Subgroups — C₁₃×#25875 #15712214

Order 3328.

1430 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2037	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1792	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₁₃×#550	—	2	1	no	—
12	C₁₃×#550	—	2	1	no	—
13	D₄²×C₁₃	—	2	2	no	—
14	D₄²×C₁₃	—	2	2	no	—
15	D₄²×C₁₃	—	2	1	no	—
16	D₄²×C₁₃	—	2	1	no	—
17	C₁₃×#535	—	2	2	no	—
18	C₁₃×#535	C₂²	1	2	yes	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#127	—	2	1	no	—
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	—	2	2	no	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#489	—	2	2	no	—
27	C₁₃×#487	—	2	1	no	—
28	C₁₃×#486	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	—	2	1	no	—
32	C₁₃×#474	—	2	1	no	—
33	C₁₃×#428	C₂²	1	2	yes	complemented
34	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#104	C₂²	1	2	yes	—
36	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
37	C₁₃×#417	C₂²	1	2	yes	—
38	C₁₃×#417	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#390	—	2	2	no	—
42	C₁₃×#390	C₂²	1	4	yes	complemented
43	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#339	C₂²	1	2	yes	complemented
45	C₁₃×H(5,𝔽₂)	—	2	8	no	—
46	C₁₃×H(5,𝔽₂)	—	4	4	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	C₂³	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	2	no	—
57	C₂²×D₄×C₁₃	D₄	1	2	yes	—
58	C₂²×D₄×C₁₃	D₄	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₃×#127	—	2	2	no	—
68	C₁₃×#127	—	2	2	no	—
69	C₁₃×#127	—	2	2	no	—
70	C₁₃×#127	—	2	1	no	—
71	C₁₃×#127	—	2	1	no	—
72	C₁₃×#127	—	2	1	no	—
73	C₁₃×#127	—	2	1	no	—
74	C₁₃×#127	D₄	1	1	yes	characteristic
75	C₁₃×#124	—	2	2	no	—
76	C₁₃×#124	—	4	8	no	—
77	C₁₃×#124	D₄	1	2	yes	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#120	—	2	4	no	—
87	C₁₃×#120	—	2	4	no	—
88	C₁₃×#120	—	2	4	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
98	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	—	2	2	no	—
110	C₁₃×#106	—	2	2	no	—
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×#104	—	2	4	no	—
114	C₁₃×#104	—	4	4	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	4	no	—
117	C₁₃×#102	—	2	2	no	—
118	C₁₃×#102	—	2	4	no	—
119	C₁₃×#100	—	4	4	no	—
120	C₁₃×#97	—	2	1	no	—
121	C₄×C₈×C₁₃	—	2	1	no	—
122	#25875	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	4	no	—
127	C₁₃×#41	—	2	4	no	—
128	C₁₃×#41	—	4	8	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	#41	1	4	yes	—
132	C₂×Q₈×C₁₃	—	4	4	no	—
133	C₂×Q₈×C₁₃	—	4	1	no	—
134	C₂×Q₈×C₁₃	—	4	1	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂×D₄×C₁₃	—	4	16	no	—
157	C₂×D₄×C₁₃	—	4	4	no	—
158	C₂×D₄×C₁₃	—	4	4	no	—
159	C₂×D₄×C₁₃	—	8	4	no	—
160	C₂×D₄×C₁₃	—	8	4	no	—
161	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	4	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	4	1	no	—
185	C₁₃×C₄⋊C₄	—	4	1	no	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	16	no	—
196	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	2	no	—
201	C₄²×C₁₃	—	2	2	no	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
207	#3498	C₂×C₁₃	1	1	yes	characteristic
208	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2858	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2037	C₂×C₁₃	1	4	yes	complemented
212	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1962	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1792	C₂×C₁₃	1	4	yes	complemented
215	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	8	no	—
220	C₂³×C₁₃	—	4	8	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	4	no	—
223	C₂³×C₁₃	—	8	4	no	—
224	C₂³×C₁₃	—	8	4	no	—
225	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	2	4	no	—
228	Q₈×C₁₃	—	8	2	no	—
229	Q₈×C₁₃	—	8	2	no	—
230	Q₈×C₁₃	#124	1	2	yes	complemented
231	D₄×C₁₃	—	2	4	no	—
232	D₄×C₁₃	—	2	1	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	4	8	no	—
235	D₄×C₁₃	—	4	8	no	—
