Subgroups — #15834889

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125411	C₂	1	1	yes	maximal, characteristic
2	#13123902	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113719	C₂	1	2	yes	maximal, complemented
4	#13113700	C₂	1	2	yes	maximal, complemented
5	#13113698	C₂	1	2	yes	maximal, complemented
6	C₈×#6104	C₂	1	2	yes	maximal, complemented
7	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113253	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113252	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	#11719182	C₂²	1	1	yes	characteristic
14	C₁₃×#436	—	2	1	no	—
15	C₁₃×#436	C₂²	1	2	yes	—
16	C₈×D₄×C₁₃	—	2	1	no	—
17	C₈×D₄×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#408	—	2	2	no	—
21	#11718749	C₄	1	1	yes	characteristic
22	#11718739	C₄	1	1	yes	characteristic
23	#11718734	C₄	1	1	yes	characteristic
24	#11718731	C₄	1	1	yes	characteristic
25	#11718699	C₄	1	2	yes	—
26	#11718699	C₄	1	2	yes	—
27	C₄×#6104	C₂²	1	2	yes	—
28	C₄×#6104	C₂²	1	2	yes	—
29	#11718586	C₂²	1	1	yes	characteristic
30	C₄×#6099	C₂²	1	1	yes	characteristic
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	#11718499	—	2	1	no	—
33	#11718495	—	2	1	no	—
34	#11718388	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	—
36	C₈×D₅₂	C₂²	1	2	yes	—
37	D₄⋊#1055	C₂²	1	2	yes	—
38	D₄⋊#1055	C₂²	1	2	yes	—
39	#11718075	C₂²	1	2	yes	—
40	#11718075	C₂²	1	2	yes	—
41	#11718072	C₂²	1	1	yes	characteristic
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718071	C₂²	1	1	yes	characteristic
44	#11718071	C₂²	1	1	yes	characteristic
45	#11718046	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×#6127	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#124	—	2	1	no	—
54	C₁₃×#121	—	2	1	no	—
55	C₁₃×#121	C₂×C₄	1	2	yes	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6104	C₂×C₄	1	2	yes	—
60	C₂×#6104	C₂×C₄	1	2	yes	—
61	#88184	—	2	1	no	—
62	#88184	C₂×C₄	1	2	yes	—
63	C₂×#6099	—	2	1	no	—
64	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
65	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
66	C₂×#6094	—	2	2	no	—
67	C₂×C₈×D₁₃	—	2	2	no	—
68	#88129	—	2	1	no	—
69	#88128	C₂×C₄	1	1	yes	characteristic
70	C₄×D₅₂	—	2	1	no	—
71	C₄×D₅₂	C₂³	1	2	yes	—
72	#88123	C₂×C₄	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	2	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₁₃	—	2	1	no	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	#88072	C₂×C₄	1	2	yes	—
84	#88072	C₂×C₄	1	2	yes	—
85	C₂²⋊#1055	—	2	1	no	—
86	#88060	—	2	2	no	—
87	#88060	—	2	2	no	—
88	#88049	C₂×C₄	1	2	yes	—
89	#88049	C₂×C₄	1	2	yes	—
90	#88047	C₂×C₄	1	2	yes	—
91	#88047	C₂×C₄	1	2	yes	—
92	C₄⋊#1055	C₂³	1	1	yes	characteristic
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	#88043	—	2	1	no	—
95	C₄×#1055	—	2	1	no	—
96	C₄×#1055	C₂×C₄	1	1	yes	characteristic
97	C₄×#1055	C₂×C₄	1	1	yes	characteristic
98	C₄×#1055	C₂³	1	2	yes	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	#18084	—	13	1	no	maximal, Sylow
102	C₁₃×#41	—	8	1	no	—
103	C₁₃×#41	—	8	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₃	—	2	2	no	—
114	#6127	—	8	1	no	—
115	#6127	—	8	1	no	—
116	C₂×D₅₂	—	2	1	no	—
117	C₂×D₅₂	—	2	1	no	—
118	C₂×D₅₂	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₁₃	—	2	2	no	—
120	C₂×Dic₂₆	—	2	1	no	—
121	C₁₃×M₁₆	—	8	2	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	8	2	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	#6104	—	2	4	no	—
136	#6104	—	4	2	no	—
137	#6103	—	2	2	no	—
138	#6103	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	1	no	—
140	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
