Subgroups — C₁₃×#24178 #15710517

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 638 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	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2037	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2004	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₁₃×#559	—	2	2	no	—
14	C₁₃×#556	—	2	1	no	—
15	C₁₃×#555	—	2	1	no	—
16	C₁₃×#553	—	2	2	no	—
17	C₁₃×#550	—	2	1	no	—
18	C₁₃×#547	—	2	1	no	—
19	C₁₃×#538	—	2	2	no	—
20	C₁₃×#535	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₁₃×#525	—	2	2	no	—
25	C₁₃×#520	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#479	—	2	2	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#475	—	2	1	no	—
31	C₁₃×#464	—	2	2	no	—
32	C₁₃×#462	—	2	1	no	—
33	C₁₃×#460	—	2	1	no	—
34	C₁₃×#428	C₂²	1	2	yes	—
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#104	C₂²	1	2	yes	—
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₁₃×#419	C₂²	1	2	yes	—
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₂×C₁₃×#100	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#388	—	2	2	no	—
45	C₁₃×#382	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
47	C₄³×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#339	C₂²	1	2	yes	—
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	D₄	1	2	yes	—
56	C₁₃×#137	—	2	4	no	—
57	C₁₃×#137	—	4	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	D₄	1	1	yes	characteristic
67	C₁₃×#126	—	2	4	no	—
68	C₁₃×#125	D₄	1	2	yes	—
69	C₁₃×#124	—	2	4	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	D₄	1	2	yes	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	1	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	1	no	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#120	—	2	4	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	—	2	1	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	—	2	2	no	—
119	C₁₃×#106	—	2	2	no	—
120	C₁₃×C₄⋊C₈	—	2	1	no	—
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×C₄⋊C₈	—	2	1	no	—
123	C₁₃×C₄⋊C₈	—	2	1	no	—
124	C₁₃×#104	—	2	4	no	—
125	C₁₃×#104	—	4	2	no	—
126	C₁₃×#103	—	2	2	no	—
127	C₁₃×#103	—	2	2	no	—
128	C₁₃×#103	—	2	2	no	—
129	C₁₃×#102	—	2	2	no	—
130	C₁₃×#100	—	4	2	no	—
131	C₁₃×#95	—	2	2	no	—
132	C₁₃×#95	—	2	2	no	—
133	#24178	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
135	C₁₃×#41	—	2	2	no	—
136	C₁₃×#41	—	2	2	no	—
137	C₁₃×#41	—	2	2	no	—
138	C₁₃×#41	—	2	2	no	—
139	C₁₃×#41	—	8	4	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	4	4	no	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×Q₁₆	—	4	4	no	—
175	C₁₃×SD₁₆	—	4	4	no	—
176	C₁₃×M₁₆	—	2	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	—	2	2	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	4	no	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	2	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	—	4	2	no	—
214	C₄²×C₁₃	—	4	1	no	—
215	C₄²×C₁₃	—	4	1	no	—
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₃	#41	1	2	yes	complemented
221	#3506	C₂×C₁₃	1	1	yes	characteristic
222	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2037	C₂×C₁₃	1	2	yes	complemented
226	#2004	C₂×C₁₃	1	2	yes	complemented
227	#1994	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1962	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1882	C₂×C₁₃	1	2	yes	complemented
230	#1860	C₂×C₁₃	1	2	yes	complemented
231	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	4	2	no	—
238	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	2	2	no	—
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	2	2	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	2	no	—
246	Q₈×C₁₃	—	8	1	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	2	no	—
256	D₄×C₁₃	—	8	1	no	—
257	D₄×C₁₃	—	8	4	no	—
258	D₄×C₁₃	—	8	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	2	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	4	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	8	2	no	—
281	C₂×C₄×C₁₃	—	8	4	no	—
282	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
283	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
284	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
285	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
292	C₈×C₁₃	—	4	2	no	—
293	C₈×C₁₃	—	4	2	no	—
294	C₂×#137	C₂²×C₁₃	1	2	yes	—
295	#559	—	2	2	no	—
296	#556	—	2	1	no	—
297	#555	—	2	1	no	—
298	#553	—	2	2	no	—
299	#550	—	2	1	no	—
300	#547	—	2	1	no	—
301	#538	—	2	2	no	—
302	#535	C₂²×C₁₃	1	2	yes	—
303	#533	C₂²×C₁₃	1	1	yes	characteristic
304	#532	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
306	#525	—	2	2	no	—
307	#520	C₂²×C₁₃	1	2	yes	—
308	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	#479	—	2	2	no	—
311	#477	—	2	1	no	—
312	#475	—	2	1	no	—
313	#464	—	2	2	no	—
314	#462	—	2	1	no	—
315	#460	—	2	1	no	—
316	#428	C₂²×C₁₃	1	2	yes	—
317	#423	C₂²×C₁₃	1	1	yes	characteristic
318	#423	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#104	C₂²×C₁₃	1	2	yes	—
320	C₂×#104	C₂²×C₁₃	1	2	yes	—
321	#419	C₂²×C₁₃	1	2	yes	—
322	#417	C₂²×C₁₃	1	2	yes	—
323	C₂×#100	C₂²×C₁₃	1	2	yes	—
324	#391	C₂²×C₁₃	1	1	yes	characteristic
325	#390	C₂²×C₁₃	1	1	yes	characteristic
326	#388	—	2	2	no	—
