Subgroups — C₁₃×#23589 #15709928

Order 3328.

1138 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×#3460	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₃×#124	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, complemented
6	C₁₃×#2037	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, complemented
9	C₁₃×#2004	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#100	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×#540	—	2	2	no	—
16	C₁₃×#538	—	2	2	no	—
17	C₁₃×#537	C₂²	1	1	yes	characteristic
18	C₁₃×#535	C₂²	1	2	yes	—
19	C₁₃×#532	—	2	2	no	—
20	C₁₃×#529	—	2	2	no	—
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₁₃×#525	—	2	2	no	—
23	C₄×C₁₃×#41	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×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×#100	C₂²	1	2	yes	—
36	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	2	2	no	—
40	C₁₃×#382	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
42	C₄³×C₁₃	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	—	2	2	no	—
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	2	yes	—
52	C₁₃×#137	—	2	4	no	—
53	C₁₃×#137	—	2	4	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×#126	—	2	4	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#124	—	2	4	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×#124	—	2	2	no	—
66	C₁₃×#123	—	2	4	no	—
67	C₁₃×#123	—	2	4	no	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	—	2	2	no	—
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#120	—	2	4	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	D₄	1	2	yes	—
81	C₄×Q₈×C₁₃	D₄	1	2	yes	—
82	C₄×D₄×C₁₃	—	2	4	no	—
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	—	2	2	no	—
87	C₄×D₄×C₁₃	D₄	1	2	yes	—
88	C₄×D₄×C₁₃	D₄	1	2	yes	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	—	2	2	no	—
91	C₁₃×#117	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
98	C₂×C₄²×C₁₃	—	2	2	no	—
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	2	no	—
106	C₁₃×#106	—	2	2	no	—
107	C₁₃×#104	—	2	4	no	—
108	C₁₃×#104	—	2	4	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#100	—	2	4	no	—
114	C₁₃×#97	—	2	2	no	—
115	C₄×C₈×C₁₃	—	2	2	no	—
116	C₁₃×#95	—	2	2	no	—
117	C₁₃×#95	—	2	2	no	—
118	#23589	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	8	4	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₁₃×Q₁₆	—	2	8	no	—
155	C₁₃×SD₁₆	—	2	8	no	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₁₃×M₁₆	—	2	2	no	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	#41	1	4	yes	complemented
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₁₃×C₂²⋊C₄	—	4	4	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	2	no	—
186	C₄²×C₁₃	—	4	2	no	—
187	C₄²×C₁₃	—	4	2	no	—
188	C₄²×C₁₃	—	4	1	no	—
189	C₄²×C₁₃	—	4	1	no	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂×D₄	1	2	yes	—
192	C₄²×C₁₃	#41	1	2	yes	complemented
193	#3460	C₂×C₁₃	1	1	yes	characteristic
194	C₄×#137	C₂×C₁₃	1	2	yes	complemented
195	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#2037	C₂×C₁₃	1	2	yes	complemented
199	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2007	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2004	C₂×C₁₃	1	2	yes	complemented
202	C₄×#104	C₂×C₁₃	1	2	yes	complemented
203	C₄×#100	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	4	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	8	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	D₄×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	8	4	no	—
223	D₄×C₁₃	—	8	2	no	—
224	D₄×C₁₃	—	8	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	8	2	no	—
248	C₂×C₄×C₁₃	—	8	2	no	—
249	C₂×C₄×C₁₃	#120	1	2	yes	—
250	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₈×C₁₃	—	2	4	no	—
257	C₈×C₁₃	—	4	2	no	—
258	C₂×#137	C₂²×C₁₃	1	2	yes	—
259	#544	C₂²×C₁₃	1	1	yes	characteristic
260	#542	—	2	2	no	—
261	#540	—	2	2	no	—
262	#538	—	2	2	no	—
263	#537	C₂²×C₁₃	1	1	yes	characteristic
264	#535	C₂²×C₁₃	1	2	yes	—
265	#532	—	2	2	no	—
266	#529	—	2	2	no	—
267	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
268	#525	—	2	2	no	—
269	C₄×#41	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
272	#441	—	2	2	no	—
273	#440	—	2	2	no	—
274	C₄×Q₁₆	—	2	2	no	—
275	C₄×SD₁₆	—	2	2	no	—
276	#428	C₂²×C₁₃	1	2	yes	—
277	C₂×#104	C₂²×C₁₃	1	2	yes	—
278	C₂×#104	C₂²×C₁₃	1	2	yes	—
279	#419	C₂²×C₁₃	1	2	yes	—
280	#417	C₂²×C₁₃	1	2	yes	—
281	C₂×#100	C₂²×C₁₃	1	2	yes	—
282	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
283	#391	C₂²×C₁₃	1	1	yes	characteristic
284	#390	C₂²×C₁₃	1	1	yes	characteristic
285	#388	—	2	2	no	—
286	#382	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	—	2	2	no	—
288	C₄³	C₂²×C₁₃	1	1	yes	characteristic
