Subgroups — C₁₃×#61378 #15747717

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 436 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	2	yes	maximal, complemented
2	C₁₃×#3389	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3384	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3081	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2948	C₂	1	2	yes	maximal
10	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₁₃×#554	—	2	2	no	—
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#554	C₂²	1	8	yes	complemented
15	C₁₃×#554	C₂²	1	4	yes	complemented
16	D₄×Q₈×C₁₃	—	2	2	no	—
17	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#544	C₂²	1	4	yes	—
19	C₁₃×#543	—	2	4	no	—
20	C₁₃×#533	C₂²	1	2	yes	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	—	2	4	no	—
23	C₁₃×#518	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#501	C₂²	1	4	yes	complemented
26	C₁₃×#501	C₂²	1	8	yes	complemented
27	C₁₃×#501	C₂²	1	4	yes	complemented
28	C₁₃×#499	C₂²	1	4	yes	complemented
29	C₁₃×#498	C₂²	1	4	yes	complemented
30	C₁₃×#478	C₂²	1	8	yes	complemented
31	C₁₃×#478	C₂²	1	8	yes	complemented
32	C₁₃×#478	C₂²	1	8	yes	complemented
33	C₁₃×#476	C₂²	1	4	yes	complemented
34	C₁₃×#476	C₂²	1	8	yes	complemented
35	C₁₃×#474	C₂²	1	4	yes	complemented
36	C₁₃×#474	C₂²	1	8	yes	complemented
37	C₁₃×#446	C₂²	1	8	yes	complemented
38	C₁₃×#442	C₂²	1	4	yes	—
39	C₁₃×#442	C₂²	1	8	yes	—
40	C₁₃×#442	C₂²	1	4	yes	—
41	C₄×C₁₃×D₈	C₂²	1	8	yes	—
42	C₁₃×#428	C₂²	1	4	yes	—
43	C₁₃×#427	C₂²	1	2	yes	—
44	C₁₃×#427	C₂²	1	2	yes	—
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	2	yes	—
47	C₁₃×#423	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	4	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₁₃×#405	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
56	C₂×C₁₃×D₈	C₂³	1	4	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×#125	—	2	4	no	—
66	C₁₃×#125	D₄	1	2	yes	—
67	C₁₃×#125	C₂³	1	8	yes	—
68	C₁₃×#125	C₂³	1	4	yes	—
69	C₁₃×C₂²⋊Q₈	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	8	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	8	no	—
78	C₁₃×C₂²⋊Q₈	—	2	8	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
83	C₄×D₄×C₁₃	—	2	4	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	C₂³	1	8	yes	—
88	C₄×D₄×C₁₃	C₂³	1	8	yes	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₁₃×#117	C₂³	1	4	yes	—
92	C₁₃×#117	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	C₂³	1	4	yes	—
100	C₁₃×#107	C₂³	1	4	yes	—
101	C₁₃×#107	C₂³	1	8	yes	—
102	C₁₃×#106	C₂³	1	4	yes	—
103	C₁₃×#106	C₂³	1	2	yes	—
104	C₁₃×#106	C₂³	1	2	yes	—
105	C₁₃×#106	C₂³	1	2	yes	—
106	C₁₃×#106	C₂³	1	2	yes	—
107	C₁₃×#106	C₂³	1	8	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
110	C₁₃×#102	C₂³	1	8	yes	—
111	C₁₃×#102	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×#97	C₂³	1	4	yes	—
114	C₁₃×#97	C₂³	1	4	yes	—
115	C₄×C₈×C₁₃	C₂³	1	4	yes	—
116	#61378	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	8	8	no	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	complemented
126	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	8	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	8	4	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×D₈	C₂×Q₈	1	16	yes	complemented
136	C₁₃×M₁₆	—	2	4	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
139	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
154	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
162	C₄²×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂⁴	1	4	yes	—
166	C₄²×C₁₃	C₂⁴	1	2	yes	—
167	#3501	C₂×C₁₃	1	2	yes	complemented
168	#3389	C₂×C₁₃	1	8	yes	complemented
169	#3384	C₂×C₁₃	1	8	yes	complemented
170	#3163	C₂×C₁₃	1	2	yes	complemented
171	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#3081	C₂×C₁₃	1	4	yes	complemented
173	#3077	C₂×C₁₃	1	2	yes	complemented
