Subgroups — C₁₃×#18694 #15705033

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1628	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1627	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1626	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1625	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#563	—	2	2	no	—
13	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#554	—	2	1	no	—
16	C₁₃×#553	—	2	1	no	—
17	D₄×Q₈×C₁₃	—	2	1	no	—
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#548	—	2	1	no	—
20	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#544	—	2	1	no	—
22	C₁₃×#542	—	2	1	no	—
23	C₁₃×#541	—	2	1	no	—
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#536	—	2	1	no	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
28	C₁₃×#529	C₂²	1	1	yes	characteristic
29	C₁₃×#529	C₂²	1	1	yes	characteristic
30	C₁₃×#496	—	2	1	no	—
31	C₁₃×#496	—	2	1	no	—
32	C₁₃×#490	—	2	1	no	—
33	C₁₃×#490	—	2	1	no	—
34	C₁₃×#486	—	2	2	no	—
35	C₁₃×#486	C₂²	1	2	yes	—
36	C₁₃×#486	C₂²	1	2	yes	—
37	C₁₃×#460	C₂²	1	2	yes	—
38	C₁₃×#460	C₂²	1	2	yes	—
39	C₁₃×#459	C₂²	1	2	yes	—
40	C₁₃×#459	C₂²	1	2	yes	—
41	C₁₃×#450	—	2	1	no	—
42	C₁₃×#450	—	2	1	no	—
43	C₁₃×#447	—	2	1	no	—
44	C₁₃×#447	—	2	1	no	—
45	C₁₃×#432	C₂²	1	1	yes	characteristic
46	C₁₃×#432	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#102	—	2	2	no	—
48	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#332	C₂²	1	2	yes	complemented
50	C₁₃×#332	C₂²	1	2	yes	complemented
51	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
53	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×D₈	—	2	2	no	—
64	C₂×C₁₃×D₈	—	2	2	no	—
65	C₂²×C₈×C₁₃	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	—	2	1	no	—
70	C₁₃×C₄⋊Q₈	—	2	1	no	—
71	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₁₃×#127	—	2	1	no	—
75	C₁₃×#127	—	2	1	no	—
76	C₁₃×#127	—	2	1	no	—
77	C₁₃×#127	C₂³	1	2	yes	—
78	C₁₃×#126	—	2	2	no	—
79	C₁₃×#126	—	2	2	no	—
80	C₁₃×#126	—	2	2	no	—
81	C₁₃×#126	—	2	1	no	—
82	C₁₃×#126	—	2	1	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	—	2	2	no	—
85	C₁₃×#125	—	2	2	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	D₄	1	1	yes	characteristic
88	C₁₃×#125	D₄	1	1	yes	characteristic
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×#124	D₄	1	1	yes	characteristic
92	C₁₃×#124	D₄	1	1	yes	characteristic
93	C₁₃×#123	—	2	2	no	—
94	C₁₃×#123	—	2	2	no	—
95	C₁₃×#123	—	2	1	no	—
96	C₁₃×#123	—	2	1	no	—
97	C₁₃×#123	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×C₂²⋊Q₈	—	2	2	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×C₂²⋊Q₈	—	2	2	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	1	no	—
107	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
108	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	1	no	—
111	C₁₃×#121	D₄	1	1	yes	characteristic
112	C₁₃×#121	D₄	1	1	yes	characteristic
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×D₄×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	—	2	2	no	—
120	C₄×D₄×C₁₃	—	2	1	no	—
121	C₄×D₄×C₁₃	—	2	1	no	—
122	C₄×D₄×C₁₃	—	2	1	no	—
123	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#117	—	2	1	no	—
126	C₁₃×#117	—	2	1	no	—
127	C₁₃×#117	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₃×#102	—	2	4	no	—
135	C₁₃×#102	—	2	4	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₁₃×C₂²⋊C₈	—	2	1	no	—
142	C₁₃×#97	—	2	1	no	—
143	C₁₃×#97	—	2	1	no	—
144	C₄×C₈×C₁₃	—	2	1	no	—
145	C₄×C₈×C₁₃	C₂³	1	2	yes	—
146	#18694	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂⁴×C₁₃	—	4	1	no	—
148	C₁₃×#41	—	8	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	8	2	no	—
154	C₂×Q₈×C₁₃	—	8	2	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	4	4	no	—
164	C₂×D₄×C₁₃	—	4	1	no	—
165	C₂×D₄×C₁₃	—	4	1	no	—
166	C₂×D₄×C₁₃	—	4	1	no	—
167	C₂×D₄×C₁₃	—	8	2	no	—
168	C₂×D₄×C₁₃	—	8	2	no	—
169	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₁₃×SD₁₆	—	8	2	no	—
180	C₁₃×SD₁₆	—	8	2	no	—
181	C₁₃×D₈	—	8	2	no	—
182	C₁₃×D₈	—	8	2	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×C₂²⋊C₄	—	2	2	no	—
