Subgroups — C₁₃×#61694 #15748033

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3334	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3294	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3226	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3186	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#480	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₂²×C₁₃×#41	—	2	1	no	—
12	C₁₃×#547	—	2	4	no	—
13	C₁₃×#547	C₂²	1	8	yes	complemented
14	C₁₃×#547	C₂²	1	4	yes	complemented
15	C₁₃×#546	—	2	4	no	—
16	D₄²×C₁₃	C₂²	1	4	yes	complemented
17	C₁₃×#537	—	2	1	no	—
18	C₁₃×#534	—	2	2	no	—
19	C₁₃×#532	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#123	—	2	2	no	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₁₃×#500	C₂²	1	4	yes	complemented
29	C₁₃×#486	C₂²	1	4	yes	complemented
30	C₁₃×#480	C₂²	1	16	yes	complemented
31	C₁₃×#480	C₂²	1	8	yes	complemented
32	C₁₃×#480	C₂²	1	4	yes	complemented
33	C₁₃×#480	C₂²	1	8	yes	complemented
34	C₁₃×#474	C₂²	1	8	yes	complemented
35	C₁₃×#474	C₂²	1	4	yes	complemented
36	C₁₃×#466	C₂²	1	16	yes	complemented
37	C₁₃×#459	C₂²	1	4	yes	complemented
38	C₁₃×#447	C₂²	1	8	yes	complemented
39	C₁₃×#447	C₂²	1	4	yes	complemented
40	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
41	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
42	C₁₃×#431	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	8	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₁₃×H(5,𝔽₂)	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	8	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	4	8	no	—
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	4	no	—
55	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	—	2	2	no	—
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂×C₁₃×D₈	C₂³	1	8	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₃×#127	C₂³	1	2	yes	—
67	C₁₃×#124	—	2	2	no	—
68	C₁₃×#123	—	2	16	no	—
69	C₁₃×#123	—	2	8	no	—
70	C₁₃×C₂²⋊Q₈	—	2	8	no	—
71	C₁₃×C₂²⋊Q₈	—	2	4	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	4	no	—
74	C₁₃×#121	—	2	4	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	C₂³	1	8	yes	—
78	C₁₃×#121	C₂³	1	4	yes	—
79	C₁₃×#121	C₂³	1	8	yes	—
80	C₁₃×#120	—	2	8	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	D₄	1	4	yes	—
84	C₄×D₄×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	C₂³	1	4	yes	—
86	C₄×D₄×C₁₃	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂³	1	8	yes	—
101	C₁₃×#107	C₂³	1	16	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₃×#102	C₂³	1	8	yes	—
104	C₁₃×#102	C₂³	1	16	yes	—
105	C₁₃×#102	C₂³	1	8	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	#61694	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
113	C₁₃×#41	—	4	32	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	—	4	8	no	—
129	C₂×D₄×C₁₃	—	4	16	no	—
130	C₂×D₄×C₁₃	—	4	16	no	—
131	C₂×D₄×C₁₃	D₈	1	8	yes	complemented
132	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	4	4	no	—
142	C₂²×C₄×C₁₃	—	4	8	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₁₃×D₈	—	4	8	no	—
151	C₂×C₈×C₁₃	—	4	8	no	—
152	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
169	C₄²×C₁₃	C₂×D₄	1	2	yes	—
170	C₄²×C₁₃	C₂⁴	1	2	yes	—
171	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#3334	C₂×C₁₃	1	8	yes	complemented
174	#3294	C₂×C₁₃	1	8	yes	complemented
175	#3226	C₂×C₁₃	1	2	yes	complemented
176	#3186	C₂×C₁₃	1	4	yes	complemented
177	#3100	C₂×C₁₃	1	2	yes	complemented
178	C₂×#480	C₂×C₁₃	1	4	yes	complemented
179	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	8	no	—
188	C₂³×C₁₃	—	8	4	no	—
189	C₂³×C₁₃	—	8	4	no	—
190	C₂³×C₁₃	C₂×D₈	1	8	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
192	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₃	—	4	8	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	2	8	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	8	no	—
199	D₄×C₁₃	—	4	16	no	—
200	D₄×C₁₃	—	4	16	no	—
201	D₄×C₁₃	—	4	4	no	—
202	D₄×C₁₃	—	8	2	no	—
203	D₄×C₁₃	—	8	4	no	—