174	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2948	C₂×C₁₃	1	2	yes	—
176	C₂×#442	C₂×C₁₃	1	1	yes	characteristic
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	8	no	—
179	C₂³×C₁₃	—	8	2	no	—
180	C₂³×C₁₃	—	8	2	no	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	4	4	no	—
183	Q₈×C₁₃	—	4	4	no	—
184	Q₈×C₁₃	—	8	2	no	—
185	Q₈×C₁₃	—	8	8	no	—
186	D₄×C₁₃	—	2	8	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	C₂²×Q₈	1	8	yes	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	8	8	no	—
195	C₂×C₄×C₁₃	—	8	4	no	—
196	C₂×C₄×C₁₃	—	8	8	no	—
197	C₂×C₄×C₁₃	—	8	2	no	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
204	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	2	4	no	—
207	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
208	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
209	#554	—	2	2	no	—
210	#554	—	2	4	no	—
211	#554	C₂²×C₁₃	1	8	yes	complemented
212	#554	C₂²×C₁₃	1	4	yes	complemented
213	D₄×Q₈	—	2	2	no	—
214	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
215	#544	C₂²×C₁₃	1	4	yes	—
216	#543	—	2	4	no	—
217	#533	C₂²×C₁₃	1	2	yes	—
218	#533	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	—	2	4	no	—
220	#518	C₂²×C₁₃	1	4	yes	—
221	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
222	#501	C₂²×C₁₃	1	4	yes	complemented
223	#501	C₂²×C₁₃	1	8	yes	complemented
224	#501	C₂²×C₁₃	1	4	yes	complemented
225	#499	C₂²×C₁₃	1	4	yes	complemented
226	#498	C₂²×C₁₃	1	4	yes	complemented
227	#478	C₂²×C₁₃	1	8	yes	complemented
228	#478	C₂²×C₁₃	1	8	yes	complemented
229	#478	C₂²×C₁₃	1	8	yes	complemented
230	#476	C₂²×C₁₃	1	4	yes	complemented
231	#476	C₂²×C₁₃	1	8	yes	complemented
232	#474	C₂²×C₁₃	1	4	yes	complemented
233	#474	C₂²×C₁₃	1	8	yes	complemented
234	#446	C₂²×C₁₃	1	8	yes	complemented
235	#442	C₂²×C₁₃	1	4	yes	—
236	#442	C₂²×C₁₃	1	8	yes	—
237	#442	C₂²×C₁₃	1	4	yes	—
238	C₄×D₈	C₂²×C₁₃	1	8	yes	—
239	#428	C₂²×C₁₃	1	4	yes	—
240	#427	C₂²×C₁₃	1	2	yes	—
241	#427	C₂²×C₁₃	1	2	yes	—
242	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
243	#424	C₂²×C₁₃	1	2	yes	—
244	#423	C₂²×C₁₃	1	1	yes	characteristic
245	#418	C₂²×C₁₃	1	4	yes	—
246	C₂×#102	C₂²×C₁₃	1	2	yes	—
247	#405	C₂²×C₁₃	1	2	yes	—
248	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	8	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	8	8	no	—
254	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
255	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	D₄×Q₈	1	2	yes	—
263	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
264	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
265	C₂²×Q₈	—	2	4	no	—
266	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂×D₈	Q₈×C₁₃	1	8	yes	complemented
269	C₂×D₈	C₂³×C₁₃	1	4	yes	—
270	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
275	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
278	#125	—	2	4	no	—
279	#125	D₄×C₁₃	1	2	yes	—
280	#125	C₂³×C₁₃	1	4	yes	—
281	#125	C₂³×C₁₃	1	8	yes	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	8	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	—	2	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	C₂³×C₁₃	1	4	yes	—
301	C₄×D₄	C₂³×C₁₃	1	4	yes	—
302	C₄×D₄	C₂³×C₁₃	1	8	yes	—
303	C₄×D₄	C₂³×C₁₃	1	8	yes	—
304	#117	C₂³×C₁₃	1	4	yes	—
305	#117	C₂³×C₁₃	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	8	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	#107	C₂³×C₁₃	1	4	yes	—
313	#107	C₂³×C₁₃	1	4	yes	—
314	#107	C₂³×C₁₃	1	8	yes	—
315	#106	C₂³×C₁₃	1	4	yes	—
316	#106	C₂³×C₁₃	1	2	yes	—
317	#106	C₂³×C₁₃	1	2	yes	—
318	#106	C₂³×C₁₃	1	2	yes	—
319	#106	C₂³×C₁₃	1	2	yes	—
320	#106	C₂³×C₁₃	1	8	yes	—
321	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
322	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
323	#102	C₂³×C₁₃	1	8	yes	—
324	#102	C₂³×C₁₃	1	8	yes	—
325	#102	C₂³×C₁₃	1	8	yes	—
326	#97	C₂³×C₁₃	1	4	yes	—
327	#97	C₂³×C₁₃	1	4	yes	—
