Subgroups — C₁₃×#60685 #15747024

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3179	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3178	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3131	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3054	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3050	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2943	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#135	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#542	C₂²	1	8	yes	—
17	C₁₃×#541	C₂²	1	4	yes	—
18	C₁₃×#540	C₂²	1	4	yes	—
19	C₁₃×#539	—	2	4	no	—
20	C₁₃×#538	—	2	4	no	—
21	C₁₃×#533	C₂²	1	2	yes	—
22	C₁₃×#532	C₂²	1	2	yes	—
23	C₁₃×#529	—	2	8	no	—
24	C₁₃×#525	C₂²	1	4	yes	—
25	C₄×C₁₃×#41	C₂²	1	4	yes	—
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₁₃×#501	C₂²	1	8	yes	complemented
28	C₁₃×#497	C₂²	1	4	yes	complemented
29	C₁₃×#496	C₂²	1	4	yes	complemented
30	C₁₃×#488	C₂²	1	8	yes	complemented
31	C₁₃×#487	C₂²	1	4	yes	complemented
32	C₁₃×#486	C₂²	1	4	yes	complemented
33	C₁₃×#470	C₂²	1	4	yes	—
34	C₁₃×#469	C₂²	1	4	yes	—
35	C₁₃×#468	C₂²	1	8	yes	—
36	C₁₃×#467	C₂²	1	4	yes	—
37	C₁₃×#466	C₂²	1	4	yes	—
38	C₁₃×#465	C₂²	1	8	yes	—
39	C₁₃×#442	C₂²	1	4	yes	complemented
40	C₁₃×#441	C₂²	1	4	yes	complemented
41	C₁₃×#440	C₂²	1	8	yes	complemented
42	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
43	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
44	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
45	C₁₃×#427	C₂²	1	2	yes	—
46	C₁₃×#427	C₂²	1	2	yes	—
47	C₁₃×#416	C₂²	1	4	yes	—
48	C₁₃×#416	C₂²	1	4	yes	—
49	C₁₃×#405	C₂²	1	8	yes	—
50	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#41	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#135	—	2	8	no	—
57	C₁₃×#135	—	2	8	no	—
58	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
62	C₂×C₁₃×D₈	C₂³	1	2	yes	—
63	C₂×C₁₃×D₈	C₂³	1	2	yes	—
64	C₂×C₁₃×M₁₆	—	2	4	no	—
65	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
66	C₂²×C₈×C₁₃	—	2	4	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₁₃×#127	C₂³	1	2	yes	—
75	C₁₃×#126	—	2	8	no	—
76	C₁₃×#126	—	2	8	no	—
77	C₁₃×#125	—	2	8	no	—
78	C₁₃×#125	C₂³	1	4	yes	—
79	C₁₃×#124	—	2	8	no	—
80	C₁₃×#124	C₂³	1	4	yes	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×#123	—	2	8	no	—
83	C₁₃×#123	—	2	8	no	—
84	C₁₃×C₂²⋊Q₈	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
87	C₁₃×#121	—	2	4	no	—
88	C₁₃×#121	—	2	8	no	—
89	C₁₃×#121	C₂³	1	8	yes	—
90	C₁₃×#120	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
93	C₄×D₄×C₁₃	—	2	8	no	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	C₂³	1	8	yes	—
97	C₁₃×#117	—	2	4	no	—
98	C₁₃×#117	D₄	1	4	yes	—
99	C₁₃×#117	C₂³	1	4	yes	—
100	C₁₃×#117	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	4	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#107	C₂³	1	4	yes	—
107	C₁₃×#107	C₂³	1	4	yes	—
108	C₁₃×#106	C₂³	1	4	yes	—
109	C₁₃×#106	C₂³	1	4	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#103	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×#102	C₂³	1	8	yes	—
114	C₁₃×#97	C₂³	1	4	yes	—
115	C₁₃×#97	C₂³	1	4	yes	—
116	C₄×C₈×C₁₃	C₂³	1	4	yes	—
117	C₄×C₈×C₁₃	C₂³	1	4	yes	—
118	#60685	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×Q₁₆	—	2	4	no	—
139	C₁₃×Q₁₆	—	2	4	no	—
140	C₁₃×SD₁₆	—	2	8	no	—
141	C₁₃×SD₁₆	—	2	8	no	—
142	C₁₃×D₈	—	2	4	no	—
143	C₁₃×D₈	—	2	4	no	—
144	C₁₃×M₁₆	—	2	8	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	8	no	—
148	C₂×C₈×C₁₃	#41	1	4	yes	—
149	C₂×C₈×C₁₃	#41	1	4	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
152	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
153	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	C₂×D₄	1	2	yes	—
170	C₄²×C₁₃	C₂×D₄	1	2	yes	—
171	C₄²×C₁₃	C₂⁴	1	2	yes	—
172	C₄²×C₁₃	C₂⁴	1	2	yes	—
173	#3455	C₂×C₁₃	1	2	yes	complemented
174	#3179	C₂×C₁₃	1	8	yes	complemented
175	#3178	C₂×C₁₃	1	8	yes	complemented
176	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#3131	C₂×C₁₃	1	2	yes	complemented
