Subgroups — C₁₃×#61015 #15747354

Order 3328.

1768 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3263	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3229	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3227	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3204	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3167	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3125	C₂	1	8	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#556	—	2	2	no	—
14	C₁₃×#555	—	2	2	no	—
15	C₁₃×#554	—	2	2	no	—
16	C₁₃×#553	—	2	2	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#548	—	2	2	no	—
19	C₁₃×#548	—	2	2	no	—
20	C₁₃×#547	—	2	2	no	—
21	C₁₃×#542	C₂²	1	4	yes	—
22	C₁₃×#542	C₂²	1	4	yes	—
23	C₁₃×#537	C₂²	1	4	yes	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	2	yes	—
26	C₁₃×#532	C₂²	1	2	yes	—
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
30	C₁₃×#520	C₂²	1	4	yes	—
31	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
32	C₁₃×#498	C₂²	1	2	yes	—
33	C₁₃×#498	C₂²	1	1	yes	characteristic
34	C₁₃×#498	C₂²	1	1	yes	characteristic
35	C₁₃×#494	C₂²	1	1	yes	characteristic
36	C₁₃×#493	C₂²	1	1	yes	characteristic
37	C₁₃×#492	C₂²	1	2	yes	—
38	C₁₃×#487	C₂²	1	2	yes	—
39	C₁₃×#487	C₂²	1	2	yes	—
40	C₁₃×#486	C₂²	1	2	yes	—
41	C₁₃×#486	C₂²	1	2	yes	—
42	C₁₃×#483	C₂²	1	8	yes	—
43	C₁₃×#481	C₂²	1	8	yes	—
44	C₁₃×#476	C₂²	1	8	yes	—
45	C₁₃×#475	C₂²	1	8	yes	—
46	C₁₃×#470	C₂²	1	4	yes	—
47	C₁₃×#469	C₂²	1	4	yes	—
48	C₁₃×#465	C₂²	1	8	yes	—
49	C₁₃×#464	C₂²	1	8	yes	—
50	C₁₃×#463	C₂²	1	8	yes	—
51	C₁₃×#452	C₂²	1	8	yes	—
52	C₁₃×#449	C₂²	1	8	yes	—
53	C₁₃×#442	C₂²	1	4	yes	—
54	C₁₃×#441	C₂²	1	4	yes	—
55	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
56	C₁₃×#433	C₂²	1	4	yes	—
57	C₁₃×#431	C₂²	1	2	yes	—
58	C₁₃×#431	C₂²	1	2	yes	—
59	C₁₃×#424	C₂²	1	2	yes	—
60	C₁₃×#408	C₂²	1	2	yes	—
61	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
69	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×D₈	C₂³	1	4	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×C₄⋊Q₈	—	2	2	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₃×#127	C₂³	1	2	yes	—
80	C₁₃×#126	—	2	4	no	—
81	C₁₃×#126	—	2	4	no	—
82	C₁₃×#125	—	2	2	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	—	2	2	no	—
87	C₁₃×#124	—	2	2	no	—
88	C₁₃×#124	C₂³	1	4	yes	—
89	C₁₃×#123	—	2	4	no	—
90	C₁₃×#123	—	2	4	no	—
91	C₁₃×C₂²⋊Q₈	—	2	4	no	—
92	C₁₃×C₂²⋊Q₈	—	2	2	no	—
93	C₁₃×C₂²⋊Q₈	—	2	2	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	C₂³	1	4	yes	—
106	C₁₃×#121	C₂³	1	4	yes	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	—	2	2	no	—
109	C₄×Q₈×C₁₃	D₄	1	2	yes	—
110	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
111	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	D₄	1	2	yes	—
119	C₄×D₄×C₁₃	D₄	1	2	yes	—
120	C₄×D₄×C₁₃	D₄	1	2	yes	—
121	C₄×D₄×C₁₃	C₂³	1	4	yes	—
122	C₄×D₄×C₁₃	C₂³	1	4	yes	—
123	C₁₃×#117	—	2	2	no	—
124	C₁₃×#117	—	2	2	no	—
125	C₁₃×#117	—	2	4	no	—
126	C₁₃×#117	C₂³	1	1	yes	characteristic
127	C₁₃×#117	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₁₃×#106	C₂³	1	8	yes	—
134	C₁₃×#106	C₂³	1	4	yes	—
135	C₁₃×#106	C₂³	1	4	yes	—
136	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
138	C₁₃×#103	C₂³	1	8	yes	—
139	C₁₃×#103	C₂³	1	8	yes	—
140	C₁₃×#102	C₂³	1	8	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×#97	C₂³	1	2	yes	—
145	C₄×C₈×C₁₃	C₂³	1	2	yes	—
146	C₄×C₈×C₁₃	C₂³	1	2	yes	—
147	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	#61015	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃×#41	—	4	2	no	—
151	C₁₃×#41	—	4	8	no	—
152	C₁₃×#41	—	8	4	no	—
153	C₁₃×#41	—	8	4	no	—
154	C₂×Q₈×C₁₃	—	2	2	no	—
155	C₂×Q₈×C₁₃	—	2	2	no	—
156	C₂×Q₈×C₁₃	—	2	4	no	—
157	C₂×Q₈×C₁₃	—	8	4	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	2	no	—
165	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×Q₁₆	—	4	4	no	—
178	C₁₃×SD₁₆	—	4	8	no	—
179	C₁₃×D₈	—	4	4	no	—
180	C₁₃×M₁₆	—	4	2	no	—
181	C₂×C₈×C₁₃	—	4	2	no	—