141	#6099	—	2	4	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	4	1	no	—
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	#6094	—	8	2	no	—
152	C₈×D₁₃	—	8	2	no	—
153	#3169	—	13	1	no	—
154	#2979	—	13	1	no	—
155	#2979	D₁₃	1	1	yes	characteristic, complemented
156	#1589	—	13	2	no	—
157	#1586	—	13	2	no	—
158	#1586	—	13	2	no	—
159	C₈×D₈	—	13	2	no	—
160	#1564	—	13	1	no	—
161	#1484	—	13	1	no	—
162	#1484	—	13	1	no	—
163	C₈×M₁₆	—	13	1	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	8	1	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	8	1	no	—
172	D₄×C₁₃	—	8	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₁₃	—	8	2	no	—
188	C₂×Dic₁₃	—	2	2	no	—
189	D₅₂	—	2	2	no	—
190	D₅₂	—	2	2	no	—
191	D₅₂	—	4	2	no	—
192	D₅₂	—	8	1	no	—
193	C₄×D₁₃	—	4	2	no	—
194	C₄×D₁₃	—	4	2	no	—
195	Dic₂₆	—	8	1	no	—
196	C₈×C₁₃	—	2	2	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	4	1	no	—
199	C₈×C₁₃	—	4	1	no	—
200	#1055	—	2	4	no	—
201	#1055	—	2	1	no	—
202	#1055	—	2	1	no	—
203	#1055	—	2	1	no	—
204	#1055	—	4	1	no	—
205	#1055	—	4	1	no	—
206	#1055	#131	1	2	yes	—
207	#532	—	13	1	no	—
208	#532	C₂×D₁₃	1	1	yes	characteristic
209	#500	—	13	1	no	—
210	#493	—	13	1	no	—
211	#486	—	13	1	no	—
212	#486	—	13	1	no	—
213	#466	—	13	2	no	—
214	#466	—	13	2	no	—
215	C₄×D₈	—	13	2	no	—
216	C₄×D₈	—	13	2	no	—
217	#436	—	2	1	no	—
218	#436	—	13	2	no	—
219	#436	—	26	1	no	—
220	#436	C₂×D₁₃	1	2	yes	—
221	C₈×D₄	—	2	1	no	—
222	C₈×D₄	—	13	2	no	—
223	C₈×D₄	—	26	1	no	—
224	C₈×D₄	C₂×D₁₃	1	2	yes	—
225	#431	—	13	1	no	—
226	#431	C₂×D₁₃	1	1	yes	characteristic
227	#431	C₂×D₁₃	1	1	yes	characteristic
228	#408	—	2	2	no	—
229	#408	—	26	2	no	—
230	C₄×M₁₆	—	13	1	no	—
231	C₂×C₄×C₈	—	13	1	no	—
232	#335	—	13	1	no	—
233	#335	—	13	1	no	—
234	#334	—	13	1	no	—
235	#334	—	13	1	no	—
236	D₄⋊C₈	—	13	2	no	—
237	D₄⋊C₈	—	13	2	no	—
238	D₄⋊C₈	—	13	2	no	—
239	D₄⋊C₈	—	13	2	no	—
240	#322	—	13	2	no	—
241	C₈²	—	13	2	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
249	C₂×D₁₃	—	4	2	no	—
250	C₂×D₁₃	—	4	2	no	—
251	C₂×D₁₃	—	4	2	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	#443	1	2	yes	—
257	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
258	C₄×C₁₃	#568	1	1	yes	characteristic
259	C₄×C₁₃	#576	1	1	yes	characteristic
260	C₄×C₁₃	#576	1	1	yes	characteristic
261	Dic₁₃	—	4	2	no	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	26	1	no	—
264	C₂×D₈	—	13	2	no	—
265	C₂×D₈	—	13	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	26	1	no	—
268	C₂×M₁₆	—	26	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	26	2	no	—
273	C₄⋊Q₈	—	13	1	no	—
274	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
275	#127	—	13	1	no	—
276	#127	C₄×D₁₃	1	1	yes	characteristic
277	#124	—	2	1	no	—
278	#124	—	26	1	no	—
279	#121	—	2	1	no	—
280	#121	—	13	2	no	—
281	#121	—	26	1	no	—
282	#121	C₄×D₁₃	1	2	yes	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	13	2	no	—
285	C₄×D₄	—	26	1	no	—
286	C₄×D₄	C₂²×D₁₃	1	2	yes	—
287	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
288	#107	—	13	2	no	—
289	#107	—	13	2	no	—
290	C₄⋊C₈	—	13	1	no	—
291	C₄⋊C₈	—	13	1	no	—
292	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
293	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
294	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
295	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
296	#102	—	13	2	no	—
297	#102	—	13	2	no	—
298	#102	—	13	2	no	—
299	#102	—	13	2	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	—	26	1	no	—
304	C₂²⋊C₈	—	26	2	no	—
305	C₂²⋊C₈	—	26	2	no	—
306	C₂²⋊C₈	C₂²⋊D₁₃	1	2	yes	—
307	#97	—	26	1	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	—	13	1	no	—