179	#3054	C₂×C₁₃	1	2	yes	complemented
180	#3050	C₂×C₁₃	1	2	yes	complemented
181	#2943	C₂×C₁₃	1	2	yes	complemented
182	C₄×#135	C₂×C₁₃	1	2	yes	complemented
183	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
188	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₃	—	2	4	no	—
190	Q₈×C₁₃	—	2	4	no	—
191	Q₈×C₁₃	—	8	4	no	—
192	D₄×C₁₃	—	2	4	no	—
193	D₄×C₁₃	—	2	4	no	—
194	D₄×C₁₃	—	4	8	no	—
195	D₄×C₁₃	—	8	4	no	—
196	D₄×C₁₃	—	8	8	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	8	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	8	no	—
206	C₂×C₄×C₁₃	—	8	8	no	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
214	C₈×C₁₃	—	2	2	no	—
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	C₂×#41	1	4	yes	—
217	C₈×C₁₃	C₂×#41	1	4	yes	—
218	C₂×#135	C₂²×C₁₃	1	2	yes	—
219	C₂×#135	C₂²×C₁₃	1	2	yes	—
220	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
221	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	#542	C₂²×C₁₃	1	8	yes	—
223	#541	C₂²×C₁₃	1	4	yes	—
224	#540	C₂²×C₁₃	1	4	yes	—
225	#539	—	2	4	no	—
226	#538	—	2	4	no	—
227	#533	C₂²×C₁₃	1	2	yes	—
228	#532	C₂²×C₁₃	1	2	yes	—
229	#529	—	2	8	no	—
230	#525	C₂²×C₁₃	1	4	yes	—
231	C₄×#41	C₂²×C₁₃	1	4	yes	—
232	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
233	#501	C₂²×C₁₃	1	8	yes	complemented
234	#497	C₂²×C₁₃	1	4	yes	complemented
235	#496	C₂²×C₁₃	1	4	yes	complemented
236	#488	C₂²×C₁₃	1	8	yes	complemented
237	#487	C₂²×C₁₃	1	4	yes	complemented
238	#486	C₂²×C₁₃	1	4	yes	complemented
239	#470	C₂²×C₁₃	1	4	yes	—
240	#469	C₂²×C₁₃	1	4	yes	—
241	#468	C₂²×C₁₃	1	8	yes	—
242	#467	C₂²×C₁₃	1	4	yes	—
243	#466	C₂²×C₁₃	1	4	yes	—
244	#465	C₂²×C₁₃	1	8	yes	—
245	#442	C₂²×C₁₃	1	4	yes	complemented
246	#441	C₂²×C₁₃	1	4	yes	complemented
247	#440	C₂²×C₁₃	1	8	yes	complemented
248	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
249	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
250	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
251	#427	C₂²×C₁₃	1	2	yes	—
252	#427	C₂²×C₁₃	1	2	yes	—
253	#416	C₂²×C₁₃	1	4	yes	—
254	#416	C₂²×C₁₃	1	4	yes	—
255	#405	C₂²×C₁₃	1	8	yes	—
256	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	4	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	—	4	8	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	#532	1	2	yes	—
267	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
268	C₄×C₁₃	—	2	4	no	—
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	8	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	#532	1	2	yes	—
274	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
275	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
276	C₂×#41	C₂³×C₁₃	1	4	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
278	#135	—	2	8	no	—
279	#135	—	2	8	no	—
280	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
281	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
282	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
283	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
284	C₂×D₈	C₂³×C₁₃	1	2	yes	—
285	C₂×D₈	C₂³×C₁₃	1	2	yes	—
286	C₂×M₁₆	—	2	4	no	—
287	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
288	C₂²×C₈	—	2	4	no	—
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
296	#127	C₂³×C₁₃	1	2	yes	—
297	#126	—	2	8	no	—
298	#126	—	2	8	no	—
299	#125	—	2	8	no	—
300	#125	C₂³×C₁₃	1	4	yes	—
301	#124	—	2	8	no	—
302	#124	C₂³×C₁₃	1	4	yes	—
303	#123	—	2	4	no	—
304	#123	—	2	8	no	—
305	#123	—	2	8	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
309	#121	—	2	4	no	—
310	#121	—	2	8	no	—
311	#121	C₂³×C₁₃	1	8	yes	—
312	#120	—	2	4	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
315	C₄×D₄	—	2	8	no	—
316	C₄×D₄	—	2	8	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	C₂³×C₁₃	1	8	yes	—
319	#117	—	2	4	no	—
320	#117	D₄×C₁₃	1	4	yes	—
321	#117	C₂³×C₁₃	1	4	yes	—
322	#117	C₂³×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
324	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
325	C₂×C₄²	—	2	4	no	—
