Subgroups — C₁₃×#24323 #15710662

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2060	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2028	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1882	C₂	1	2	yes	maximal
10	C₁₃×#1859	C₂	1	2	yes	maximal
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#554	—	2	1	no	—
16	C₁₃×#554	—	2	2	no	—
17	D₄×Q₈×C₁₃	—	2	2	no	—
18	D₄×Q₈×C₁₃	—	2	1	no	—
19	C₁₃×#544	—	2	2	no	—
20	C₁₃×#544	C₂²	1	2	yes	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#520	C₂²	1	2	yes	—
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×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×#441	—	2	1	no	—
32	C₁₃×#440	—	2	1	no	—
33	C₄×C₁₃×Q₁₆	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	1	no	—
35	C₁₃×#428	C₂²	1	2	yes	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₁₃×#419	C₂²	1	1	yes	characteristic
40	C₁₃×#419	C₂²	1	2	yes	—
41	C₁₃×#417	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₃×#395	—	2	2	no	—
44	C₁₃×#391	C₂²	1	2	yes	—
45	C₁₃×#389	—	2	2	no	—
46	C₁₃×#384	C₂²	1	2	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#343	C₂²	1	2	yes	—
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₁₃×#339	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	—	2	2	no	—
55	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#137	—	2	2	no	—
58	C₁₃×#137	Q₈	1	4	yes	complemented
59	C₂×C₁₃×Q₁₆	—	2	1	no	—
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	4	no	—
67	C₁₃×C₄⋊Q₈	—	2	2	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	2	1	no	—
70	C₁₃×C₄⋊Q₈	—	2	1	no	—
71	C₁₃×C₄⋊Q₈	—	2	1	no	—
72	C₁₃×C₄⋊Q₈	—	2	1	no	—
73	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
74	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	D₄	1	2	yes	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	4	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	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×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₁₃×#117	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#107	—	2	2	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×#104	—	2	4	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#97	—	2	1	no	—
133	C₄×C₈×C₁₃	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	4	no	—
136	#24323	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₁₃×#41	—	2	1	no	—
138	C₁₃×#41	—	2	1	no	—
139	C₁₃×#41	C₂×Q₈	1	2	yes	—
140	C₁₃×#41	#41	1	2	yes	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	2	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	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	8	2	no	—
152	C₂×Q₈×C₁₃	—	8	4	no	—
153	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	complemented
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
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	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×Q₁₆	—	2	4	no	—
169	C₁₃×SD₁₆	—	2	4	no	—
170	C₁₃×M₁₆	—	2	1	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	1	no	—
173	C₁₃×M₁₆	—	2	1	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	C₂×Q₈	1	2	yes	complemented
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	8	4	no	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	2	no	—
214	C₄²×C₁₃	—	2	2	no	—
215	C₄²×C₁₃	—	4	1	no	—
216	C₄²×C₁₃	—	4	1	no	—
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	C₂×D₄	1	1	yes	characteristic
221	#3503	C₂×C₁₃	1	1	yes	characteristic
222	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
224	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2060	C₂×C₁₃	1	2	yes	complemented
226	#2028	C₂×C₁₃	1	2	yes	complemented
227	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1882	C₂×C₁₃	1	2	yes	—
230	#1859	C₂×C₁₃	1	2	yes	—
231	#1806	C₂×C₁₃	1	1	yes	characteristic
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	4	4	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	Q₈×C₁₃	—	8	2	no	—
243	Q₈×C₁₃	—	8	4	no	—
244	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	2	2	no	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	8	4	no	—
271	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
274	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	2	no	—
284	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
285	Q₈²	—	2	1	no	—
286	#557	—	2	1	no	—
287	#554	—	2	1	no	—
288	#554	—	2	2	no	—
289	D₄×Q₈	—	2	2	no	—
290	D₄×Q₈	—	2	1	no	—
291	#544	—	2	2	no	—
292	#544	C₂²×C₁₃	1	2	yes	—
293	#533	—	2	1	no	—
294	#533	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	—	2	1	no	—
296	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	#520	C₂²×C₁₃	1	2	yes	—
298	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
300	#479	—	2	2	no	—
301	#477	—	2	1	no	—
302	#475	—	2	1	no	—
303	#441	—	2	1	no	—
304	#440	—	2	1	no	—
305	C₄×Q₁₆	—	2	1	no	—
306	C₄×SD₁₆	—	2	1	no	—
307	#428	C₂²×C₁₃	1	2	yes	—
308	#428	C₂²×C₁₃	1	1	yes	characteristic
309	#423	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#104	C₂²×C₁₃	1	2	yes	—
311	#419	C₂²×C₁₃	1	2	yes	—
312	#419	C₂²×C₁₃	1	1	yes	characteristic
313	#417	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
315	#395	—	2	2	no	—
316	#391	C₂²×C₁₃	1	2	yes	—
317	#389	—	2	2	no	—