214	C₁₃×C₂²⋊C₄	—	2	2	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	2	1	no	—
217	C₁₃×C₂²⋊C₄	—	2	1	no	—
218	C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₁₃×C₂²⋊C₄	—	2	1	no	—
222	C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₄²×C₁₃	—	2	2	no	—
226	C₄²×C₁₃	—	2	2	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
233	#3552	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1628	C₂×C₁₃	1	2	yes	complemented
238	#1627	C₂×C₁₃	1	2	yes	complemented
239	#1626	C₂×C₁₃	1	2	yes	complemented
240	#1625	C₂×C₁₃	1	2	yes	complemented
241	#1556	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	4	2	no	—
247	C₂³×C₁₃	—	8	2	no	—
248	C₂³×C₁₃	—	8	2	no	—
249	C₂³×C₁₃	—	8	2	no	—
250	C₂³×C₁₃	#120	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	2	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	4	2	no	—
254	Q₈×C₁₃	—	4	2	no	—
255	Q₈×C₁₃	—	8	2	no	—
256	Q₈×C₁₃	—	8	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	4	2	no	—
261	D₄×C₁₃	—	4	2	no	—
262	D₄×C₁₃	—	4	2	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	4	2	no	—
265	D₄×C₁₃	—	4	2	no	—
266	D₄×C₁₃	—	8	2	no	—
267	D₄×C₁₃	—	8	2	no	—
268	D₄×C₁₃	—	8	2	no	—
269	D₄×C₁₃	—	8	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	8	2	no	—
284	C₂×C₄×C₁₃	—	8	2	no	—
285	C₂×C₄×C₁₃	—	8	2	no	—
286	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
288	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₈×C₁₃	—	4	2	no	—
293	C₈×C₁₃	—	4	2	no	—
294	C₈×C₁₃	—	4	2	no	—
295	#563	—	2	2	no	—
296	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	#554	—	2	1	no	—
299	#553	—	2	1	no	—
300	D₄×Q₈	—	2	1	no	—
301	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#548	—	2	1	no	—
303	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	#544	—	2	1	no	—
305	#542	—	2	1	no	—
306	#541	—	2	1	no	—
307	#539	—	2	2	no	—
308	#536	—	2	1	no	—
309	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
311	#529	C₂²×C₁₃	1	1	yes	characteristic
312	#529	C₂²×C₁₃	1	1	yes	characteristic
313	#496	—	2	1	no	—
314	#496	—	2	1	no	—
315	#490	—	2	1	no	—
316	#490	—	2	1	no	—
317	#486	—	2	2	no	—
318	#486	C₂²×C₁₃	1	2	yes	—
319	#486	C₂²×C₁₃	1	2	yes	—
320	#460	C₂²×C₁₃	1	2	yes	—
321	#460	C₂²×C₁₃	1	2	yes	—
322	#459	C₂²×C₁₃	1	2	yes	—
323	#459	C₂²×C₁₃	1	2	yes	—
324	#450	—	2	1	no	—
325	#450	—	2	1	no	—
326	#447	—	2	1	no	—
327	#447	—	2	1	no	—
328	#432	C₂²×C₁₃	1	1	yes	characteristic
329	#432	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	—	2	2	no	—
331	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
332	#332	C₂²×C₁₃	1	2	yes	complemented
333	#332	C₂²×C₁₃	1	2	yes	complemented
334	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
335	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
336	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
337	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	8	2	no	—
347	C₂²×C₁₃	—	8	2	no	—
348	C₂²×C₁₃	—	8	2	no	—
349	C₂²×C₁₃	—	16	4	no	—
350	C₂²×C₁₃	#454	1	2	yes	—
351	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	#576	1	2	yes	—
365	C₄×C₁₃	#577	1	2	yes	—
366	C₂×#41	—	2	1	no	—
367	C₂²×Q₈	—	2	1	no	—
368	C₂²×Q₈	—	2	1	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×D₈	—	2	2	no	—
375	C₂×D₈	—	2	2	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	—	2	1	no	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
383	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	#127	—	2	1	no	—
386	#127	—	2	1	no	—
387	#127	—	2	1	no	—
388	#127	C₂³×C₁₃	1	2	yes	—
389	#126	—	2	2	no	—
390	#126	—	2	2	no	—
391	#126	—	2	2	no	—
392	#126	—	2	1	no	—
393	#126	—	2	1	no	—
394	#125	—	2	2	no	—
395	#125	—	2	2	no	—
396	#125	—	2	2	no	—
397	#125	—	2	1	no	—
398	#125	D₄×C₁₃	1	1	yes	characteristic
399	#125	D₄×C₁₃	1	1	yes	characteristic
400	#124	—	2	2	no	—
401	#124	—	2	1	no	—
402	#124	D₄×C₁₃	1	1	yes	characteristic
403	#124	D₄×C₁₃	1	1	yes	characteristic
404	#123	—	2	2	no	—
405	#123	—	2	2	no	—
406	#123	—	2	1	no	—
407	#123	—	2	1	no	—
408	#123	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	2	1	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	2	1	no	—
