Subgroups — C₁₃×#23594 #15709933

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2007	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2005	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₁₃×#544	C₂²	1	1	yes	characteristic
14	C₁₃×#542	—	2	2	no	—
15	C₁₃×#541	—	2	2	no	—
16	C₁₃×#539	—	2	2	no	—
17	C₁₃×#537	C₂²	1	1	yes	characteristic
18	C₁₃×#536	C₂²	1	2	yes	—
19	C₁₃×#533	—	2	2	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	—	2	2	no	—
23	C₄×C₁₃×#41	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#441	—	2	2	no	—
27	C₁₃×#440	—	2	2	no	—
28	C₄×C₁₃×Q₁₆	—	2	2	no	—
29	C₄×C₁₃×SD₁₆	—	2	2	no	—
30	C₁₃×#428	C₂²	1	2	yes	—
31	C₂×C₁₃×#104	C₂²	1	2	yes	—
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#419	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#101	C₂²	1	2	yes	—
36	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#387	—	2	2	no	—
40	C₁₃×#387	—	2	2	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#376	C₂²	1	1	yes	characteristic
43	C₁₃×#343	C₂²	1	1	yes	characteristic
44	C₁₃×#343	C₂²	1	1	yes	characteristic
45	C₁₃×#339	C₂²	1	2	yes	—
46	C₁₃×#339	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#137	—	2	4	no	—
51	C₁₃×#137	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×#126	—	2	4	no	—
61	C₁₃×#126	—	2	4	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×#125	—	2	4	no	—
64	C₁₃×#125	—	2	2	no	—
65	C₁₃×#124	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#123	—	2	4	no	—
68	C₁₃×#123	—	2	4	no	—
69	C₁₃×C₂²⋊Q₈	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	2	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	D₄	1	2	yes	—
82	C₄×Q₈×C₁₃	D₄	1	2	yes	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	D₄	1	2	yes	—
87	C₄×D₄×C₁₃	D₄	1	2	yes	—
88	C₁₃×#117	—	2	4	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	D₄	1	2	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	—	2	2	no	—
103	C₁₃×#106	—	2	2	no	—
104	C₁₃×#104	—	2	4	no	—
105	C₁₃×#104	—	2	4	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#103	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#101	—	2	4	no	—
111	C₁₃×#97	—	2	2	no	—
112	C₄×C₈×C₁₃	—	2	2	no	—
113	C₁₃×#95	—	2	2	no	—
114	C₁₃×#95	—	2	2	no	—
115	C₁₃×#95	—	2	2	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	#23594	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₁₃	#41	1	2	yes	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×Q₁₆	—	2	8	no	—
149	C₁₃×SD₁₆	—	2	8	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	#41	1	4	yes	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₄²×C₁₃	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	4	2	no	—
185	C₄²×C₁₃	C₂×D₄	1	2	yes	—
186	C₄²×C₁₃	C₂×D₄	1	2	yes	—
187	C₄²×C₁₃	#41	1	2	yes	—
188	#3461	C₂×C₁₃	1	1	yes	characteristic
189	C₄×#137	C₂×C₁₃	1	2	yes	complemented
190	#2327	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2040	C₂×C₁₃	1	1	yes	characteristic
193	#2038	C₂×C₁₃	1	2	yes	complemented
194	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2007	C₂×C₁₃	1	1	yes	characteristic
196	#2005	C₂×C₁₃	1	2	yes	complemented
197	#1759	C₂×C₁₃	1	2	yes	complemented
198	C₄×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	4	no	—
202	Q₈×C₁₃	—	2	2	no	—
203	Q₈×C₁₃	—	2	2	no	—
204	Q₈×C₁₃	—	4	2	no	—
205	Q₈×C₁₃	—	4	2	no	—
206	Q₈×C₁₃	—	4	2	no	—
207	Q₈×C₁₃	—	8	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	8	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	8	2	no	—
238	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#120	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
245	C₈×C₁₃	—	2	4	no	—
246	C₈×C₁₃	—	4	2	no	—
247	C₂×#137	C₂²×C₁₃	1	2	yes	—
248	#544	C₂²×C₁₃	1	1	yes	characteristic
249	#542	—	2	2	no	—
250	#541	—	2	2	no	—
251	#539	—	2	2	no	—
252	#537	C₂²×C₁₃	1	1	yes	characteristic
253	#536	C₂²×C₁₃	1	2	yes	—
254	#533	—	2	2	no	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	#529	—	2	2	no	—
257	#529	—	2	2	no	—
258	C₄×#41	C₂²×C₁₃	1	2	yes	—
259	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	#441	—	2	2	no	—
262	#440	—	2	2	no	—
263	C₄×Q₁₆	—	2	2	no	—
264	C₄×SD₁₆	—	2	2	no	—
265	#428	C₂²×C₁₃	1	2	yes	—
266	C₂×#104	C₂²×C₁₃	1	2	yes	—
267	C₂×#104	C₂²×C₁₃	1	2	yes	—
268	#419	C₂²×C₁₃	1	2	yes	—
269	#417	C₂²×C₁₃	1	2	yes	—
270	C₂×#101	C₂²×C₁₃	1	2	yes	—