328	C₄×C₈	C₂³×C₁₃	1	4	yes	—
329	C₂×C₁₃	—	2	2	no	—
330	C₂×C₁₃	—	4	8	no	—
331	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
332	C₂×C₁₃	#3585	1	2	yes	—
333	C₂⁴	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	8	8	no	—
338	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	complemented
342	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	D₈	C₂×Q₈×C₁₃	1	16	yes	complemented
352	M₁₆	—	2	4	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
355	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
356	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
357	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
367	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
368	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
369	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₄²	C₂⁴×C₁₃	1	4	yes	—
382	C₄²	C₂⁴×C₁₃	1	2	yes	—
383	C₁₃	#61378	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	4	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	Q₈	—	4	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	8	8	no	—
392	Q₈	—	8	2	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	4	no	—
395	D₄	C₂²×Q₈×C₁₃	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	—	8	8	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
410	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
411	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	4	no	—
414	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
421	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	8	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	D₄×Q₈×C₁₃	1	2	yes	—
429	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
430	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	4	8	no	—
433	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
434	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3501	C₂	semidirect
2. C₁₃×#3389	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3163	C₂	semidirect
5. C₁₃×#3162	C₂	semidirect
6. C₁₃×#3081	C₂	semidirect
7. C₁₃×#3077	C₂	semidirect
8. C₁₃×#2961	C₂	semidirect
14. C₁₃×#554	C₂²	semidirect
15. C₁₃×#554	C₂²	semidirect
17. D₄×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×#501	C₂²	semidirect
26. C₁₃×#501	C₂²	semidirect
27. C₁₃×#501	C₂²	semidirect
28. C₁₃×#499	C₂²	semidirect
29. C₁₃×#498	C₂²	semidirect
30. C₁₃×#478	C₂²	semidirect
31. C₁₃×#478	C₂²	semidirect
32. C₁₃×#478	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#476	C₂²	semidirect
35. C₁₃×#474	C₂²	semidirect
36. C₁₃×#474	C₂²	semidirect
37. C₁₃×#446	C₂²	semidirect
55. C₂×C₁₃×D₈	Q₈	semidirect
116. #61378	C₁₃	direct (N × H)
125. C₂×D₄×C₁₃	C₂×Q₈	semidirect
135. C₁₃×D₈	C₂×Q₈	semidirect
138. C₂×C₈×C₁₃	C₂×Q₈	semidirect
167. #3501	C₂×C₁₃	semidirect
168. #3389	C₂×C₁₃	semidirect
169. #3384	C₂×C₁₃	semidirect
170. #3163	C₂×C₁₃	semidirect
171. #3162	C₂×C₁₃	semidirect
172. #3081	C₂×C₁₃	semidirect
173. #3077	C₂×C₁₃	semidirect
174. #2961	C₂×C₁₃	semidirect
211. #554	C₂²×C₁₃	semidirect
212. #554	C₂²×C₁₃	semidirect
214. D₄×Q₈	C₂²×C₁₃	semidirect
222. #501	C₂²×C₁₃	semidirect
223. #501	C₂²×C₁₃	semidirect
224. #501	C₂²×C₁₃	semidirect
225. #499	C₂²×C₁₃	semidirect
226. #498	C₂²×C₁₃	semidirect
227. #478	C₂²×C₁₃	semidirect
228. #478	C₂²×C₁₃	semidirect
229. #478	C₂²×C₁₃	semidirect
230. #476	C₂²×C₁₃	semidirect
231. #476	C₂²×C₁₃	semidirect
232. #474	C₂²×C₁₃	semidirect
233. #474	C₂²×C₁₃	semidirect
234. #446	C₂²×C₁₃	semidirect
268. C₂×D₈	Q₈×C₁₃	semidirect
341. C₂×D₄	C₂×Q₈×C₁₃	semidirect
351. D₈	C₂×Q₈×C₁₃	semidirect
354. C₂×C₈	C₂×Q₈×C₁₃	semidirect
383. C₁₃	#61378	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×#3501	2
C₁₃×#3389	2
C₁₃×#3384	2
C₁₃×#3163	2
C₁₃×#3162	2
C₁₃×#3081	2
C₁₃×#3077	2
C₁₃×#2961	2
C₁₃×#2948	2
C₂×C₁₃×#442	2
#61378	13

Subgroups — C13×#61378 #15747717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61378 #15747717