Subgroups — #15832931

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124879	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113670	C₂	1	2	yes	maximal, complemented
4	#13113663	C₂	1	2	yes	maximal, complemented
5	#13113658	C₂	1	2	yes	maximal, complemented
6	#13113646	C₂	1	2	yes	maximal, complemented
7	#13113622	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113278	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113249	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	—	2	1	no	—
14	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
15	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
16	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#435	—	2	1	no	—
19	C₈×D₄×C₁₃	—	2	1	no	—
20	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#433	—	2	1	no	—
22	C₁₃×#432	C₂²	1	1	yes	characteristic
23	C₁₃×#405	—	2	1	no	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×#88060	—	2	1	no	—
26	#11718727	C₄	1	2	yes	—
27	#11718718	C₄	1	2	yes	—
28	#11718707	C₄	1	1	yes	characteristic
29	#11718705	C₄	1	1	yes	characteristic
30	#11718697	C₄	1	1	yes	characteristic
31	#11718695	C₄	1	1	yes	characteristic
32	C₄×#6106	C₂²	1	2	yes	—
33	C₄×#6104	C₂²	1	2	yes	—
34	#11718586	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	C₈×D₅₂	—	2	1	no	—
38	C₈×D₅₂	—	2	1	no	—
39	C₈×D₅₂	C₂²	1	2	yes	—
40	C₈×D₅₂	C₂²	1	2	yes	—
41	Q₈⋊#1055	C₂²	1	2	yes	complemented
42	D₄⋊#1055	C₂²	1	2	yes	complemented
43	#11718075	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	complemented
46	#11718071	C₂²	1	2	yes	complemented
47	#11718047	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
55	C₁₃×#126	—	2	1	no	—
56	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
57	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#123	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#117	—	2	1	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×#6106	C₂×C₄	1	2	yes	—
67	C₂×#6104	C₂×C₄	1	2	yes	—
68	C₂×#6103	—	2	1	no	—
69	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×#6099	—	2	1	no	—
71	C₂²×#1055	—	2	1	no	—
72	C₂×C₈×D₁₃	—	2	2	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	C₂×C₈×D₁₃	—	4	4	no	—
75	C₄×D₅₂	—	2	1	no	—
76	C₄×D₅₂	—	2	1	no	—
77	C₄×D₅₂	C₂×C₄	1	2	yes	—
78	C₄×D₅₂	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₂²⋊C₈	—	2	1	no	—
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₁₃×C₂²⋊C₈	—	2	1	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₁₃×#97	—	2	1	no	—
88	C₄×C₈×C₁₃	—	2	1	no	—
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	#88075	C₂×C₄	1	2	yes	—
94	#88072	C₂×C₄	1	2	yes	—
95	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
97	#88060	—	2	2	no	—
98	#88060	—	2	2	no	—
99	#88049	C₂×C₄	1	2	yes	—
100	#88049	C₂×C₄	1	2	yes	—
101	#88048	C₂×C₄	1	2	yes	—
102	#88047	C₂×C₄	1	2	yes	—
103	C₄⋊#1055	—	2	1	no	—
104	C₄⋊#1055	C₂×C₄	1	2	yes	—
105	C₄⋊#1055	C₂³	1	2	yes	—
106	#88043	—	2	1	no	—
107	C₄×#1055	C₂³	1	2	yes	—
108	C₄×#1055	C₂³	1	2	yes	—
109	#17914	—	13	1	no	maximal, Sylow
110	C₂³×D₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×Dic₁₃	—	2	1	no	—
119	C₂×D₅₂	—	2	1	no	—
120	C₂×D₅₂	—	2	4	no	—
121	C₂×D₅₂	C₂²×C₄	1	2	yes	—
122	C₂×C₄×D₁₃	—	2	2	no	—
123	C₂×C₄×D₁₃	—	2	2	no	—
124	C₂×C₄×D₁₃	—	4	2	no	—
125	C₂×C₄×D₁₃	—	4	2	no	—
126	C₁₃×M₁₆	—	4	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	4	1	no	—
131	C₂×C₈×C₁₃	—	4	2	no	—
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	#41	1	1	yes	characteristic
151	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
152	#6106	—	2	4	no	—
153	#6104	—	2	4	no	—
154	#6103	—	2	2	no	—
155	#6103	—	2	2	no	—
156	C₄⋊Dic₁₃	—	2	1	no	—
157	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
