Subgroups — C₁₃×#61588 #15747927

Order 3328.

2150 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3333	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3278	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3007	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
12	C₁₃×#554	—	2	4	no	—
13	C₁₃×#554	C₂²	1	4	yes	complemented
14	C₁₃×#550	—	2	4	no	—
15	C₁₃×#550	C₂²	1	8	yes	—
16	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
17	C₁₃×#544	—	2	1	no	—
18	C₁₃×#543	—	2	2	no	—
19	C₁₃×#533	C₂²	1	2	yes	—
20	C₂×C₁₃×#127	—	2	1	no	—
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₁₃×#121	—	2	2	no	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₁₃×#518	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#492	C₂²	1	4	yes	complemented
30	C₁₃×#486	C₂²	1	4	yes	complemented
31	C₁₃×#484	C₂²	1	4	yes	—
32	C₁₃×#480	C₂²	1	8	yes	complemented
33	C₁₃×#477	C₂²	1	4	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#462	C₂²	1	4	yes	complemented
36	C₁₃×#460	C₂²	1	8	yes	complemented
37	C₁₃×#452	C₂²	1	16	yes	complemented
38	C₁₃×#451	C₂²	1	4	yes	—
39	C₁₃×#450	C₂²	1	8	yes	—
40	C₁₃×#448	C₂²	1	8	yes	complemented
41	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	—
44	C₁₃×#417	C₂²	1	8	yes	complemented
45	C₁₃×#407	C₂²	1	4	yes	—
46	C₂×C₁₃×#41	—	2	4	no	—
47	C₂×C₁₃×#41	—	4	8	no	—
48	C₂×C₁₃×#41	C₂³	1	8	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#137	—	4	16	no	—
60	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
63	C₁₃×C₄⋊Q₈	—	2	4	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×#127	—	2	8	no	—
67	C₁₃×#127	—	2	2	no	—
68	C₁₃×#127	C₂³	1	4	yes	—
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×C₂²⋊Q₈	—	2	4	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	16	no	—
80	C₁₃×#121	C₂³	1	8	yes	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	—	2	4	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	8	no	—
88	C₄×D₄×C₁₃	D₄	1	4	yes	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₁₃×#117	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#107	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	16	yes	—
106	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₄×C₈×C₁₃	C₂³	1	4	yes	—
109	#61588	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
112	C₁₃×#41	—	2	16	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	2	4	no	—
119	C₂×Q₈×C₁₃	—	4	8	no	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	4	8	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	8	2	no	—
132	C₂×D₄×C₁₃	—	8	4	no	—
133	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
134	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	4	4	no	—
141	C₂²×C₄×C₁₃	—	4	8	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₁₃×Q₁₆	—	2	16	no	—
149	C₁₃×SD₁₆	—	4	16	no	—
150	C₁₃×M₁₆	—	4	8	no	—
151	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	—	2	4	no	—
170	C₄²×C₁₃	C₂×D₄	1	2	yes	—
171	C₄²×C₁₃	C₂⁴	1	2	yes	—
172	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
174	#3333	C₂×C₁₃	1	8	yes	complemented
175	#3278	C₂×C₁₃	1	8	yes	complemented
176	#3208	C₂×C₁₃	1	2	yes	complemented
177	#3193	C₂×C₁₃	1	4	yes	complemented
178	#3104	C₂×C₁₃	1	2	yes	complemented
179	#3007	C₂×C₁₃	1	4	yes	complemented
180	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	4	4	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	2	4	no	—
191	Q₈×C₁₃	—	2	2	no	—
192	Q₈×C₁₃	—	2	8	no	—
193	Q₈×C₁₃	—	8	2	no	—
194	Q₈×C₁₃	—	8	4	no	—
195	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
196	D₄×C₁₃	—	2	8	no	—
197	D₄×C₁₃	—	2	8	no	—
