Subgroups — C₁₃×#24722 #15711061

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2078	C₂	1	2	yes	maximal
6	C₁₃×#2052	C₂	1	2	yes	maximal
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1952	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1930	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#477	—	2	1	no	—
17	C₁₃×#477	—	2	1	no	—
18	C₁₃×#477	—	2	1	no	—
19	C₁₃×#477	—	2	2	no	—
20	C₁₃×#476	—	2	1	no	—
21	C₁₃×#475	—	2	1	no	—
22	C₁₃×#474	—	2	1	no	—
23	C₁₃×#441	—	2	1	no	—
24	C₁₃×#440	—	2	1	no	—
25	C₄×C₁₃×Q₁₆	—	2	1	no	—
26	C₄×C₁₃×SD₁₆	—	2	1	no	—
27	C₁₃×#433	—	2	2	no	—
28	C₁₃×#432	—	2	1	no	—
29	C₁₃×#431	—	2	1	no	—
30	C₂×C₁₃×#108	C₂²	1	2	yes	—
31	C₁₃×#428	C₂²	1	2	yes	—
32	C₁₃×#428	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#107	C₂²	1	2	yes	—
34	C₁₃×#423	C₂²	1	1	yes	characteristic
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#419	C₂²	1	1	yes	characteristic
38	C₁₃×#417	C₂²	1	2	yes	—
39	C₁₃×#417	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	2	yes	—
41	C₂×C₁₃×#101	C₂²	1	2	yes	—
42	C₁₃×#408	C₂²	1	2	yes	—
43	C₁₃×#405	C₂²	1	2	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
45	C₁₃×#343	C₂²	1	2	yes	—
46	C₁₃×#343	C₂²	1	2	yes	—
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#341	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	—	2	1	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#137	—	2	2	no	—
53	C₁₃×#137	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×Q₈×C₁₃	—	2	1	no	—
67	C₄×Q₈×C₁₃	—	2	1	no	—
68	C₄×Q₈×C₁₃	—	2	1	no	—
69	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₁₃×#117	—	2	1	no	—
76	C₁₃×#117	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#108	—	2	4	no	—
85	C₁₃×#107	—	2	2	no	—
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×#107	—	2	1	no	—
88	C₁₃×#107	—	2	2	no	—
89	C₁₃×#106	—	2	1	no	—
90	C₁₃×#106	—	2	2	no	—
91	C₁₃×C₄⋊C₈	—	2	1	no	—
92	C₁₃×C₄⋊C₈	—	2	1	no	—
93	C₁₃×C₄⋊C₈	—	2	1	no	—
94	C₁₃×C₄⋊C₈	—	2	1	no	—
95	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
98	C₁₃×#103	—	2	1	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#103	—	2	1	no	—
103	C₁₃×#103	—	2	1	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#101	—	2	4	no	—
107	C₁₃×C₂²⋊C₈	—	2	2	no	—
108	C₁₃×C₂²⋊C₈	—	2	2	no	—
109	C₁₃×#97	—	2	2	no	—
110	C₁₃×#97	—	2	1	no	—
111	C₄×C₈×C₁₃	—	2	2	no	—
112	C₄×C₈×C₁₃	—	2	1	no	—
113	#24722	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	4	1	no	—
124	C₂×Q₈×C₁₃	—	4	1	no	—
125	C₂×Q₈×C₁₃	—	8	2	no	—
126	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	#41	1	2	yes	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×Q₁₆	—	2	4	no	—
140	C₁₃×SD₁₆	—	2	4	no	—
141	C₁₃×M₁₆	—	2	1	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	1	no	—
146	C₁₃×M₁₆	—	2	1	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	#41	1	2	yes	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	4	1	no	—
164	C₁₃×C₄⋊C₄	—	4	1	no	—
165	C₁₃×C₄⋊C₄	—	4	1	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	4	1	no	—
176	C₄²×C₁₃	—	4	1	no	—
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	#3079	C₂×C₁₃	1	1	yes	characteristic
182	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
184	#2925	C₂×C₁₃	1	1	yes	characteristic
185	#2078	C₂×C₁₃	1	2	yes	—
186	#2052	C₂×C₁₃	1	2	yes	—
187	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1952	C₂×C₁₃	1	2	yes	complemented
189	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1930	C₂×C₁₃	1	2	yes	complemented
191	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	1	no	—
196	Q₈×C₁₃	—	2	1	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	4	1	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	Q₈×C₁₃	—	8	2	no	—
201	Q₈×C₁₃	—	8	2	no	—
202	D₄×C₁₃	—	2	1	no	—
203	D₄×C₁₃	—	2	1	no	—
204	D₄×C₁₃	—	4	1	no	—
205	D₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	1	no	—
220	C₂×C₄×C₁₃	—	8	1	no	—
221	C₂×C₄×C₁₃	—	8	2	no	—
222	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
231	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
232	C₈×C₁₃	—	2	2	no	—
233	C₈×C₁₃	—	2	2	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₈×C₁₃	—	4	1	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
242	#477	—	2	1	no	—
243	#477	—	2	1	no	—
244	#477	—	2	1	no	—
245	#477	—	2	2	no	—
246	#476	—	2	1	no	—
247	#475	—	2	1	no	—
248	#474	—	2	1	no	—
249	#441	—	2	1	no	—
250	#440	—	2	1	no	—
251	C₄×Q₁₆	—	2	1	no	—
252	C₄×SD₁₆	—	2	1	no	—
253	#433	—	2	2	no	—
254	#432	—	2	1	no	—
255	#431	—	2	1	no	—
256	C₂×#108	C₂²×C₁₃	1	2	yes	—
257	#428	C₂²×C₁₃	1	2	yes	—
258	#428	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#107	C₂²×C₁₃	1	2	yes	—