417	C₂²⋊Q₈	—	2	1	no	—
418	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
419	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
420	#121	—	2	2	no	—
421	#121	—	2	1	no	—
422	#121	D₄×C₁₃	1	1	yes	characteristic
423	#121	D₄×C₁₃	1	1	yes	characteristic
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
436	#117	—	2	1	no	—
437	#117	—	2	1	no	—
438	#117	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
444	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
445	#102	—	2	4	no	—
446	#102	—	2	4	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	C₂²⋊C₈	—	2	1	no	—
453	#97	—	2	1	no	—
454	#97	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	C₄×C₈	C₂³×C₁₃	1	2	yes	—
457	C₂×C₁₃	—	2	2	no	—
458	C₂×C₁₃	—	8	1	no	—
459	C₂×C₁₃	—	8	1	no	—
460	C₂×C₁₃	—	16	2	no	—
461	C₂×C₁₃	#3008	1	1	yes	characteristic
462	C₂×C₁₃	#3010	1	1	yes	characteristic
463	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
464	C₂⁴	—	4	1	no	—
465	#41	—	8	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	8	2	no	—
471	C₂×Q₈	—	8	2	no	—
472	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	—	8	2	no	—
485	C₂×D₄	—	8	2	no	—
486	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	SD₁₆	—	8	2	no	—
497	SD₁₆	—	8	2	no	—
498	D₈	—	8	2	no	—
499	D₈	—	8	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	4	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
525	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
550	C₁₃	#18694	1	1	yes	characteristic, direct product factor, Sylow
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	8	2	no	—
555	C₂³	—	8	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₁₃×#120	1	1	yes	characteristic
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	Q₈	—	8	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	2	no	—
575	D₄	—	8	2	no	—
576	D₄	—	8	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
594	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
595	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₈	—	4	2	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	16	4	no	—
614	C₂²	C₁₃×#454	1	2	yes	—
615	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	C₁₃×#576	1	2	yes	—
629	C₄	C₁₃×#577	1	2	yes	—
630	C₂	—	2	2	no	—
631	C₂	—	8	1	no	—
632	C₂	—	8	1	no	—
633	C₂	—	16	2	no	—
634	C₂	C₁₃×#3008	1	1	yes	characteristic
635	C₂	C₁₃×#3010	1	1	yes	characteristic
636	C₂	C₂×C₁₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₁₃×#3552	C₂	semidirect
2. C₁₃×#3217	C₂	semidirect
3. C₁₃×#3217	C₂	semidirect
4. C₂×C₁₃×#486	C₂	semidirect
5. C₁₃×#1628	C₂	semidirect
6. C₁₃×#1627	C₂	semidirect
7. C₁₃×#1626	C₂	semidirect
8. C₁₃×#1625	C₂	semidirect
9. C₁₃×#1556	C₂	semidirect
10. C₁₃×#1494	C₂	semidirect
11. C₁₃×#1494	C₂	semidirect
13. C₁₃×#557	C₂²	semidirect
14. C₁₃×#556	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
49. C₁₃×#332	C₂²	semidirect
50. C₁₃×#332	C₂²	semidirect
51. C₁₃×Q₈⋊C₈	C₂²	semidirect
52. C₁₃×Q₈⋊C₈	C₂²	semidirect
53. C₁₃×D₄⋊C₈	C₂²	semidirect
54. C₁₃×D₄⋊C₈	C₂²	semidirect
146. #18694	C₁₃	direct (N × H)
233. #3552	C₂×C₁₃	semidirect
234. #3217	C₂×C₁₃	semidirect
235. #3217	C₂×C₁₃	semidirect
236. C₂×#486	C₂×C₁₃	semidirect
237. #1628	C₂×C₁₃	semidirect
238. #1627	C₂×C₁₃	semidirect
239. #1626	C₂×C₁₃	semidirect
240. #1625	C₂×C₁₃	semidirect
241. #1556	C₂×C₁₃	semidirect
242. #1494	C₂×C₁₃	semidirect
243. #1494	C₂×C₁₃	semidirect
296. #557	C₂²×C₁₃	semidirect
297. #556	C₂²×C₁₃	semidirect
301. D₄×Q₈	C₂²×C₁₃	semidirect
303. #547	C₂²×C₁₃	semidirect
332. #332	C₂²×C₁₃	semidirect
333. #332	C₂²×C₁₃	semidirect
334. Q₈⋊C₈	C₂²×C₁₃	semidirect
335. Q₈⋊C₈	C₂²×C₁₃	semidirect
336. D₄⋊C₈	C₂²×C₁₃	semidirect
337. D₄⋊C₈	C₂²×C₁₃	semidirect
550. C₁₃	#18694	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×#3552	2
C₁₃×#3217	2
C₂×C₁₃×#486	2
C₁₃×#1628	2
C₁₃×#1627	2
C₁₃×#1626	2
C₁₃×#1625	2
C₁₃×#1556	2
C₁₃×#1494	2
#18694	13

Subgroups — C13×#18694 #15705033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18694 #15705033