198	D₄×C₁₃	—	4	16	no	—
199	D₄×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	4	8	no	—
201	D₄×C₁₃	—	8	4	no	—
202	D₄×C₁₃	—	8	8	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	16	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	#137	1	4	yes	complemented
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
223	C₈×C₁₃	—	2	8	no	—
224	C₂²×#41	C₂²×C₁₃	1	2	yes	—
225	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
226	#554	—	2	4	no	—
227	#554	C₂²×C₁₃	1	4	yes	complemented
228	#550	—	2	4	no	—
229	#550	C₂²×C₁₃	1	8	yes	—
230	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
231	#544	—	2	1	no	—
232	#543	—	2	2	no	—
233	#533	C₂²×C₁₃	1	2	yes	—
234	C₂×#127	—	2	1	no	—
235	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
237	C₂×#121	—	2	2	no	—
238	C₂×#121	C₂²×C₁₃	1	2	yes	—
239	#518	—	2	1	no	—
240	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×D₄	—	2	1	no	—
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	#492	C₂²×C₁₃	1	4	yes	complemented
244	#486	C₂²×C₁₃	1	4	yes	complemented
245	#484	C₂²×C₁₃	1	4	yes	—
246	#480	C₂²×C₁₃	1	8	yes	complemented
247	#477	C₂²×C₁₃	1	4	yes	complemented
248	#468	C₂²×C₁₃	1	16	yes	complemented
249	#462	C₂²×C₁₃	1	4	yes	complemented
250	#460	C₂²×C₁₃	1	8	yes	complemented
251	#452	C₂²×C₁₃	1	16	yes	complemented
252	#451	C₂²×C₁₃	1	4	yes	—
253	#450	C₂²×C₁₃	1	8	yes	—
254	#448	C₂²×C₁₃	1	8	yes	complemented
255	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
256	#436	C₂²×C₁₃	1	8	yes	complemented
257	#431	C₂²×C₁₃	1	2	yes	—
258	#417	C₂²×C₁₃	1	8	yes	complemented
259	#407	C₂²×C₁₃	1	4	yes	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	4	no	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	8	4	no	—
269	C₂²×C₁₃	—	8	8	no	—
270	C₂²×C₁₃	C₂×#137	1	2	yes	—
271	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	2	4	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	C₂×#137	1	4	yes	—
280	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	4	8	no	—
283	C₂×#41	C₂³×C₁₃	1	8	yes	—
284	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
294	#137	—	4	16	no	—
295	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
296	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
297	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
298	C₄⋊Q₈	—	2	4	no	—
299	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
300	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
301	#127	—	2	8	no	—
302	#127	—	2	2	no	—
303	#127	C₂³×C₁₃	1	4	yes	—
304	#125	—	2	4	no	—
305	#125	—	2	2	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	8	no	—
310	C₂²⋊Q₈	—	2	8	no	—
311	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
312	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
313	#121	—	2	4	no	—
314	#121	—	2	16	no	—
315	#121	C₂³×C₁₃	1	8	yes	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
319	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	8	no	—
323	C₄×D₄	D₄×C₁₃	1	4	yes	—
324	C₄×D₄	C₂³×C₁₃	1	4	yes	—
325	#117	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#107	C₂³×C₁₃	1	8	yes	—
337	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
338	#103	C₂³×C₁₃	1	8	yes	—
339	#103	C₂³×C₁₃	1	8	yes	—
340	#102	C₂³×C₁₃	1	16	yes	—
341	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
342	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
343	C₄×C₈	C₂³×C₁₃	1	4	yes	—
344	C₂×C₁₃	—	2	2	no	—
345	C₂×C₁₃	—	4	4	no	—
346	C₂×C₁₃	—	8	4	no	—
347	C₂×C₁₃	#3484	1	1	yes	characteristic
348	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
349	C₂×C₁₃	#3585	1	1	yes	characteristic
