Subgroups — C₁₃×#26272 #15712611

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3096	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2037	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1974	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1883	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#535	C₂²	1	2	yes	—
16	C₁₃×#520	C₂²	1	2	yes	—
17	C₁₃×#496	—	2	2	no	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#493	—	2	1	no	—
20	C₁₃×#482	—	2	2	no	—
21	C₁₃×#482	—	2	2	no	—
22	C₁₃×#481	—	2	2	no	—
23	C₁₃×#480	—	2	2	no	—
24	C₁₃×#440	—	2	2	no	—
25	C₄×C₁₃×Q₁₆	—	2	1	no	—
26	C₄×C₁₃×D₈	—	2	1	no	—
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#418	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₁₃×#100	C₂²	1	2	yes	—
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₁₃×#405	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#339	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
48	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	2	2	no	—
69	C₁₃×#120	—	4	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	C₂³	1	1	yes	characteristic
75	C₁₃×#117	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#108	—	2	2	no	—
82	C₁₃×#107	—	2	1	no	—
83	C₁₃×#107	—	2	1	no	—
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×#107	D₄	1	1	yes	characteristic
86	C₁₃×#107	D₄	1	1	yes	characteristic
87	C₁₃×#106	—	2	2	no	—
88	C₁₃×#106	D₄	1	1	yes	characteristic
89	C₁₃×#106	D₄	1	1	yes	characteristic
90	C₁₃×#104	—	4	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#100	—	4	2	no	—
98	C₁₃×C₂²⋊C₈	—	2	2	no	—
99	C₁₃×C₂²⋊C₈	—	2	2	no	—
100	C₁₃×#97	—	2	1	no	—
101	C₁₃×#97	—	2	1	no	—
102	C₄×C₈×C₁₃	—	2	1	no	—
103	C₄×C₈×C₁₃	—	2	1	no	—
104	C₄×C₈×C₁₃	—	2	2	no	—
105	#26272	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	4	2	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×Q₁₆	—	2	2	no	—
128	C₁₃×SD₁₆	—	2	4	no	—
129	C₁₃×SD₁₆	—	4	4	no	—
130	C₁₃×D₈	—	2	2	no	—
131	C₁₃×D₈	—	4	4	no	—
132	C₁₃×D₈	—	4	2	no	—
133	C₁₃×D₈	—	4	2	no	—
134	C₁₃×M₁₆	—	2	1	no	—
135	C₁₃×M₁₆	—	2	1	no	—
136	C₁₃×M₁₆	—	2	2	no	—
137	C₁₃×M₁₆	—	2	1	no	—
138	C₁₃×M₁₆	—	2	2	no	—
139	C₁₃×M₁₆	#41	1	2	yes	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	#41	1	2	yes	—
150	C₂×C₈×C₁₃	#41	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	4	2	no	—
163	C₁₃×C₂²⋊C₄	—	8	4	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	4	2	no	—
169	#3155	C₂×C₁₃	1	1	yes	characteristic
170	#3096	C₂×C₁₃	1	2	yes	complemented
171	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2051	C₂×C₁₃	1	2	yes	complemented
173	#2037	C₂×C₁₃	1	2	yes	complemented
174	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1974	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1883	C₂×C₁₃	1	2	yes	complemented
179	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	8	2	no	—
185	C₂³×C₁₃	—	8	2	no	—
186	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	2	2	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	4	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	16	2	no	—
198	D₄×C₁₃	—	16	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	8	2	no	—
211	C₂×C₄×C₁₃	—	16	2	no	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₈×C₁₃	—	2	1	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	2	2	no	—
221	C₈×C₁₃	—	4	1	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	#123	1	2	yes	—
224	C₈×C₁₃	#123	1	2	yes	—
225	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
226	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
227	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
228	#535	C₂²×C₁₃	1	2	yes	—
229	#520	C₂²×C₁₃	1	2	yes	—
230	#496	—	2	2	no	—
231	#495	—	2	1	no	—
232	#493	—	2	1	no	—
233	#482	—	2	2	no	—
234	#482	—	2	2	no	—
235	#481	—	2	2	no	—
236	#480	—	2	2	no	—
237	#440	—	2	2	no	—
238	C₄×Q₁₆	—	2	1	no	—
239	C₄×D₈	—	2	1	no	—
240	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
242	#428	C₂²×C₁₃	1	2	yes	—
243	#427	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#104	C₂²×C₁₃	1	2	yes	—
246	#418	C₂²×C₁₃	1	2	yes	—
247	#417	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#100	C₂²×C₁₃	1	2	yes	—
250	#408	C₂²×C₁₃	1	2	yes	—
251	#405	C₂²×C₁₃	1	1	yes	characteristic
252	#405	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
254	#390	C₂²×C₁₃	1	2	yes	—
255	#343	C₂²×C₁₃	1	2	yes	—
256	#339	C₂²×C₁₃	1	1	yes	characteristic
257	#339	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	8	4	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	16	2	no	—
268	C₂²×C₁₃	#540	1	1	yes	characteristic