158	#6099	—	4	2	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	4	2	no	—
162	C₂×#1055	C₂²×C₄	1	2	yes	—
163	C₂×#1055	C₂²×C₄	1	2	yes	—
164	C₈×D₁₃	—	4	4	no	—
165	C₈×D₁₃	—	4	4	no	—
166	#3105	—	13	1	no	—
167	#2966	D₁₃	1	1	yes	characteristic, complemented
168	C₂×C₈×D₄	—	13	1	no	—
169	#1582	—	13	2	no	—
170	#1581	—	13	2	no	—
171	#1580	—	13	2	no	—
172	SD₁₆⋊C₈	—	13	2	no	—
173	#1573	—	13	1	no	—
174	#1490	—	13	1	no	—
175	#1483	—	13	1	no	—
176	#1451	—	13	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
179	C₂²×D₁₃	—	2	4	no	—
180	C₂²×D₁₃	—	2	2	no	—
181	C₂²×D₁₃	—	4	2	no	—
182	C₂²×D₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	4	2	no	—
203	D₅₂	—	2	4	no	—
204	D₅₂	—	2	2	no	—
205	D₅₂	#131	1	4	yes	—
206	C₄×D₁₃	—	4	4	no	—
207	C₄×D₁₃	—	4	2	no	—
208	C₄×D₁₃	—	4	2	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
215	#1055	—	2	2	no	—
216	#1055	—	2	2	no	—
217	#1055	—	4	2	no	—
218	#1055	—	4	2	no	—
219	C₂³×C₈	—	26	1	no	—
220	#529	C₂×D₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	—	13	1	no	—
222	#484	—	13	1	no	—
223	#481	—	13	1	no	—
224	#478	—	13	2	no	—
225	#463	—	13	2	no	—
226	#450	—	13	1	no	—
227	#447	—	13	1	no	—
228	#446	C₂×D₁₃	1	1	yes	characteristic, complemented
229	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
230	C₄×SD₁₆	—	13	2	no	—
231	C₄×D₈	—	13	2	no	—
232	#436	C₂×D₁₃	1	1	yes	characteristic, complemented
233	#435	—	2	1	no	—
234	C₈×D₄	—	2	1	no	—
235	C₈×D₄	—	13	2	no	—
236	C₈×D₄	—	13	2	no	—
237	C₈×D₄	—	26	1	no	—
238	C₈×D₄	—	26	1	no	—
239	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
240	#433	—	2	1	no	—
241	#432	C₂×D₁₃	1	1	yes	characteristic
242	#431	—	13	1	no	—
243	C₂×C₄⋊C₈	—	13	1	no	—
244	C₂×C₂²⋊C₈	—	26	1	no	—
245	#405	—	2	1	no	—
246	C₄×M₁₆	—	13	1	no	—
247	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
248	#335	—	13	2	no	—
249	#334	—	13	2	no	—
250	Q₈⋊C₈	—	13	2	no	—
251	D₄⋊C₈	—	13	2	no	—
252	D₄⋊C₈	—	13	2	no	—
253	D₄⋊C₈	—	13	2	no	—
254	#322	—	13	2	no	—
255	#322	—	13	2	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	#444	1	2	yes	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂×D₁₃	—	2	4	no	—
264	C₂×D₁₃	—	4	8	no	—
265	C₂×D₁₃	—	4	2	no	—
266	C₂×D₁₃	—	4	2	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	—	4	1	no	—
274	C₄×C₁₃	C₂×#131	1	2	yes	—
275	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₄×C₁₃	#575	1	1	yes	characteristic
277	Dic₁₃	—	4	2	no	—
278	C₂²×D₄	—	13	1	no	—
279	C₂³×C₄	—	26	1	no	—
280	C₂×SD₁₆	—	13	2	no	—
281	C₂×D₈	—	13	2	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	26	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	26	1	no	—
286	C₂²×C₈	—	26	2	no	—
287	C₂²×C₈	—	26	2	no	—
288	C₂²×C₈	—	52	4	no	—
289	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
291	#126	—	2	1	no	—
292	#125	C₄×D₁₃	1	1	yes	characteristic
293	#124	C₄×D₁₃	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
296	#121	C₄×D₁₃	1	1	yes	characteristic
297	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	13	2	no	—
300	C₄×D₄	—	13	2	no	—
301	C₄×D₄	—	26	1	no	—
302	C₄×D₄	—	26	1	no	—
303	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	13	1	no	—
306	C₂×C₂²⋊C₄	—	26	1	no	—
307	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
308	#107	—	13	2	no	—
309	#106	—	13	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	13	2	no	—
313	C₄⋊C₈	—	13	2	no	—
314	C₄⋊C₈	—	26	1	no	—
315	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
317	#103	—	13	2	no	—
318	#102	—	13	2	no	—
319	#102	—	13	2	no	—
320	#102	—	13	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	13	1	no	—
325	C₂²⋊C₈	—	13	1	no	—
326	C₂²⋊C₈	—	26	2	no	—