350	C₂⁴	—	2	2	no	—
351	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
352	#41	—	2	16	no	—
353	#41	—	4	8	no	—
354	#41	—	4	16	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
361	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	8	2	no	—
372	C₂×D₄	—	8	4	no	—
373	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
374	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
388	Q₁₆	—	2	16	no	—
389	SD₁₆	—	4	16	no	—
390	M₁₆	—	4	8	no	—
391	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
402	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
403	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	4	no	—
410	C₄²	C₂×D₄×C₁₃	1	2	yes	—
411	C₄²	C₂⁴×C₁₃	1	2	yes	—
412	C₁₃	#61588	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
421	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
422	Q₈	—	2	4	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	2	8	no	—
425	Q₈	—	8	4	no	—
426	Q₈	—	8	2	no	—
427	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
428	D₄	—	2	8	no	—
429	D₄	—	2	8	no	—
430	D₄	—	4	16	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	8	no	—
433	D₄	—	8	4	no	—
434	D₄	—	8	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	8	4	no	—
448	C₂×C₄	—	8	4	no	—
449	C₂×C₄	C₁₃×#137	1	4	yes	complemented
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
454	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
455	C₈	—	2	8	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	8	4	no	—
465	C₂²	—	8	8	no	—
466	C₂²	C₂×C₁₃×#137	1	2	yes	—
467	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	C₂×C₁₃×#137	1	4	yes	—
476	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
477	C₂	—	2	2	no	—
478	C₂	—	4	4	no	—
479	C₂	—	8	4	no	—
480	C₂	C₁₃×#3484	1	1	yes	characteristic
481	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
482	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3278	C₂	semidirect
5. C₁₃×#3208	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3104	C₂	semidirect
8. C₁₃×#3007	C₂	semidirect
9. C₁₃×#2975	C₂	semidirect
11. C₂×C₁₃×#137	C₂²	semidirect
13. C₁₃×#554	C₂²	semidirect
16. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
32. C₁₃×#480	C₂²	semidirect
33. C₁₃×#477	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#462	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
37. C₁₃×#452	C₂²	semidirect
40. C₁₃×#448	C₂²	semidirect
41. C₄×C₁₃×Q₁₆	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
44. C₁₃×#417	C₂²	semidirect
109. #61588	C₁₃	direct (N × H)
172. #3501	C₂×C₁₃	semidirect
174. #3333	C₂×C₁₃	semidirect
175. #3278	C₂×C₁₃	semidirect
176. #3208	C₂×C₁₃	semidirect
177. #3193	C₂×C₁₃	semidirect
178. #3104	C₂×C₁₃	semidirect
179. #3007	C₂×C₁₃	semidirect
180. #2975	C₂×C₁₃	semidirect
217. C₂×C₄×C₁₃	#137	semidirect
225. C₂×#137	C₂²×C₁₃	semidirect
227. #554	C₂²×C₁₃	semidirect
230. D₄×Q₈	C₂²×C₁₃	semidirect
243. #492	C₂²×C₁₃	semidirect
244. #486	C₂²×C₁₃	semidirect
246. #480	C₂²×C₁₃	semidirect
247. #477	C₂²×C₁₃	semidirect
248. #468	C₂²×C₁₃	semidirect
249. #462	C₂²×C₁₃	semidirect
250. #460	C₂²×C₁₃	semidirect
251. #452	C₂²×C₁₃	semidirect
254. #448	C₂²×C₁₃	semidirect
255. C₄×Q₁₆	C₂²×C₁₃	semidirect
256. #436	C₂²×C₁₃	semidirect
258. #417	C₂²×C₁₃	semidirect
412. C₁₃	#61588	direct (N × H)
449. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3501	2
C₂×C₁₃×#550	2
C₁₃×#3333	2
C₁₃×#3278	2
C₁₃×#3208	2
C₁₃×#3193	2
C₁₃×#3104	2
C₁₃×#3007	2
C₁₃×#2975	2
#61588	13

Subgroups — C13×#61588 #15747927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61588 #15747927