Subgroups — C₁₃×#61665 #15748004

Order 3328.

2008 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3328	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3302	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×Q₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3276	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3202	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3011	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₁₃×#137	C₂²	1	4	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
15	C₁₃×#563	—	2	2	no	—
16	C₁₃×#559	—	2	1	no	—
17	Q₈²×C₁₃	—	2	1	no	—
18	C₁₃×#556	C₂²	1	4	yes	—
19	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
20	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
21	C₁₃×#547	—	2	4	no	—
22	C₁₃×#547	C₂²	1	4	yes	—
23	C₁₃×#542	—	2	4	no	—
24	C₁₃×#536	—	2	2	no	—
25	C₁₃×#536	C₂²	1	4	yes	—
26	C₁₃×#536	C₂²	1	2	yes	—
27	C₁₃×#533	C₂²	1	2	yes	—
28	C₁₃×#532	—	2	1	no	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
33	C₁₃×#494	C₂²	1	4	yes	—
34	C₁₃×#487	C₂²	1	4	yes	—
35	C₁₃×#485	C₂²	1	8	yes	—
36	C₁₃×#485	C₂²	1	4	yes	—
37	C₁₃×#475	C₂²	1	2	yes	—
38	C₁₃×#474	C₂²	1	2	yes	—
39	C₁₃×#470	C₂²	1	8	yes	—
40	C₁₃×#467	C₂²	1	8	yes	—
41	C₁₃×#462	C₂²	1	4	yes	—
42	C₁₃×#462	C₂²	1	2	yes	—
43	C₁₃×#462	C₂²	1	4	yes	—
44	C₁₃×#461	C₂²	1	2	yes	—
45	C₁₃×#452	C₂²	1	4	yes	—
46	C₁₃×#452	C₂²	1	8	yes	—
47	C₁₃×#451	C₂²	1	8	yes	—
48	C₁₃×#451	C₂²	1	8	yes	—
49	C₁₃×#451	C₂²	1	8	yes	—
50	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
51	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
52	C₁₃×#436	C₂²	1	4	yes	—
53	C₈×D₄×C₁₃	C₂²	1	4	yes	—
54	C₁₃×#431	C₂²	1	2	yes	—
55	C₁₃×#419	C₂²	1	4	yes	—
56	C₁₃×#416	C₂²	1	4	yes	—
57	C₁₃×#408	C₂²	1	4	yes	—
58	C₁₃×2₋¹⁺⁴	—	4	4	no	—
59	C₁₃×2₋¹⁺⁴	—	4	4	no	—
60	C₂×C₁₃×#41	—	2	2	no	—
61	C₂×C₁₃×#41	—	2	4	no	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂³	1	4	yes	—
64	C₂×C₁₃×#41	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
69	C₁₃×#137	—	4	8	no	—
70	C₂×C₁₃×Q₁₆	—	4	8	no	—
71	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
72	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	4	no	—
79	C₁₃×C₄⋊Q₈	—	2	4	no	—
80	C₁₃×C₄⋊Q₈	—	2	4	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×#127	D₄	1	1	yes	characteristic
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#125	—	2	2	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	—	2	4	no	—
92	C₁₃×#124	—	2	4	no	—
93	C₁₃×#124	D₄	1	2	yes	—
94	C₁₃×#123	—	2	4	no	—
95	C₁₃×#123	—	2	4	no	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×C₂²⋊Q₈	—	2	8	no	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	D₄	1	4	yes	—
106	C₄×Q₈×C₁₃	—	2	4	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	C₂³	1	2	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	—
115	C₁₃×#117	—	2	2	no	—
116	C₁₃×#117	—	2	1	no	—
117	C₁₃×#117	C₂³	1	4	yes	—
118	C₁₃×#117	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₄²×C₁₃	—	2	1	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#106	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₃×#103	C₂³	1	8	yes	—
128	C₁₃×#103	C₂³	1	4	yes	—
129	C₁₃×#103	C₂³	1	8	yes	—
130	C₁₃×#103	C₂³	1	4	yes	—
131	C₁₃×#103	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₄×C₈×C₁₃	C₂³	1	4	yes	—
136	#61665	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₁₃×#41	—	2	2	no	—
138	C₁₃×#41	—	2	2	no	—
139	C₁₃×#41	—	2	8	no	—
140	C₁₃×#41	—	4	2	no	—
141	C₁₃×#41	—	4	2	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	8	no	—
144	C₁₃×#41	—	4	16	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	8	no	—
150	C₂×Q₈×C₁₃	—	4	4	no	—
151	C₂×Q₈×C₁₃	—	4	2	no	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	—	4	8	no	—
154	C₂×Q₈×C₁₃	—	4	4	no	—
155	C₂×Q₈×C₁₃	—	4	4	no	—
156	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
158	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
159	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₁₃×Q₁₆	—	2	8	no	—
176	C₁₃×Q₁₆	—	4	8	no	—
177	C₁₃×Q₁₆	—	4	8	no	—
178	C₁₃×SD₁₆	—	2	8	no	—
179	C₁₃×M₁₆	—	4	4	no	—
180	C₂×C₈×C₁₃	—	4	4	no	—
181	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
182	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	2	4	no	—