260	#423	C₂²×C₁₃	1	1	yes	characteristic
261	#423	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
263	#419	C₂²×C₁₃	1	1	yes	characteristic
264	#417	C₂²×C₁₃	1	2	yes	—
265	#417	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#103	C₂²×C₁₃	1	2	yes	—
267	C₂×#101	C₂²×C₁₃	1	2	yes	—
268	#408	C₂²×C₁₃	1	2	yes	—
269	#405	C₂²×C₁₃	1	2	yes	—
270	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
271	#343	C₂²×C₁₃	1	2	yes	—
272	#343	C₂²×C₁₃	1	2	yes	—
273	#343	C₂²×C₁₃	1	2	yes	—
274	#341	C₂²×C₁₃	1	2	yes	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	—	4	1	no	—
280	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
281	C₂²×C₁₃	#552	1	1	yes	characteristic
282	C₂²×C₁₃	#556	1	1	yes	characteristic
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	8	1	no	—
291	C₄×C₁₃	—	8	2	no	—
292	C₄×C₁₃	#473	1	2	yes	—
293	C₄×C₁₃	#525	1	1	yes	characteristic
294	C₄×C₁₃	#536	1	1	yes	characteristic
295	C₄×C₁₃	#547	1	1	yes	characteristic
296	C₄×C₁₃	#548	1	1	yes	characteristic
297	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
300	#137	—	2	2	no	—
301	#137	—	2	2	no	—
302	C₂×Q₁₆	—	2	1	no	—
303	C₂×SD₁₆	—	2	1	no	—
304	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
306	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
307	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
318	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
322	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	#117	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	#108	—	2	4	no	—
333	#107	—	2	2	no	—
334	#107	—	2	2	no	—
335	#107	—	2	1	no	—
336	#107	—	2	2	no	—
337	#106	—	2	1	no	—
338	#106	—	2	2	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
344	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
345	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
346	#103	—	2	1	no	—
347	#103	—	2	2	no	—
348	#103	—	2	2	no	—
349	#103	—	2	2	no	—
350	#103	—	2	1	no	—
351	#103	—	2	1	no	—
352	#102	—	2	1	no	—
353	#102	—	2	2	no	—
354	#101	—	2	4	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	—	2	2	no	—
357	#97	—	2	2	no	—
358	#97	—	2	1	no	—
359	C₄×C₈	—	2	2	no	—
360	C₄×C₈	—	2	1	no	—
361	C₂×C₁₃	—	2	1	no	—
362	C₂×C₁₃	—	2	1	no	—
363	C₂×C₁₃	—	8	1	no	—
364	C₂×C₁₃	#2415	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
366	C₂×C₁₃	#3068	1	1	yes	characteristic
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	4	1	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	—	8	2	no	—
379	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂×Q₈	C₁₃×#41	1	2	yes	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
390	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	SD₁₆	—	2	4	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	C₁₃×#41	1	2	yes	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₁₃	#24722	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³	—	2	1	no	—
436	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
437	Q₈	—	2	2	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	8	2	no	—
444	Q₈	—	8	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	8	1	no	—
463	C₂×C₄	—	8	1	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
466	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
467	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
468	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
487	C₂²	C₁₃×#552	1	1	yes	characteristic
488	C₂²	C₁₃×#556	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	C₁₃×#473	1	2	yes	—
499	C₄	C₁₃×#525	1	1	yes	characteristic
500	C₄	C₁₃×#536	1	1	yes	characteristic
501	C₄	C₁₃×#547	1	1	yes	characteristic
502	C₄	C₁₃×#548	1	1	yes	characteristic
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	1	no	—
506	C₂	C₁₃×#2415	1	1	yes	characteristic
507	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
508	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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. C₂×C₁₃×#477	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1952	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1930	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
113. #24722	C₁₃	direct (N × H)
182. C₂×#477	C₂×C₁₃	semidirect
187. #1997	C₂×C₁₃	semidirect
188. #1952	C₂×C₁₃	semidirect
189. #1950	C₂×C₁₃	semidirect
190. #1930	C₂×C₁₃	semidirect
191. #1801	C₂×C₁₃	semidirect
434. C₁₃	#24722	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×#3079	2
C₂×C₁₃×#477	2
C₄×C₁₃×#137	2
C₁₃×#2925	2
C₁₃×#2078	2
C₁₃×#2052	2
C₁₃×#1997	2
C₁₃×#1952	2
C₁₃×#1950	2
C₁₃×#1930	2
C₁₃×#1801	2
#24722	13

Subgroups — C13×#24722 #15711061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24722 #15711061