182	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
183	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
209	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₄²×C₁₃	C₂⁴	1	2	yes	—
220	#3511	C₂×C₁₃	1	2	yes	complemented
221	#3263	C₂×C₁₃	1	4	yes	complemented
222	#3229	C₂×C₁₃	1	2	yes	complemented
223	#3227	C₂×C₁₃	1	2	yes	complemented
224	#3210	C₂×C₁₃	1	2	yes	complemented
225	#3207	C₂×C₁₃	1	2	yes	complemented
226	#3204	C₂×C₁₃	1	4	yes	complemented
227	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#3167	C₂×C₁₃	1	2	yes	complemented
230	#3125	C₂×C₁₃	1	8	yes	complemented
231	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
235	Q₈×C₁₃	—	2	8	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	4	no	—
238	Q₈×C₁₃	—	4	4	no	—
239	Q₈×C₁₃	—	8	4	no	—
240	D₄×C₁₃	—	2	8	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	8	no	—
244	D₄×C₁₃	—	4	4	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	8	4	no	—
247	D₄×C₁₃	—	8	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	8	4	no	—
258	C₂×C₄×C₁₃	—	8	4	no	—
259	C₂×C₄×C₁₃	—	8	4	no	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
267	C₈×C₁₃	—	2	4	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	2	2	no	—
270	#556	—	2	2	no	—
271	#555	—	2	2	no	—
272	#554	—	2	2	no	—
273	#553	—	2	2	no	—
274	#553	—	2	2	no	—
275	#548	—	2	2	no	—
276	#548	—	2	2	no	—
277	#547	—	2	2	no	—
278	#542	C₂²×C₁₃	1	4	yes	—
279	#542	C₂²×C₁₃	1	4	yes	—
280	#537	C₂²×C₁₃	1	4	yes	—
281	#533	C₂²×C₁₃	1	2	yes	—
282	#533	C₂²×C₁₃	1	2	yes	—
283	#532	C₂²×C₁₃	1	2	yes	—
284	#532	C₂²×C₁₃	1	2	yes	—
285	#532	C₂²×C₁₃	1	2	yes	—
286	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
287	#520	C₂²×C₁₃	1	4	yes	—
288	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
289	#498	C₂²×C₁₃	1	2	yes	—
290	#498	C₂²×C₁₃	1	1	yes	characteristic
291	#498	C₂²×C₁₃	1	1	yes	characteristic
292	#494	C₂²×C₁₃	1	1	yes	characteristic
293	#493	C₂²×C₁₃	1	1	yes	characteristic
294	#492	C₂²×C₁₃	1	2	yes	—
295	#487	C₂²×C₁₃	1	2	yes	—
296	#487	C₂²×C₁₃	1	2	yes	—
297	#486	C₂²×C₁₃	1	2	yes	—
298	#486	C₂²×C₁₃	1	2	yes	—
299	#483	C₂²×C₁₃	1	8	yes	—
300	#481	C₂²×C₁₃	1	8	yes	—
301	#476	C₂²×C₁₃	1	8	yes	—
302	#475	C₂²×C₁₃	1	8	yes	—
303	#470	C₂²×C₁₃	1	4	yes	—
304	#469	C₂²×C₁₃	1	4	yes	—
305	#465	C₂²×C₁₃	1	8	yes	—
306	#464	C₂²×C₁₃	1	8	yes	—
307	#463	C₂²×C₁₃	1	8	yes	—
308	#452	C₂²×C₁₃	1	8	yes	—
309	#449	C₂²×C₁₃	1	8	yes	—
310	#442	C₂²×C₁₃	1	4	yes	—
311	#441	C₂²×C₁₃	1	4	yes	—
312	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
313	#433	C₂²×C₁₃	1	4	yes	—
314	#431	C₂²×C₁₃	1	2	yes	—
315	#431	C₂²×C₁₃	1	2	yes	—
316	#424	C₂²×C₁₃	1	2	yes	—
317	#408	C₂²×C₁₃	1	2	yes	—
318	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	—	4	4	no	—
336	C₄×C₁₃	—	4	4	no	—
337	C₄×C₁₃	#577	1	4	yes	—
338	C₄×C₁₃	#585	1	2	yes	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	C₂³×C₁₃	1	4	yes	—
342	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
343	C₂²×Q₈	—	2	2	no	—
344	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
345	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
346	C₂×D₈	C₂³×C₁₃	1	4	yes	—
347	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
348	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
352	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
353	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
354	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
355	#127	C₂³×C₁₃	1	2	yes	—
356	#126	—	2	4	no	—
357	#126	—	2	4	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#124	—	2	4	no	—
361	#124	—	2	4	no	—
362	#124	—	2	2	no	—
363	#124	—	2	2	no	—
364	#124	C₂³×C₁₃	1	4	yes	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	4	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
373	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
374	#121	—	2	4	no	—
375	#121	—	2	4	no	—
376	#121	—	2	4	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	C₂³×C₁₃	1	4	yes	—