327	#382	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₂²⋊C₄	—	2	2	no	—
329	C₄³	C₂²×C₁₃	1	1	yes	characteristic
330	#343	C₂²×C₁₃	1	2	yes	—
331	#339	C₂²×C₁₃	1	2	yes	—
332	#339	C₂²×C₁₃	1	2	yes	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	8	2	no	—
343	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
344	C₂²×C₁₃	#525	1	1	yes	characteristic
345	C₂²×C₁₃	#537	1	1	yes	characteristic
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	2	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	#455	1	2	yes	—
358	C₄×C₁₃	#546	1	1	yes	characteristic
359	C₄×C₁₃	#547	1	1	yes	characteristic
360	C₄×C₁₃	#548	1	1	yes	characteristic
361	C₄×C₁₃	#550	1	1	yes	characteristic
362	C₂×#41	—	2	2	no	—
363	C₂×#41	C₂³×C₁₃	1	2	yes	—
364	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂³×C₄	D₄×C₁₃	1	2	yes	—
367	#137	—	2	4	no	—
368	#137	—	4	2	no	—
369	C₂×Q₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
372	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
373	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
374	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
375	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
376	#127	—	2	2	no	—
377	#127	D₄×C₁₃	1	1	yes	characteristic
378	#126	—	2	4	no	—
379	#125	D₄×C₁₃	1	2	yes	—
380	#124	—	2	4	no	—
381	#124	—	2	2	no	—
382	#124	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	D₄×C₁₃	1	2	yes	—
385	#123	—	2	4	no	—
386	#123	—	2	4	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	#121	—	2	2	no	—
391	#121	—	2	4	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	2	no	—
395	#121	—	2	2	no	—
396	#120	—	2	4	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	4	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	#117	—	2	2	no	—
414	#117	—	2	2	no	—
415	#117	C₂³×C₁₃	1	2	yes	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	2	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	#107	—	2	2	no	—
430	#106	—	2	2	no	—
431	C₄⋊C₈	—	2	1	no	—
432	C₄⋊C₈	—	2	1	no	—
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	#104	—	2	4	no	—
436	#104	—	4	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#102	—	2	2	no	—
441	#100	—	4	2	no	—
442	#95	—	2	2	no	—
443	#95	—	2	2	no	—
444	C₂×C₁₃	—	2	1	no	—
445	C₂×C₁₃	—	2	1	no	—
446	C₂×C₁₃	—	8	2	no	—
447	C₂×C₁₃	—	8	2	no	—
448	C₂×C₁₃	#2407	1	1	yes	characteristic
449	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
450	C₂×C₁₃	#3018	1	1	yes	characteristic
451	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	8	4	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
465	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
491	Q₁₆	—	4	4	no	—
492	SD₁₆	—	4	4	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	4	2	no	—
530	C₄²	—	4	2	no	—
531	C₄²	—	4	1	no	—
532	C₄²	—	4	1	no	—
533	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₄²	C₁₃×#41	1	2	yes	complemented
538	C₁₃	#24178	1	1	yes	characteristic, direct product factor, Sylow
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	Q₈	—	2	2	no	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	8	1	no	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	8	1	no	—
564	D₄	—	8	4	no	—
565	D₄	—	8	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	—	8	4	no	—
589	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
590	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
591	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
592	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
596	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
597	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
612	C₂²	C₁₃×#525	1	1	yes	characteristic
613	C₂²	C₁₃×#537	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	8	1	no	—
625	C₄	C₁₃×#455	1	2	yes	—
626	C₄	C₁₃×#546	1	1	yes	characteristic
627	C₄	C₁₃×#547	1	1	yes	characteristic
628	C₄	C₁₃×#548	1	1	yes	characteristic
629	C₄	C₁₃×#550	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	2	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₃×#2407	1	1	yes	characteristic
635	C₂	C₂×C₁₃×#455	1	1	yes	characteristic
636	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3506	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3078	C₂	semidirect
3. C₁₃×#3037	C₂	semidirect
4. C₄×C₁₃×#124	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#2004	C₂	semidirect
7. C₁₃×#1994	C₂	semidirect
8. C₁₃×#1962	C₂	semidirect
9. C₁₃×#1882	C₂	semidirect
10. C₁₃×#1860	C₂	semidirect
11. C₁₃×#1800	C₂	semidirect
133. #24178	C₁₃	direct (N × H)
148. C₂×Q₈×C₁₃	#41	semidirect
220. C₄²×C₁₃	#41	semidirect
222. #3078	C₂×C₁₃	semidirect
223. #3037	C₂×C₁₃	semidirect
224. C₄×#124	C₂×C₁₃	semidirect
225. #2037	C₂×C₁₃	semidirect
226. #2004	C₂×C₁₃	semidirect
227. #1994	C₂×C₁₃	semidirect
228. #1962	C₂×C₁₃	semidirect
229. #1882	C₂×C₁₃	semidirect
230. #1860	C₂×C₁₃	semidirect
231. #1800	C₂×C₁₃	semidirect
465. C₂×Q₈	C₁₃×#41	semidirect
537. C₄²	C₁₃×#41	semidirect
538. C₁₃	#24178	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×#3078	2
C₁₃×#3037	2
C₄×C₁₃×#124	2
C₁₃×#2037	2
C₁₃×#2004	2
C₁₃×#1994	2
C₁₃×#1962	2
C₁₃×#1882	2
C₁₃×#1860	2
C₁₃×#1800	2
#24178	13

Subgroups — C13×#24178 #15710517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24178 #15710517