204	D₄×C₁₃	C₂×D₈	1	16	yes	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	16	no	—
216	C₂×C₄×C₁₃	—	4	8	no	—
217	C₂×C₄×C₁₃	—	4	8	no	—
218	C₂×C₄×C₁₃	—	4	8	no	—
219	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₁₃	—	2	8	no	—
226	C₂×H(5,𝔽₂)	—	2	1	no	—
227	C₂²×#41	—	2	1	no	—
228	#547	—	2	4	no	—
229	#547	C₂²×C₁₃	1	4	yes	complemented
230	#547	C₂²×C₁₃	1	8	yes	complemented
231	#546	—	2	4	no	—
232	D₄²	C₂²×C₁₃	1	4	yes	complemented
233	#537	—	2	1	no	—
234	#534	—	2	2	no	—
235	#532	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	C₂×#123	—	2	2	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×#121	C₂²×C₁₃	1	4	yes	—
240	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
241	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
244	#500	C₂²×C₁₃	1	4	yes	complemented
245	#486	C₂²×C₁₃	1	4	yes	complemented
246	#480	C₂²×C₁₃	1	8	yes	complemented
247	#480	C₂²×C₁₃	1	16	yes	complemented
248	#480	C₂²×C₁₃	1	4	yes	complemented
249	#480	C₂²×C₁₃	1	8	yes	complemented
250	#474	C₂²×C₁₃	1	4	yes	complemented
251	#474	C₂²×C₁₃	1	8	yes	complemented
252	#466	C₂²×C₁₃	1	16	yes	complemented
253	#459	C₂²×C₁₃	1	4	yes	complemented
254	#447	C₂²×C₁₃	1	4	yes	complemented
255	#447	C₂²×C₁₃	1	8	yes	complemented
256	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
257	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
258	#431	C₂²×C₁₃	1	2	yes	complemented
259	C₂×#107	C₂²×C₁₃	1	8	yes	complemented
260	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
261	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	4	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	4	no	—
266	C₂²×C₁₃	—	4	8	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	8	4	no	—
274	C₂²×C₁₃	—	16	8	no	—
275	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
276	C₂²×C₁₃	C₂²×D₈	1	8	yes	—
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	4	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	C₂²×D₈	1	4	yes	—
285	C₄×C₁₃	#585	1	2	yes	—
286	H(5,𝔽₂)	—	4	8	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	—	4	8	no	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×D₄	—	2	4	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×D₈	C₂³×C₁₃	1	8	yes	—
302	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
305	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
306	#127	C₂³×C₁₃	1	2	yes	—
307	#124	—	2	2	no	—
308	#123	—	2	16	no	—
309	#123	—	2	8	no	—
310	C₂²⋊Q₈	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	#121	—	2	4	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	#121	—	2	2	no	—
316	#121	—	2	4	no	—
317	#121	C₂³×C₁₃	1	4	yes	—
318	#121	C₂³×C₁₃	1	8	yes	—
319	#121	C₂³×C₁₃	1	8	yes	—
320	#120	—	2	8	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	D₄×C₁₃	1	4	yes	—
324	C₄×D₄	C₂³×C₁₃	1	4	yes	—
325	C₄×D₄	C₂³×C₁₃	1	4	yes	—
326	C₄×D₄	C₂³×C₁₃	1	4	yes	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	4	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	#107	C₂³×C₁₃	1	8	yes	—
341	#107	C₂³×C₁₃	1	16	yes	—
342	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
343	#102	C₂³×C₁₃	1	8	yes	—
344	#102	C₂³×C₁₃	1	16	yes	—
345	#102	C₂³×C₁₃	1	8	yes	—
346	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
347	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
348	C₄×C₈	C₂³×C₁₃	1	4	yes	—
349	C₂×C₁₃	—	2	2	no	—
350	C₂×C₁₃	—	2	8	no	—
351	C₂×C₁₃	—	8	2	no	—
352	C₂×C₁₃	—	8	4	no	—
353	C₂×C₁₃	#3485	1	1	yes	characteristic
354	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
355	C₂×C₁₃	#3586	1	1	yes	characteristic
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
359	#41	—	4	32	no	—
360	#41	—	4	16	no	—
361	#41	—	4	8	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	16	no	—
376	C₂×D₄	—	4	16	no	—
377	C₂×D₄	C₁₃×D₈	1	8	yes	complemented
378	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
379	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
380	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	8	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