206	C₄²×C₁₃	—	2	4	no	—
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	2	yes	—
210	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3499	C₂×C₁₃	1	1	yes	characteristic
212	#3328	C₂×C₁₃	1	4	yes	complemented
213	#3302	C₂×C₁₃	1	4	yes	complemented
214	D₄×Q₁₆	C₂×C₁₃	1	4	yes	complemented
215	#3276	C₂×C₁₃	1	4	yes	complemented
216	#3209	C₂×C₁₃	1	2	yes	complemented
217	#3202	C₂×C₁₃	1	4	yes	complemented
218	#3107	C₂×C₁₃	1	2	yes	complemented
219	#3011	C₂×C₁₃	1	4	yes	complemented
220	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	1	no	—
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	2	4	no	—
227	Q₈×C₁₃	—	2	4	no	—
228	Q₈×C₁₃	—	2	4	no	—
229	Q₈×C₁₃	—	4	2	no	—
230	Q₈×C₁₃	—	4	8	no	—
231	Q₈×C₁₃	—	4	4	no	—
232	Q₈×C₁₃	—	4	4	no	—
233	Q₈×C₁₃	—	8	4	no	—
234	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	8	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	8	no	—
241	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	4	8	no	—
254	C₂×C₄×C₁₃	—	4	8	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	4	no	—
257	C₂×C₄×C₁₃	—	8	4	no	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
263	C₈×C₁₃	—	2	4	no	—
264	C₈×C₁₃	—	2	4	no	—
265	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
266	C₂×#137	C₂²×C₁₃	1	4	yes	—
267	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
268	#563	—	2	2	no	—
269	#559	—	2	1	no	—
270	Q₈²	—	2	1	no	—
271	#556	C₂²×C₁₃	1	4	yes	—
272	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
273	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
274	#547	—	2	4	no	—
275	#547	C₂²×C₁₃	1	4	yes	—
276	#542	—	2	4	no	—
277	#536	—	2	2	no	—
278	#536	C₂²×C₁₃	1	2	yes	—
279	#536	C₂²×C₁₃	1	4	yes	—
280	#533	C₂²×C₁₃	1	2	yes	—
281	#532	—	2	1	no	—
282	#532	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊Q₈	—	2	1	no	—
284	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
286	#494	C₂²×C₁₃	1	4	yes	—
287	#487	C₂²×C₁₃	1	4	yes	—
288	#485	C₂²×C₁₃	1	8	yes	—
289	#485	C₂²×C₁₃	1	4	yes	—
290	#475	C₂²×C₁₃	1	2	yes	—
291	#474	C₂²×C₁₃	1	2	yes	—
292	#470	C₂²×C₁₃	1	8	yes	—
293	#467	C₂²×C₁₃	1	8	yes	—
294	#462	C₂²×C₁₃	1	4	yes	—
295	#462	C₂²×C₁₃	1	2	yes	—
296	#462	C₂²×C₁₃	1	4	yes	—
297	#461	C₂²×C₁₃	1	2	yes	—
298	#452	C₂²×C₁₃	1	4	yes	—
299	#452	C₂²×C₁₃	1	8	yes	—
300	#451	C₂²×C₁₃	1	8	yes	—
301	#451	C₂²×C₁₃	1	8	yes	—
302	#451	C₂²×C₁₃	1	8	yes	—
303	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
304	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
305	#436	C₂²×C₁₃	1	4	yes	—
306	C₈×D₄	C₂²×C₁₃	1	4	yes	—
307	#431	C₂²×C₁₃	1	2	yes	—
308	#419	C₂²×C₁₃	1	4	yes	—
309	#416	C₂²×C₁₃	1	4	yes	—
310	#408	C₂²×C₁₃	1	4	yes	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	4	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	8	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	4	4	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	#578	1	4	yes	—
327	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	2₋¹⁺⁴	—	4	4	no	—
330	2₋¹⁺⁴	—	4	4	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×#41	C₂³×C₁₃	1	4	yes	—
335	C₂×#41	C₂³×C₁₃	1	2	yes	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
338	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
339	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
340	#137	—	4	8	no	—
341	C₂×Q₁₆	—	4	8	no	—
342	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
343	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
344	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
345	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
346	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	—	2	4	no	—
350	C₄⋊Q₈	—	2	4	no	—
351	C₄⋊Q₈	—	2	4	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
356	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
357	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
358	#127	D₄×C₁₃	1	1	yes	characteristic
359	#126	—	2	8	no	—
360	#125	—	2	2	no	—
361	#124	—	2	2	no	—
362	#124	—	2	4	no	—
363	#124	—	2	4	no	—
364	#124	D₄×C₁₃	1	2	yes	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	#123	—	2	4	no	—
368	#123	—	2	8	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	8	no	—
371	C₂²⋊Q₈	—	2	8	no	—