236	D₄×C₁₃	—	4	4	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	8	2	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	4	no	—
247	D₄×C₁₃	—	8	4	no	—
248	D₄×C₁₃	#124	1	2	yes	complemented
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
268	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
274	C₈×C₁₃	—	4	2	no	—
275	C₈×C₁₃	—	4	2	no	—
276	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
277	#550	—	2	1	no	—
278	#550	—	2	1	no	—
279	D₄²	—	2	2	no	—
280	D₄²	—	2	2	no	—
281	D₄²	—	2	1	no	—
282	D₄²	—	2	1	no	—
283	#535	—	2	2	no	—
284	#535	C₂²×C₁₃	1	2	yes	—
285	#532	—	2	1	no	—
286	#532	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#127	—	2	1	no	—
289	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#124	—	2	2	no	—
291	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
292	#489	—	2	2	no	—
293	#487	—	2	1	no	—
294	#486	—	2	1	no	—
295	#477	—	2	1	no	—
296	#476	—	2	1	no	—
297	#475	—	2	1	no	—
298	#474	—	2	1	no	—
299	#428	C₂²×C₁₃	1	2	yes	complemented
300	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#104	C₂²×C₁₃	1	2	yes	—
302	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
303	#417	C₂²×C₁₃	1	2	yes	—
304	#417	C₂²×C₁₃	1	4	yes	complemented
305	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
306	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	#390	—	2	2	no	—
308	#390	C₂²×C₁₃	1	4	yes	complemented
309	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#339	C₂²×C₁₃	1	2	yes	complemented
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	4	1	no	—
315	C₂²×C₁₃	—	4	1	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	4	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	8	8	no	—
323	C₂²×C₁₃	—	16	8	no	—
324	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
325	C₂²×C₁₃	#546	1	2	yes	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	8	2	no	—
334	C₄×C₁₃	#453	1	2	yes	—
335	C₄×C₁₃	#455	1	2	yes	—
336	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
337	C₄×C₁₃	#535	1	1	yes	characteristic
338	C₄×C₁₃	#546	1	2	yes	—
339	H(5,𝔽₂)	—	2	8	no	—
340	H(5,𝔽₂)	—	4	4	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	C₂³×C₁₃	1	2	yes	—
344	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	D₄×C₁₃	1	2	yes	—
352	C₂²×D₄	D₄×C₁₃	1	2	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
354	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
355	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
361	#127	—	2	2	no	—
362	#127	—	2	2	no	—
363	#127	—	2	2	no	—
364	#127	—	2	1	no	—
365	#127	—	2	1	no	—
366	#127	—	2	1	no	—
367	#127	—	2	1	no	—
368	#127	D₄×C₁₃	1	1	yes	characteristic
369	#124	—	2	2	no	—
370	#124	—	4	8	no	—
371	#124	D₄×C₁₃	1	2	yes	—
372	#121	—	2	2	no	—
373	#121	—	2	2	no	—
374	#121	—	2	4	no	—
375	#121	—	2	4	no	—
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#120	—	2	4	no	—
381	#120	—	2	4	no	—
382	#120	—	2	4	no	—
383	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
384	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
392	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
393	#117	—	2	1	no	—
394	#117	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₂²⋊C₄	—	2	8	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	#107	—	2	2	no	—
404	#106	—	2	2	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	#104	—	2	4	no	—
408	#104	—	4	4	no	—
409	#103	—	2	2	no	—
410	#103	—	2	4	no	—
411	#102	—	2	2	no	—
412	#102	—	2	4	no	—
413	#100	—	4	4	no	—
414	#97	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₂×C₁₃	—	2	2	no	—
417	C₂×C₁₃	—	4	2	no	—
418	C₂×C₁₃	—	8	4	no	—
419	C₂×C₁₃	—	8	2	no	—
420	C₂×C₁₃	#2435	1	1	yes	characteristic
421	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
422	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
423	C₂⁴	—	2	4	no	—
424	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