318	#384	C₂²×C₁₃	1	2	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	#343	C₂²×C₁₃	1	2	yes	—
321	#343	C₂²×C₁₃	1	2	yes	—
322	#339	C₂²×C₁₃	1	2	yes	—
323	#339	C₂²×C₁₃	1	2	yes	—
324	#339	C₂²×C₁₃	1	2	yes	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₃	#548	1	1	yes	characteristic
332	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	4	4	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	—	4	2	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	#456	1	2	yes	—
346	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
347	C₄×C₁₃	#536	1	1	yes	characteristic
348	C₄×C₁₃	#548	1	1	yes	characteristic
349	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
350	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×Q₈	—	2	2	no	—
352	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	#137	—	2	2	no	—
355	#137	Q₈×C₁₃	1	4	yes	complemented
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
360	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	—	2	2	no	—
363	C₄⋊Q₈	—	2	4	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
372	#125	—	2	4	no	—
373	#125	—	2	2	no	—
374	#125	—	2	2	no	—
375	#125	D₄×C₁₃	1	2	yes	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
393	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	4	no	—
398	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
399	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
400	#117	—	2	2	no	—
401	#117	—	2	1	no	—
402	#117	C₂³×C₁₃	1	1	yes	characteristic
403	#117	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	#107	—	2	1	no	—
417	#107	—	2	2	no	—
418	#106	—	2	1	no	—
419	#106	—	2	2	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	—	2	1	no	—
422	#104	—	2	4	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#102	—	2	1	no	—
429	#97	—	2	1	no	—
430	C₄×C₈	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	4	no	—
433	C₂×C₁₃	—	2	1	no	—
434	C₂×C₁₃	—	2	1	no	—
435	C₂×C₁₃	—	4	2	no	—
436	C₂×C₁₃	#2409	1	1	yes	characteristic
437	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
438	C₂×C₁₃	#3019	1	1	yes	characteristic
439	#41	—	2	1	no	—
440	#41	—	2	1	no	—
441	#41	C₂×Q₈×C₁₃	1	2	yes	—
442	#41	C₁₃×#41	1	2	yes	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	8	2	no	—
454	C₂×Q₈	—	8	4	no	—
455	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	complemented
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
470	Q₁₆	—	2	4	no	—
471	SD₁₆	—	2	4	no	—
472	M₁₆	—	2	1	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	1	no	—
475	M₁₆	—	2	1	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	C₂×Q₈×C₁₃	1	2	yes	complemented
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	8	4	no	—
501	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
502	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
504	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₄²	—	2	4	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	4	1	no	—
518	C₄²	—	4	1	no	—
519	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₁₃	#24323	1	1	yes	characteristic, direct product factor, Sylow
524	C₂³	—	2	1	no	—
525	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	Q₈	—	2	1	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	2	no	—
529	Q₈	—	4	4	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	8	2	no	—
535	Q₈	—	8	4	no	—
536	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
537	D₄	—	2	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	1	no	—
540	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
564	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
565	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
566	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
571	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
572	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
582	C₂²	C₁₃×#548	1	1	yes	characteristic
583	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	4	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	8	1	no	—
596	C₄	C₁₃×#456	1	2	yes	—
597	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
598	C₄	C₁₃×#536	1	1	yes	characteristic
599	C₄	C₁₃×#548	1	1	yes	characteristic
600	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	C₁₃×#2409	1	1	yes	characteristic
605	C₂	C₂×C₁₃×#456	1	1	yes	characteristic
606	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2060	C₂	semidirect
6. C₁₃×#2028	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1986	C₂	semidirect
58. C₁₃×#137	Q₈	semidirect
136. #24323	C₁₃	direct (N × H)
154. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
175. C₁₃×M₁₆	C₂×Q₈	semidirect
222. #3078	C₂×C₁₃	semidirect
224. #2567	C₂×C₁₃	semidirect
225. #2060	C₂×C₁₃	semidirect
226. #2028	C₂×C₁₃	semidirect
227. #1997	C₂×C₁₃	semidirect
228. #1986	C₂×C₁₃	semidirect
355. #137	Q₈×C₁₃	semidirect
456. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
477. M₁₆	C₂×Q₈×C₁₃	semidirect
523. C₁₃	#24323	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×#3503	2
C₁₃×#3078	2
C₄×C₁₃×#137	2
C₁₃×#2567	2
C₁₃×#2060	2
C₁₃×#2028	2
C₁₃×#1997	2
C₁₃×#1986	2
C₁₃×#1882	2
C₁₃×#1859	2
C₁₃×#1806	2
#24323	13

Subgroups — C13×#24323 #15710662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24323 #15710662