	semidirect
205. #3100	C₂×C₁₃	semidirect
206. C₂×#459	C₂×C₁₃	semidirect
207. #2988	C₂×C₁₃	semidirect
220. Q₈×C₁₃	C₂×D₈	semidirect
236. D₄×C₁₃	C₂×D₈	semidirect
237. D₄×C₁₃	H(5,𝔽₂)	semidirect
250. C₂×C₄×C₁₃	C₂×D₈	semidirect
261. C₂²×D₈	C₂²×C₁₃	semidirect
263. #550	C₂²×C₁₃	semidirect
264. #550	C₂²×C₁₃	semidirect
265. D₄×Q₈	C₂²×C₁₃	semidirect
267. #547	C₂²×C₁₃	semidirect
270. D₄²	C₂²×C₁₃	semidirect
271. D₄²	C₂²×C₁₃	semidirect
273. #532	C₂²×C₁₃	semidirect
274. #532	C₂²×C₁₃	semidirect
275. C₂×#127	C₂²×C₁₃	semidirect
278. C₂×C₄×D₄	C₂²×C₁₃	semidirect
279. #493	C₂²×C₁₃	semidirect
280. #486	C₂²×C₁₃	semidirect
281. #480	C₂²×C₁₃	semidirect
282. #474	C₂²×C₁₃	semidirect
283. #474	C₂²×C₁₃	semidirect
284. #474	C₂²×C₁₃	semidirect
285. #466	C₂²×C₁₃	semidirect
286. #459	C₂²×C₁₃	semidirect
287. #459	C₂²×C₁₃	semidirect
288. #459	C₂²×C₁₃	semidirect
289. #459	C₂²×C₁₃	semidirect
290. #459	C₂²×C₁₃	semidirect
291. #459	C₂²×C₁₃	semidirect
292. #447	C₂²×C₁₃	semidirect
293. #447	C₂²×C₁₃	semidirect
294. C₈×Q₈	C₂²×C₁₃	semidirect
295. C₄×D₈	C₂²×C₁₃	semidirect
296. C₄×D₈	C₂²×C₁₃	semidirect
297. C₈×D₄	C₂²×C₁₃	semidirect
298. #431	C₂²×C₁₃	semidirect
299. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
300. C₂×#102	C₂²×C₁₃	semidirect
412. #41	C₁₃×D₈	semidirect
475. C₁₃	#61947	direct (N × H)
488. Q₈	C₂×C₁₃×D₈	semidirect
504. D₄	C₂×C₁₃×D₈	semidirect
505. D₄	C₁₃×H(5,𝔽₂)	semidirect
518. C₂×C₄	C₂×C₁₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3498	2
D₄×C₁₃×#41	2
C₁₃×#3391	2
C₁₃×#3358	2
C₁₃×#3294	2
D₄×C₁₃×D₈	2
C₁₃×#3245	2
C₁₃×#3205	2
C₁₃×#3100	2
C₂×C₁₃×#459	2
C₁₃×#2988	2
#61947	13

Subgroups — C13×#61947 #15748286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61947 #15748286