372	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
373	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
375	#121	—	2	4	no	—
376	#121	D₄×C₁₃	1	4	yes	—
377	C₄×Q₈	—	2	4	no	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
380	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	C₂³×C₁₃	1	2	yes	—
385	C₄×D₄	C₂³×C₁₃	1	4	yes	—
386	#117	—	2	2	no	—
387	#117	—	2	1	no	—
388	#117	C₂³×C₁₃	1	1	yes	characteristic
389	#117	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	4	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
394	#107	C₂³×C₁₃	1	4	yes	—
395	#106	C₂³×C₁₃	1	4	yes	—
396	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
397	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
398	#103	C₂³×C₁₃	1	8	yes	—
399	#103	C₂³×C₁₃	1	4	yes	—
400	#103	C₂³×C₁₃	1	8	yes	—
401	#103	C₂³×C₁₃	1	4	yes	—
402	#103	C₂³×C₁₃	1	4	yes	—
403	#102	C₂³×C₁₃	1	4	yes	—
404	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
405	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
406	C₄×C₈	C₂³×C₁₃	1	4	yes	—
407	C₂×C₁₃	—	4	1	no	—
408	C₂×C₁₃	—	4	4	no	—
409	C₂×C₁₃	—	4	2	no	—
410	C₂×C₁₃	#3484	1	1	yes	characteristic
411	C₂×C₁₃	C₂×#578	1	2	yes	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	8	no	—
415	#41	—	4	2	no	—
416	#41	—	4	2	no	—
417	#41	—	4	4	no	—
418	#41	—	4	8	no	—
419	#41	—	4	16	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	8	no	—
425	C₂×Q₈	—	4	4	no	—
426	C₂×Q₈	—	4	2	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×Q₈	—	4	8	no	—
429	C₂×Q₈	—	4	4	no	—
430	C₂×Q₈	—	4	4	no	—
431	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
432	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
433	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
434	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
450	Q₁₆	—	2	8	no	—
451	Q₁₆	—	4	8	no	—
452	Q₁₆	—	4	8	no	—
453	SD₁₆	—	2	8	no	—
454	M₁₆	—	4	4	no	—
455	C₂×C₈	—	4	4	no	—
456	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
457	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	2	4	no	—
482	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₄²	C₂⁴×C₁₃	1	2	yes	—
485	C₁₃	#61665	1	1	yes	characteristic, direct product factor, Sylow
486	C₂³	—	2	1	no	—
487	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	2	4	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	8	no	—
496	Q₈	—	4	4	no	—
497	Q₈	—	4	4	no	—
498	Q₈	—	8	4	no	—
499	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
500	D₄	—	2	4	no	—
501	D₄	—	2	8	no	—
502	D₄	—	2	1	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	8	no	—
506	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
525	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
527	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
528	C₈	—	2	4	no	—
529	C₈	—	2	4	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	8	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
537	C₄	—	2	2	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	4	no	—
545	C₄	C₁₃×#578	1	4	yes	—
546	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
547	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂	—	4	1	no	—
549	C₂	—	4	4	no	—
550	C₂	—	4	2	no	—
551	C₂	C₁₃×#3484	1	1	yes	characteristic
552	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
3. C₁₃×#3328	C₂	semidirect
4. C₁₃×#3302	C₂	semidirect
5. D₄×C₁₃×Q₁₆	C₂	semidirect
6. C₁₃×#3276	C₂	semidirect
7. C₁₃×#3209	C₂	semidirect
8. C₁₃×#3202	C₂	semidirect
9. C₁₃×#3107	C₂	semidirect
10. C₁₃×#3011	C₂	semidirect
11. C₁₃×#2979	C₂	semidirect
136. #61665	C₁₃	direct (N × H)
210. #3550	C₂×C₁₃	semidirect
212. #3328	C₂×C₁₃	semidirect
213. #3302	C₂×C₁₃	semidirect
214. D₄×Q₁₆	C₂×C₁₃	semidirect
215. #3276	C₂×C₁₃	semidirect
216. #3209	C₂×C₁₃	semidirect
217. #3202	C₂×C₁₃	semidirect
218. #3107	C₂×C₁₃	semidirect
219. #3011	C₂×C₁₃	semidirect
220. #2979	C₂×C₁₃	semidirect
485. C₁₃	#61665	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×#3550	2
C₁₃×#3499	2
C₁₃×#3328	2
C₁₃×#3302	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3276	2
C₁₃×#3209	2
C₁₃×#3202	2
C₁₃×#3107	2
C₁₃×#3011	2
C₁₃×#2979	2
#61665	13

Subgroups — C13×#61665 #15748004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61665 #15748004