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
328	#107	C₂³×C₁₃	1	4	yes	—
329	#107	C₂³×C₁₃	1	4	yes	—
330	#106	C₂³×C₁₃	1	4	yes	—
331	#106	C₂³×C₁₃	1	4	yes	—
332	#103	C₂³×C₁₃	1	8	yes	—
333	#103	C₂³×C₁₃	1	8	yes	—
334	#102	C₂³×C₁₃	1	8	yes	—
335	#102	C₂³×C₁₃	1	8	yes	—
336	#97	C₂³×C₁₃	1	4	yes	—
337	#97	C₂³×C₁₃	1	4	yes	—
338	C₄×C₈	C₂³×C₁₃	1	4	yes	—
339	C₄×C₈	C₂³×C₁₃	1	4	yes	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	4	2	no	—
342	C₂×C₁₃	—	8	4	no	—
343	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
344	C₂×C₁₃	#3584	1	2	yes	—
345	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
346	#41	—	2	8	no	—
347	#41	—	2	8	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
364	Q₁₆	—	2	4	no	—
365	Q₁₆	—	2	4	no	—
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	2	8	no	—
368	D₈	—	2	4	no	—
369	D₈	—	2	4	no	—
370	M₁₆	—	2	8	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	8	no	—
374	C₂×C₈	C₁₃×#41	1	4	yes	—
375	C₂×C₈	C₁₃×#41	1	4	yes	—
376	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
377	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
378	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
379	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
386	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	8	no	—
395	C₄²	C₂×D₄×C₁₃	1	2	yes	—
396	C₄²	C₂×D₄×C₁₃	1	2	yes	—
397	C₄²	C₂⁴×C₁₃	1	2	yes	—
398	C₄²	C₂⁴×C₁₃	1	2	yes	—
399	C₁₃	#60685	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
405	Q₈	—	2	4	no	—
406	Q₈	—	2	4	no	—
407	Q₈	—	8	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	4	8	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
428	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
429	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	C₂×C₁₃×#41	1	4	yes	—
433	C₈	C₂×C₁₃×#41	1	4	yes	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	4	no	—
440	C₂²	C₁₃×#532	1	2	yes	—
441	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	8	no	—
446	C₄	—	4	4	no	—
447	C₄	C₁₃×#532	1	2	yes	—
448	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
449	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
450	C₂	—	2	2	no	—
451	C₂	—	4	2	no	—
452	C₂	—	8	4	no	—
453	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
454	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₁₃×#3179	C₂	semidirect
3. C₁₃×#3178	C₂	semidirect
4. C₁₃×#3162	C₂	semidirect
5. C₁₃×#3150	C₂	semidirect
6. C₁₃×#3131	C₂	semidirect
7. C₁₃×#3054	C₂	semidirect
8. C₁₃×#3050	C₂	semidirect
9. C₁₃×#2943	C₂	semidirect
10. C₄×C₁₃×#135	C₂	semidirect
11. C₂×C₁₃×#405	C₂	semidirect
27. C₁₃×#501	C₂²	semidirect
28. C₁₃×#497	C₂²	semidirect
29. C₁₃×#496	C₂²	semidirect
30. C₁₃×#488	C₂²	semidirect
31. C₁₃×#487	C₂²	semidirect
32. C₁₃×#486	C₂²	semidirect
39. C₁₃×#442	C₂²	semidirect
40. C₁₃×#441	C₂²	semidirect
41. C₁₃×#440	C₂²	semidirect
42. C₄×C₁₃×Q₁₆	C₂²	semidirect
43. C₄×C₁₃×SD₁₆	C₂²	semidirect
44. C₄×C₁₃×D₈	C₂²	semidirect
118. #60685	C₁₃	direct (N × H)
173. #3455	C₂×C₁₃	semidirect
174. #3179	C₂×C₁₃	semidirect
175. #3178	C₂×C₁₃	semidirect
176. #3162	C₂×C₁₃	semidirect
177. #3150	C₂×C₁₃	semidirect
178. #3131	C₂×C₁₃	semidirect
179. #3054	C₂×C₁₃	semidirect
180. #3050	C₂×C₁₃	semidirect
181. #2943	C₂×C₁₃	semidirect
182. C₄×#135	C₂×C₁₃	semidirect
183. C₂×#405	C₂×C₁₃	semidirect
233. #501	C₂²×C₁₃	semidirect
234. #497	C₂²×C₁₃	semidirect
235. #496	C₂²×C₁₃	semidirect
236. #488	C₂²×C₁₃	semidirect
237. #487	C₂²×C₁₃	semidirect
238. #486	C₂²×C₁₃	semidirect
245. #442	C₂²×C₁₃	semidirect
246. #441	C₂²×C₁₃	semidirect
247. #440	C₂²×C₁₃	semidirect
248. C₄×Q₁₆	C₂²×C₁₃	semidirect
249. C₄×SD₁₆	C₂²×C₁₃	semidirect
250. C₄×D₈	C₂²×C₁₃	semidirect
399. C₁₃	#60685	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×#3455	2
C₁₃×#3179	2
C₁₃×#3178	2
C₁₃×#3162	2
C₁₃×#3150	2
C₁₃×#3131	2
C₁₃×#3054	2
C₁₃×#3050	2
C₁₃×#2943	2
C₄×C₁₃×#135	2
C₂×C₁₃×#405	2
#60685	13

Subgroups — C13×#60685 #15747024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60685 #15747024