310	C₄×C₈	—	13	1	no	—
311	C₄×C₈	—	13	1	no	—
312	C₄×C₈	—	13	1	no	—
313	C₄×C₈	—	13	2	no	—
314	C₄×C₈	—	26	1	no	—
315	C₄×C₈	C₂²×D₁₃	1	2	yes	—
316	C₂×C₁₃	—	4	1	no	—
317	C₂×C₁₃	—	8	2	no	—
318	C₂×C₁₃	#2935	1	1	yes	characteristic
319	C₂×C₁₃	#2948	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
321	D₁₃	—	8	2	no	—
322	#41	—	8	1	no	—
323	#41	—	8	1	no	—
324	#41	—	104	1	no	—
325	#41	—	104	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	26	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	13	2	no	—
332	C₂×D₄	—	26	2	no	—
333	C₂×D₄	—	26	1	no	—
334	C₂×D₄	—	26	1	no	—
335	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	26	2	no	—
338	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	#6127	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
341	D₈	—	26	4	no	—
342	D₈	—	52	2	no	—
343	M₁₆	—	8	2	no	—
344	M₁₆	—	26	4	no	—
345	M₁₆	—	104	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	8	2	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	52	1	no	—
358	C₂×C₈	—	104	2	no	—
359	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
360	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	13	2	no	—
363	C₄⋊C₄	—	26	1	no	—
364	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	26	2	no	—
368	C₂²⋊C₄	—	26	2	no	—
369	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
370	C₄²	#6127	1	1	yes	characteristic
371	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
372	C₄²	C₂³×D₁₃	1	1	yes	characteristic
373	C₁₃	#18084	1	1	yes	characteristic, complemented, Sylow
374	C₂³	—	2	2	no	—
375	C₂³	—	26	2	no	—
376	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
377	Q₈	—	8	1	no	—
378	Q₈	—	104	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	2	no	—
384	D₄	—	26	2	no	—
385	D₄	—	26	2	no	—
386	D₄	—	52	2	no	—
387	D₄	—	104	1	no	—
388	D₄	—	104	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	52	2	no	—
399	C₂×C₄	—	52	2	no	—
400	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
401	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#6127	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	13	2	no	—
411	C₈	—	26	4	no	—
412	C₈	—	26	1	no	—
413	C₈	—	26	1	no	—
414	C₈	—	26	1	no	—
415	C₈	—	52	1	no	—
416	C₈	—	52	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	52	2	no	—
424	C₂²	—	52	2	no	—
425	C₂²	—	52	2	no	—
426	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	52	2	no	—
432	C₄	#11718805	1	2	yes	—
433	C₄	D₁₃×#131	1	1	yes	characteristic
434	C₄	#11719455	1	1	yes	characteristic
435	C₄	#11719540	1	1	yes	characteristic
436	C₄	#11719540	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	104	2	no	—
440	C₂	#13123578	1	1	yes	characteristic
441	C₂	#13123686	1	1	yes	characteristic
442	C₂	C₂×#11718805	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2979	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125411	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2979	D₁₃
hypocenter	C₁₃	#18084
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2979

Complements

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

N	H ≅ G/N	type
2. #13123902	C₂	semidirect
3. #13113719	C₂	semidirect
4. #13113700	C₂	semidirect
5. #13113698	C₂	semidirect
6. C₈×#6104	C₂	semidirect
7. #13113582	C₂	semidirect
8. #13113253	C₂	semidirect
9. #13113252	C₂	semidirect
10. #13113117	C₂	semidirect
11. C₁₃×#2979	C₂	semidirect
155. #2979	D₁₃	semidirect
373. C₁₃	#18084	semidirect

Maximal subgroups

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

subgroup	index
#13125411	2
#13123902	2
#13113719	2
#13113700	2
#13113698	2
C₈×#6104	2
#13113582	2
#13113253	2
#13113252	2
#13113117	2
C₁₃×#2979	2
#18084	13