425	#41	—	2	2	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	4	8	no	—
429	#41	—	4	4	no	—
430	#41	—	4	4	no	—
431	#41	C₁₃×#41	1	4	yes	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
436	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	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	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	16	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	8	4	no	—
460	C₂×D₄	—	8	4	no	—
461	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	4	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	4	16	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	4	2	no	—
503	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₁₃	#25875	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	2	1	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	8	no	—
512	C₂³	—	4	8	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	2	4	no	—
520	Q₈	—	8	2	no	—
521	Q₈	—	8	2	no	—
522	Q₈	C₁₃×#124	1	2	yes	complemented
523	D₄	—	2	4	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	4	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	4	no	—
536	D₄	—	8	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	4	no	—
539	D₄	—	8	4	no	—
540	D₄	C₁₃×#124	1	2	yes	complemented
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
559	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
560	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
561	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
565	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
566	C₈	—	4	2	no	—
567	C₈	—	4	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	8	8	no	—
580	C₂²	—	16	8	no	—
581	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
582	C₂²	C₁₃×#546	1	2	yes	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	2	no	—
591	C₄	C₁₃×#453	1	2	yes	—
592	C₄	C₁₃×#455	1	2	yes	—
593	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
594	C₄	C₁₃×#535	1	1	yes	characteristic
595	C₄	C₁₃×#546	1	2	yes	—
596	C₂	—	2	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	8	4	no	—
599	C₂	—	8	2	no	—
600	C₂	C₁₃×#2435	1	1	yes	characteristic
601	C₂	C₂×C₁₃×#453	1	1	yes	characteristic
602	C₂	C₂×C₁₃×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3498	C₂
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. C₁₃×#3141	C₂	semidirect
3. C₁₃×#3079	C₂	semidirect
4. C₁₃×#2858	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#1965	C₂	semidirect
7. C₁₃×#1962	C₂	semidirect
8. C₁₃×#1792	C₂	semidirect
9. C₄×C₁₃×#104	C₂	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₁₃×#428	C₂²	semidirect
34. C₁₃×#423	C₂²	semidirect
36. C₂×C₁₃×#104	C₂²	semidirect
38. C₁₃×#417	C₂²	semidirect
39. C₂×C₁₃×#100	C₂²	semidirect
40. C₄×C₁₃×M₁₆	C₂²	semidirect
42. C₁₃×#390	C₂²	semidirect
43. C₄³×C₁₃	C₂²	semidirect
44. C₁₃×#339	C₂²	semidirect
122. #25875	C₁₃	direct (N × H)
208. #3141	C₂×C₁₃	semidirect
209. #3079	C₂×C₁₃	semidirect
210. #2858	C₂×C₁₃	semidirect
211. #2037	C₂×C₁₃	semidirect
212. #1965	C₂×C₁₃	semidirect
213. #1962	C₂×C₁₃	semidirect
214. #1792	C₂×C₁₃	semidirect
215. C₄×#104	C₂×C₁₃	semidirect
230. Q₈×C₁₃	#124	semidirect
248. D₄×C₁₃	#124	semidirect
287. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
299. #428	C₂²×C₁₃	semidirect
300. #423	C₂²×C₁₃	semidirect
302. C₂×#104	C₂²×C₁₃	semidirect
304. #417	C₂²×C₁₃	semidirect
305. C₂×#100	C₂²×C₁₃	semidirect
306. C₄×M₁₆	C₂²×C₁₃	semidirect
308. #390	C₂²×C₁₃	semidirect
309. C₄³	C₂²×C₁₃	semidirect
310. #339	C₂²×C₁₃	semidirect
507. C₁₃	#25875	direct (N × H)
522. Q₈	C₁₃×#124	semidirect
540. D₄	C₁₃×#124	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3498	2
C₁₃×#3141	2
C₁₃×#3079	2
C₁₃×#2858	2
C₁₃×#2037	2
C₁₃×#1965	2
C₁₃×#1962	2
C₁₃×#1792	2
C₄×C₁₃×#104	2
#25875	13

Subgroups — C13×#25875 #15712214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25875 #15712214