396	D₈	—	4	8	no	—
397	C₂×C₈	—	4	8	no	—
398	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
406	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
407	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
408	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₂⁴×C₁₃	1	2	yes	—
417	C₁₃	#61694	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	8	no	—
426	C₂³	—	8	4	no	—
427	C₂³	—	8	4	no	—
428	C₂³	C₂×C₁₃×D₈	1	8	yes	—
429	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
430	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	Q₈	—	4	8	no	—
432	Q₈	—	4	4	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	8	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	8	no	—
437	D₄	—	4	16	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	4	no	—
440	D₄	—	8	4	no	—
441	D₄	—	8	2	no	—
442	D₄	C₂×C₁₃×D₈	1	16	yes	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	16	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
463	C₈	—	2	8	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	16	8	no	—
477	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
478	C₂²	C₂²×C₁₃×D₈	1	8	yes	—
479	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	C₂²×C₁₃×D₈	1	4	yes	—
487	C₄	C₁₃×#585	1	2	yes	—
488	C₂	—	2	2	no	—
489	C₂	—	2	8	no	—
490	C₂	—	8	2	no	—
491	C₂	—	8	4	no	—
492	C₂	C₁₃×#3485	1	1	yes	characteristic
493	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
494	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#3496	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3334	C₂	semidirect
4. C₁₃×#3294	C₂	semidirect
5. C₁₃×#3226	C₂	semidirect
6. C₁₃×#3186	C₂	semidirect
7. C₁₃×#3100	C₂	semidirect
8. C₂×C₁₃×#480	C₂	semidirect
9. C₁₃×#2972	C₂	semidirect
13. C₁₃×#547	C₂²	semidirect
14. C₁₃×#547	C₂²	semidirect
16. D₄²×C₁₃	C₂²	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
27. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
28. C₁₃×#500	C₂²	semidirect
29. C₁₃×#486	C₂²	semidirect
30. C₁₃×#480	C₂²	semidirect
31. C₁₃×#480	C₂²	semidirect
32. C₁₃×#480	C₂²	semidirect
33. C₁₃×#480	C₂²	semidirect
34. C₁₃×#474	C₂²	semidirect
35. C₁₃×#474	C₂²	semidirect
36. C₁₃×#466	C₂²	semidirect
37. C₁₃×#459	C₂²	semidirect
38. C₁₃×#447	C₂²	semidirect
39. C₁₃×#447	C₂²	semidirect
40. C₄×C₁₃×D₈	C₂²	semidirect
41. C₈×D₄×C₁₃	C₂²	semidirect
42. C₁₃×#431	C₂²	semidirect
43. C₂×C₁₃×#107	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
109. #61694	C₁₃	direct (N × H)
131. C₂×D₄×C₁₃	D₈	semidirect
171. #3496	C₂×C₁₃	semidirect
172. C₂×#547	C₂×C₁₃	semidirect
173. #3334	C₂×C₁₃	semidirect
174. #3294	C₂×C₁₃	semidirect
175. #3226	C₂×C₁₃	semidirect
176. #3186	C₂×C₁₃	semidirect
177. #3100	C₂×C₁₃	semidirect
178. C₂×#480	C₂×C₁₃	semidirect
179. #2972	C₂×C₁₃	semidirect
229. #547	C₂²×C₁₃	semidirect
230. #547	C₂²×C₁₃	semidirect
232. D₄²	C₂²×C₁₃	semidirect
236. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
240. C₂×#121	C₂²×C₁₃	semidirect
242. C₂×C₄×D₄	C₂²×C₁₃	semidirect
243. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
244. #500	C₂²×C₁₃	semidirect
245. #486	C₂²×C₁₃	semidirect
246. #480	C₂²×C₁₃	semidirect
247. #480	C₂²×C₁₃	semidirect
248. #480	C₂²×C₁₃	semidirect
249. #480	C₂²×C₁₃	semidirect
250. #474	C₂²×C₁₃	semidirect
251. #474	C₂²×C₁₃	semidirect
252. #466	C₂²×C₁₃	semidirect
253. #459	C₂²×C₁₃	semidirect
254. #447	C₂²×C₁₃	semidirect
255. #447	C₂²×C₁₃	semidirect
256. C₄×D₈	C₂²×C₁₃	semidirect
257. C₈×D₄	C₂²×C₁₃	semidirect
258. #431	C₂²×C₁₃	semidirect
259. C₂×#107	C₂²×C₁₃	semidirect
260. C₂×#102	C₂²×C₁₃	semidirect
261. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
377. C₂×D₄	C₁₃×D₈	semidirect
417. C₁₃	#61694	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×#3496	2
C₂×C₁₃×#547	2
C₁₃×#3334	2
C₁₃×#3294	2
C₁₃×#3226	2
C₁₃×#3186	2
C₁₃×#3100	2
C₂×C₁₃×#480	2
C₁₃×#2972	2
#61694	13

Subgroups — C13×#61694 #15748033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61694 #15748033