289	#343	C₂²×C₁₃	1	1	yes	characteristic
290	#343	C₂²×C₁₃	1	1	yes	characteristic
291	#339	C₂²×C₁₃	1	2	yes	—
292	#339	C₂²×C₁₃	1	2	yes	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	8	2	no	—
303	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
304	C₂²×C₁₃	#525	1	1	yes	characteristic
305	C₂²×C₁₃	#532	1	1	yes	characteristic
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	8	1	no	—
316	C₄×C₁₃	#455	1	2	yes	—
317	C₄×C₁₃	#525	1	2	yes	—
318	C₄×C₁₃	#532	1	2	yes	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	C₂³×C₁₃	1	2	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂³×C₄	D₄×C₁₃	1	2	yes	—
324	#137	—	2	4	no	—
325	#137	—	2	4	no	—
326	C₂×Q₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	2	2	no	—
328	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
329	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
330	C₄⋊Q₈	—	2	2	no	—
331	#127	—	2	2	no	—
332	#126	—	2	4	no	—
333	#125	—	2	2	no	—
334	#124	—	2	4	no	—
335	#124	—	2	2	no	—
336	#124	—	2	2	no	—
337	#124	—	2	2	no	—
338	#123	—	2	4	no	—
339	#123	—	2	4	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	4	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#120	—	2	4	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	D₄×C₁₃	1	2	yes	—
353	C₄×Q₈	D₄×C₁₃	1	2	yes	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	D₄×C₁₃	1	2	yes	—
360	C₄×D₄	D₄×C₁₃	1	2	yes	—
361	#117	—	2	2	no	—
362	#117	—	2	2	no	—
363	#117	C₂³×C₁₃	1	2	yes	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	#107	—	2	2	no	—
378	#106	—	2	2	no	—
379	#104	—	2	4	no	—
380	#104	—	2	4	no	—
381	#103	—	2	2	no	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#102	—	2	2	no	—
385	#100	—	2	4	no	—
386	#97	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	C₂×C₁₃	—	2	1	no	—
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	—	8	2	no	—
393	C₂×C₁₃	—	8	2	no	—
394	C₂×C₁₃	#2388	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
396	C₂×C₁₃	#3018	1	1	yes	characteristic
397	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	8	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
408	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
432	Q₁₆	—	2	8	no	—
433	SD₁₆	—	2	8	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	C₁₃×#41	1	4	yes	complemented
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	4	2	no	—
465	C₄²	—	4	2	no	—
466	C₄²	—	4	1	no	—
467	C₄²	—	4	1	no	—
468	C₄²	C₂×D₄×C₁₃	1	2	yes	—
469	C₄²	C₂×D₄×C₁₃	1	2	yes	—
470	C₄²	C₁₃×#41	1	2	yes	complemented
471	C₁₃	#23589	1	1	yes	characteristic, direct product factor, Sylow
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
479	Q₈	—	2	4	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	8	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	4	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	C₁₃×#120	1	2	yes	—
518	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
519	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
524	C₈	—	2	4	no	—
525	C₈	—	4	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
537	C₂²	C₁₃×#525	1	1	yes	characteristic
538	C₂²	C₁₃×#532	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	1	no	—
549	C₄	C₁₃×#455	1	2	yes	—
550	C₄	C₁₃×#525	1	2	yes	—
551	C₄	C₁₃×#532	1	2	yes	—
552	C₂	—	2	1	no	—
553	C₂	—	2	1	no	—
554	C₂	—	8	2	no	—
555	C₂	—	8	2	no	—
556	C₂	C₁₃×#2388	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#455	1	1	yes	characteristic
558	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×#120
prime radical	C₁₃×#3460	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₄×C₁₃×#124	C₂	semidirect
4. C₁₃×#2061	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2037	C₂	semidirect
7. C₁₃×#2028	C₂	semidirect
8. C₁₃×#2007	C₂	semidirect
9. C₁₃×#2004	C₂	semidirect
10. C₄×C₁₃×#104	C₂	semidirect
11. C₄×C₁₃×#100	C₂	semidirect
118. #23589	C₁₃	direct (N × H)
130. C₂×Q₈×C₁₃	#41	semidirect
159. C₁₃×M₁₆	#41	semidirect
192. C₄²×C₁₃	#41	semidirect
194. C₄×#137	C₂×C₁₃	semidirect
195. C₄×#124	C₂×C₁₃	semidirect
196. #2061	C₂×C₁₃	semidirect
197. #2040	C₂×C₁₃	semidirect
198. #2037	C₂×C₁₃	semidirect
199. #2028	C₂×C₁₃	semidirect
200. #2007	C₂×C₁₃	semidirect
201. #2004	C₂×C₁₃	semidirect
202. C₄×#104	C₂×C₁₃	semidirect
203. C₄×#100	C₂×C₁₃	semidirect
408. C₂×Q₈	C₁₃×#41	semidirect
437. M₁₆	C₁₃×#41	semidirect
470. C₄²	C₁₃×#41	semidirect
471. C₁₃	#23589	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×#3460	2
C₄×C₁₃×#137	2
C₄×C₁₃×#124	2
C₁₃×#2061	2
C₁₃×#2040	2
C₁₃×#2037	2
C₁₃×#2028	2
C₁₃×#2007	2
C₁₃×#2004	2
C₄×C₁₃×#104	2
C₄×C₁₃×#100	2
#23589	13

Subgroups — C13×#23589 #15709928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23589 #15709928