382	#121	C₂³×C₁₃	1	4	yes	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	D₄×C₁₃	1	2	yes	—
386	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
387	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	4	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	D₄×C₁₃	1	2	yes	—
395	C₄×D₄	D₄×C₁₃	1	2	yes	—
396	C₄×D₄	D₄×C₁₃	1	2	yes	—
397	C₄×D₄	C₂³×C₁₃	1	4	yes	—
398	C₄×D₄	C₂³×C₁₃	1	4	yes	—
399	#117	—	2	2	no	—
400	#117	—	2	2	no	—
401	#117	—	2	4	no	—
402	#117	C₂³×C₁₃	1	2	yes	—
403	#117	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	#106	C₂³×C₁₃	1	8	yes	—
410	#106	C₂³×C₁₃	1	4	yes	—
411	#106	C₂³×C₁₃	1	4	yes	—
412	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
413	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
414	#103	C₂³×C₁₃	1	8	yes	—
415	#103	C₂³×C₁₃	1	8	yes	—
416	#102	C₂³×C₁₃	1	8	yes	—
417	#102	C₂³×C₁₃	1	8	yes	—
418	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
419	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
420	#97	C₂³×C₁₃	1	2	yes	—
421	C₄×C₈	C₂³×C₁₃	1	2	yes	—
422	C₄×C₈	C₂³×C₁₃	1	2	yes	—
423	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₁₃	—	4	2	no	—
426	C₂×C₁₃	—	4	1	no	—
427	C₂×C₁₃	—	8	4	no	—
428	C₂×C₁₃	#3449	1	1	yes	characteristic
429	C₂×C₁₃	C₂×#577	1	2	yes	—
430	#41	—	4	2	no	—
431	#41	—	4	8	no	—
432	#41	—	8	4	no	—
433	#41	—	8	4	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	8	4	no	—
438	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	Q₁₆	—	4	4	no	—
458	SD₁₆	—	4	8	no	—
459	D₈	—	4	4	no	—
460	M₁₆	—	4	2	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
463	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
464	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
479	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
489	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
490	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₄²	—	2	4	no	—
493	C₄²	—	2	4	no	—
494	C₄²	C₂×D₄×C₁₃	1	2	yes	—
495	C₄²	C₂×D₄×C₁₃	1	2	yes	—
496	C₄²	C₂×D₄×C₁₃	1	2	yes	—
497	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₄²	C₂⁴×C₁₃	1	2	yes	—
500	C₁₃	#61015	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	4	no	—
502	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
504	Q₈	—	2	8	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	4	no	—
507	Q₈	—	4	4	no	—
508	Q₈	—	8	4	no	—
509	D₄	—	2	8	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	8	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	8	4	no	—
516	D₄	—	8	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	8	4	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
535	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
536	C₈	—	2	4	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	C₁₃×#577	1	4	yes	—
557	C₄	C₁₃×#585	1	2	yes	—
558	C₂	—	4	2	no	—
559	C₂	—	4	1	no	—
560	C₂	—	8	4	no	—
561	C₂	C₁₃×#3449	1	1	yes	characteristic
562	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3263	C₂	semidirect
3. C₁₃×#3229	C₂	semidirect
4. C₁₃×#3227	C₂	semidirect
5. C₁₃×#3210	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3204	C₂	semidirect
8. C₁₃×#3185	C₂	semidirect
9. C₁₃×#3184	C₂	semidirect
10. C₁₃×#3167	C₂	semidirect
11. C₁₃×#3125	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
149. #61015	C₁₃	direct (N × H)
220. #3511	C₂×C₁₃	semidirect
221. #3263	C₂×C₁₃	semidirect
222. #3229	C₂×C₁₃	semidirect
223. #3227	C₂×C₁₃	semidirect
224. #3210	C₂×C₁₃	semidirect
225. #3207	C₂×C₁₃	semidirect
226. #3204	C₂×C₁₃	semidirect
227. #3185	C₂×C₁₃	semidirect
228. #3184	C₂×C₁₃	semidirect
229. #3167	C₂×C₁₃	semidirect
230. #3125	C₂×C₁₃	semidirect
231. #2922	C₂×C₁₃	semidirect
500. C₁₃	#61015	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×#3511	2
C₁₃×#3263	2
C₁₃×#3229	2
C₁₃×#3227	2
C₁₃×#3210	2
C₁₃×#3207	2
C₁₃×#3204	2
C₁₃×#3185	2
C₁₃×#3184	2
C₁₃×#3167	2
C₁₃×#3125	2
C₁₃×#2922	2
#61015	13

Subgroups — C13×#61015 #15747354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61015 #15747354