327	C₂²⋊C₈	—	26	2	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	26	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	13	2	no	—
333	C₄×C₈	—	13	2	no	—
334	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	8	1	no	—
340	C₂×C₁₃	#2929	1	1	yes	characteristic
341	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
343	D₁₃	—	4	4	no	—
344	C₂⁴	—	26	1	no	—
345	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	13	2	no	—
348	C₂×D₄	—	26	4	no	—
349	C₂×D₄	—	26	1	no	—
350	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	—	26	2	no	—
354	C₂²×C₄	—	26	2	no	—
355	C₂²×C₄	—	52	2	no	—
356	C₂²×C₄	—	52	2	no	—
357	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
358	C₂²×C₄	#6127	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
360	SD₁₆	—	26	4	no	—
361	D₈	—	26	4	no	—
362	M₁₆	—	4	2	no	—
363	M₁₆	—	52	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	13	2	no	—
370	C₂×C₈	—	13	2	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	—	26	2	no	—
373	C₂×C₈	—	52	4	no	—
374	C₂×C₈	—	52	2	no	—
375	C₂×C₈	—	52	4	no	—
376	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	13	2	no	—
385	C₄⋊C₄	—	26	1	no	—
386	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
387	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	26	2	no	—
394	C₂²⋊C₄	—	26	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
397	C₄²	#6127	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
399	C₄²	C₂³×D₁₃	1	1	yes	characteristic
400	C₁₃	#17914	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	26	4	no	—
403	C₂³	—	26	2	no	—
404	C₂³	—	52	2	no	—
405	C₂³	—	52	2	no	—
406	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	13	4	no	—
411	D₄	—	26	4	no	—
412	D₄	—	26	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	52	4	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	52	2	no	—
427	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×#6127	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	26	2	no	—
439	C₈	—	26	2	no	—
440	C₈	—	52	2	no	—
441	C₈	—	52	2	no	—
442	C₈	#88203	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	26	4	no	—
449	C₂²	—	52	8	no	—
450	C₂²	—	52	2	no	—
451	C₂²	—	52	2	no	—
452	C₂²	#11718806	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	52	2	no	—
462	C₄	D₁₃×#131	1	2	yes	—
463	C₄	C₂×#88203	1	1	yes	characteristic
464	C₄	#11719527	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	52	4	no	—
468	C₂	#13123528	1	1	yes	characteristic
469	C₂	C₄×#88203	1	1	yes	characteristic
470	C₂	C₂×#11718806	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×#2966	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11718697	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2966	D₁₃
hypocenter	C₁₃	#17914
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₅₂	C₂	semidirect
3. #13113670	C₂	semidirect
4. #13113663	C₂	semidirect
5. #13113658	C₂	semidirect
6. #13113646	C₂	semidirect
7. #13113622	C₂	semidirect
8. #13113278	C₂	semidirect
9. #13113249	C₂	semidirect
10. #13113125	C₂	semidirect
11. C₁₃×#2966	C₂	semidirect
15. C₁₃×#446	C₂²	semidirect
16. C₈×Q₈×C₁₃	C₂²	semidirect
17. C₁₃×#436	C₂²	semidirect
20. C₈×D₄×C₁₃	C₂²	semidirect
41. Q₈⋊#1055	C₂²	semidirect
42. D₄⋊#1055	C₂²	semidirect
45. #11718072	C₂²	semidirect
46. #11718071	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. #11718046	C₂²	semidirect
167. #2966	D₁₃	semidirect
228. #446	C₂×D₁₃	semidirect
229. C₈×Q₈	C₂×D₁₃	semidirect
232. #436	C₂×D₁₃	semidirect
239. C₈×D₄	C₂×D₁₃	semidirect
400. C₁₃	#17914	semidirect

Maximal subgroups

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

subgroup	index
#13124879	2
C₂×C₈×D₅₂	2
#13113670	2
#13113663	2
#13113658	2
#13113646	2
#13113622	2
#13113278	2
#13113249	2
#13113125	2
C₁₃×#2966	2
#17914	13