269	C₂²×C₁₃	D₄²	1	1	yes	characteristic
270	C₂²×C₁₃	#559	1	1	yes	characteristic
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	1	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
279	C₄×C₁₃	#532	1	1	yes	characteristic
280	C₄×C₁₃	#546	1	1	yes	characteristic
281	C₄×C₁₃	#550	1	1	yes	characteristic
282	C₂×#41	C₂³×C₁₃	1	2	yes	—
283	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
284	AGL(1,ℤ/8)	—	2	4	no	—
285	AGL(1,ℤ/8)	—	4	2	no	—
286	#135	—	2	2	no	—
287	#135	—	2	2	no	—
288	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	—	2	1	no	—
293	C₂×D₈	—	2	1	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
297	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
299	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	#127	—	2	2	no	—
303	#124	—	2	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#120	—	4	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	4	2	no	—
310	#117	—	2	2	no	—
311	#117	C₂³×C₁₃	1	1	yes	characteristic
312	#117	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
315	C₂×C₂²⋊C₄	—	4	2	no	—
316	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
317	#108	—	2	2	no	—
318	#108	—	2	2	no	—
319	#107	—	2	1	no	—
320	#107	—	2	1	no	—
321	#107	—	2	2	no	—
322	#107	D₄×C₁₃	1	1	yes	characteristic
323	#107	D₄×C₁₃	1	1	yes	characteristic
324	#106	—	2	2	no	—
325	#106	D₄×C₁₃	1	1	yes	characteristic
326	#106	D₄×C₁₃	1	1	yes	characteristic
327	#104	—	4	2	no	—
328	#103	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#100	—	4	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	#97	—	2	1	no	—
338	#97	—	2	1	no	—
339	C₄×C₈	—	2	1	no	—
340	C₄×C₈	—	2	1	no	—
341	C₄×C₈	—	2	2	no	—
342	C₂×C₁₃	—	2	1	no	—
343	C₂×C₁₃	—	2	1	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	—	16	2	no	—
346	C₂×C₁₃	#2445	1	1	yes	characteristic
347	C₂×C₁₃	#3290	1	1	yes	characteristic
348	C₂×C₁₃	#3292	1	1	yes	characteristic
349	C₂⁴	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
370	Q₁₆	—	2	2	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	4	4	no	—
373	D₈	—	2	2	no	—
374	D₈	—	4	4	no	—
375	D₈	—	4	2	no	—
376	D₈	—	4	2	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	C₁₃×#41	1	2	yes	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₈	C₁₃×#41	1	2	yes	—
393	C₂×C₈	C₁₃×#41	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	8	4	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	4	2	no	—
412	C₁₃	#26272	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	8	2	no	—
418	C₂³	—	8	2	no	—
419	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	16	2	no	—
431	D₄	—	16	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	16	2	no	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
449	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
450	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	2	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	2	no	—
456	C₈	C₁₃×#123	1	2	yes	—
457	C₈	C₁₃×#123	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	16	2	no	—
468	C₂²	C₁₃×#540	1	1	yes	characteristic
469	C₂²	D₄²×C₁₃	1	1	yes	characteristic
470	C₂²	C₁₃×#559	1	1	yes	characteristic
471	C₄	—	4	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
479	C₄	C₁₃×#532	1	1	yes	characteristic
480	C₄	C₁₃×#546	1	1	yes	characteristic
481	C₄	C₁₃×#550	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	8	2	no	—
485	C₂	—	16	2	no	—
486	C₂	C₁₃×#2445	1	1	yes	characteristic
487	C₂	C₁₃×#3290	1	1	yes	characteristic
488	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3155	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3096	C₂	semidirect
3. C₁₃×#2951	C₂	semidirect
4. C₁₃×#2051	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#1978	C₂	semidirect
7. C₁₃×#1974	C₂	semidirect
8. C₁₃×#1970	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1883	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
105. #26272	C₁₃	direct (N × H)
170. #3096	C₂×C₁₃	semidirect
171. #2951	C₂×C₁₃	semidirect
172. #2051	C₂×C₁₃	semidirect
173. #2037	C₂×C₁₃	semidirect
174. #1978	C₂×C₁₃	semidirect
175. #1974	C₂×C₁₃	semidirect
176. #1970	C₂×C₁₃	semidirect
177. #1952	C₂×C₁₃	semidirect
178. #1883	C₂×C₁₃	semidirect
179. #1772	C₂×C₁₃	semidirect
412. C₁₃	#26272	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×#3155	2
C₁₃×#3096	2
C₁₃×#2951	2
C₁₃×#2051	2
C₁₃×#2037	2
C₁₃×#1978	2
C₁₃×#1974	2
C₁₃×#1970	2
C₁₃×#1952	2
C₁₃×#1883	2
C₁₃×#1772	2
#26272	13

Subgroups — C13×#26272 #15712611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26272 #15712611