271	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
272	#391	C₂²×C₁₃	1	1	yes	characteristic
273	#391	C₂²×C₁₃	1	1	yes	characteristic
274	#387	—	2	2	no	—
275	#387	—	2	2	no	—
276	#382	C₂²×C₁₃	1	1	yes	characteristic
277	#376	C₂²×C₁₃	1	1	yes	characteristic
278	#343	C₂²×C₁₃	1	1	yes	characteristic
279	#343	C₂²×C₁₃	1	1	yes	characteristic
280	#339	C₂²×C₁₃	1	2	yes	—
281	#339	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
288	C₂²×C₁₃	#525	1	1	yes	characteristic
289	C₂²×C₁₃	#532	1	1	yes	characteristic
290	C₄×C₁₃	—	2	1	no	—
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	2	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	8	1	no	—
301	C₄×C₁₃	—	8	1	no	—
302	C₄×C₁₃	#525	1	2	yes	—
303	C₄×C₁₃	#532	1	2	yes	—
304	C₂×#41	C₂³×C₁₃	1	2	yes	—
305	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
307	#137	—	2	4	no	—
308	#137	—	2	4	no	—
309	C₂×Q₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	2	2	no	—
311	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	#126	—	2	4	no	—
318	#126	—	2	4	no	—
319	#125	—	2	2	no	—
320	#125	—	2	4	no	—
321	#125	—	2	2	no	—
322	#124	—	2	2	no	—
323	#124	—	2	2	no	—
324	#123	—	2	4	no	—
325	#123	—	2	4	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	#121	—	2	2	no	—
332	#121	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	D₄×C₁₃	1	2	yes	—
339	C₄×Q₈	D₄×C₁₃	1	2	yes	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	D₄×C₁₃	1	2	yes	—
344	C₄×D₄	D₄×C₁₃	1	2	yes	—
345	#117	—	2	4	no	—
346	#117	—	2	2	no	—
347	#117	C₂³×C₁₃	1	2	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	D₄×C₁₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	#107	—	2	2	no	—
360	#106	—	2	2	no	—
361	#104	—	2	4	no	—
362	#104	—	2	4	no	—
363	#103	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#102	—	2	2	no	—
367	#101	—	2	4	no	—
368	#97	—	2	2	no	—
369	C₄×C₈	—	2	2	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₂×C₁₃	—	2	1	no	—
376	C₂×C₁₃	—	2	1	no	—
377	C₂×C₁₃	—	8	2	no	—
378	C₂×C₁₃	#2388	1	1	yes	characteristic
379	C₂×C₁₃	#3020	1	1	yes	characteristic
380	C₂×C₁₃	#3022	1	1	yes	characteristic
381	#41	—	2	2	no	—
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
394	C₂×Q₈	C₁₃×#41	1	2	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
410	Q₁₆	—	2	8	no	—
411	SD₁₆	—	2	8	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	C₁₃×#41	1	4	yes	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	4	2	no	—
447	C₄²	C₂×D₄×C₁₃	1	2	yes	—
448	C₄²	C₂×D₄×C₁₃	1	2	yes	—
449	C₄²	C₁₃×#41	1	2	yes	—
450	C₁₃	#23594	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	2	no	—
452	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	8	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	8	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
491	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
492	C₂×C₄	C₁₃×#120	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
496	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
497	C₈	—	2	4	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
505	C₂²	C₁₃×#525	1	1	yes	characteristic
506	C₂²	C₁₃×#532	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	C₁₃×#525	1	2	yes	—
520	C₄	C₁₃×#532	1	2	yes	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	8	2	no	—
524	C₂	C₁₃×#2388	1	1	yes	characteristic
525	C₂	C₁₃×#3020	1	1	yes	characteristic
526	C₂	C₁₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#537	C₂²
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. C₄×C₁₃×#137	C₂	semidirect
3. C₁₃×#2327	C₂	semidirect
4. C₁₃×#2061	C₂	semidirect
6. C₁₃×#2038	C₂	semidirect
7. C₁₃×#2028	C₂	semidirect
9. C₁₃×#2005	C₂	semidirect
10. C₁₃×#1759	C₂	semidirect
11. C₄×C₁₃×#101	C₂	semidirect
118. #23594	C₁₃	direct (N × H)
189. C₄×#137	C₂×C₁₃	semidirect
190. #2327	C₂×C₁₃	semidirect
191. #2061	C₂×C₁₃	semidirect
193. #2038	C₂×C₁₃	semidirect
194. #2028	C₂×C₁₃	semidirect
196. #2005	C₂×C₁₃	semidirect
197. #1759	C₂×C₁₃	semidirect
198. C₄×#101	C₂×C₁₃	semidirect
450. C₁₃	#23594	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×#3461	2
C₄×C₁₃×#137	2
C₁₃×#2327	2
C₁₃×#2061	2
C₁₃×#2040	2
C₁₃×#2038	2
C₁₃×#2028	2
C₁₃×#2007	2
C₁₃×#2005	2
C₁₃×#1759	2
C₄×C₁₃×#101	2
#23594	13

Subgroups — C13×#23594 #15709933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23594 #15709933