Subgroups — #15833215

Order 3328.

672 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	#13123812	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718673	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113750	C₂	1	2	yes	maximal, complemented
4	#13113739	C₂	1	2	yes	maximal, complemented
5	#13113680	C₂	1	2	yes	maximal, complemented
6	#13113666	C₂	1	2	yes	maximal, complemented
7	#13113621	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113279	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113249	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#529	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6099	—	2	1	no	—
15	C₁₃×#484	C₄	1	1	yes	characteristic
16	C₁₃×#481	C₄	1	1	yes	characteristic
17	C₁₃×#478	C₄	1	2	yes	—
18	C₁₃×#463	C₄	1	2	yes	—
19	C₁₃×#450	C₄	1	1	yes	characteristic
20	C₁₃×#447	C₄	1	1	yes	characteristic
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×D₈	C₂²	1	2	yes	—
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#1055	—	2	1	no	—
25	#11718685	C₂²	1	1	yes	characteristic, complemented
26	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
27	#11718673	—	2	1	no	—
28	#11718673	—	2	1	no	—
29	#11718673	C₂²	1	2	yes	—
30	#11718673	C₂²	1	2	yes	—
31	#11718673	C₂²	1	1	yes	characteristic, complemented
32	#11718672	—	2	1	no	—
33	D₄×#1055	—	2	1	no	—
34	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
35	#11718661	—	2	1	no	—
36	#11718658	—	2	1	no	—
37	#11718587	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₄×#6099	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	complemented
42	D₄⋊#1055	C₂²	1	2	yes	—
43	D₄⋊#1055	C₂²	1	2	yes	—
44	D₄⋊#1055	C₂²	1	2	yes	complemented
45	#11718050	C₂²	1	2	yes	complemented
46	#11718049	C₂²	1	2	yes	complemented
47	#11718047	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
53	C₁₃×#126	—	2	1	no	—
54	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#123	—	2	1	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×#6099	—	2	1	no	—
71	C₂×#6099	—	2	1	no	—
72	C₂×#6099	—	2	2	no	—
73	C₂×#6099	—	2	2	no	—
74	C₂×#6099	—	4	4	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	1	no	—
77	C₂²×#1055	D₄	1	1	yes	characteristic
78	C₂²×#1055	D₄	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₃×#103	C₂×C₄	1	2	yes	—
83	C₁₃×#102	C₂×C₄	1	2	yes	—
84	C₁₃×#102	C₂×C₄	1	2	yes	—
85	C₁₃×#102	C₂×C₄	1	2	yes	—
86	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	2	yes	—
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	C₂²⋊#1055	—	2	1	no	—
92	C₂²⋊#1055	—	2	2	no	—
93	C₂²⋊#1055	—	2	2	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	C₂³	1	1	yes	characteristic
98	C₄⋊#1055	C₂³	1	2	yes	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	#88043	—	2	1	no	—
101	#88043	—	2	1	no	—
102	#88043	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	#17938	—	13	1	no	maximal, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₁₃×SD₁₆	—	4	2	no	—
127	C₁₃×D₈	—	4	2	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃	#41	1	1	yes	characteristic
149	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
150	#6099	—	4	2	no	—
151	#6099	—	4	4	no	—
152	#6099	—	4	2	no	—
153	#6099	—	4	4	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	1	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	4	1	no	—
160	C₂×#1055	—	4	2	no	—
161	C₂×#1055	—	4	2	no	—
162	C₂×#1055	C₂×D₄	1	1	yes	characteristic
163	C₂×#1055	C₂×D₄	1	1	yes	characteristic
164	C₂×#1055	C₂×D₄	1	1	yes	characteristic
165	C₂×#1055	C₂×D₄	1	1	yes	characteristic
166	#3105	D₁₃	1	1	yes	characteristic
167	#2966	—	13	1	no	—
168	C₂×#436	—	13	1	no	—
169	#1594	—	13	2	no	—
170	#1592	—	13	2	no	—
171	#1583	—	13	2	no	—
172	#1581	—	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	—	2	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	—	4	2	no	—
182	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	2	2	no	—
211	#1055	—	2	1	no	—
212	#1055	—	2	1	no	—
213	#1055	—	2	1	no	—
214	#1055	—	4	2	no	—
215	#1055	—	4	1	no	—
216	#1055	—	4	2	no	—
217	#1055	—	4	1	no	—
218	#1055	AGL(1,ℤ/8)	1	2	yes	—
219	C₂²×M₁₆	—	26	1	no	—
220	#529	C₂×D₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
222	#484	Dic₁₃	1	1	yes	characteristic
223	#481	Dic₁₃	1	1	yes	characteristic
224	#478	Dic₁₃	1	2	yes	—
225	#463	Dic₁₃	1	2	yes	—
226	#450	Dic₁₃	1	1	yes	characteristic
227	#447	Dic₁₃	1	1	yes	characteristic
228	#446	—	13	1	no	—
229	C₈×Q₈	—	13	1	no	—
230	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
231	C₄×D₈	C₂×D₁₃	1	2	yes	—
232	#436	—	13	2	no	—
233	#436	—	13	2	no	—
234	#436	—	13	1	no	—
235	#436	—	26	1	no	—
236	#436	—	26	1	no	—
237	#435	—	26	1	no	—
238	C₈×D₄	—	13	1	no	—
239	C₈×D₄	—	26	1	no	—
240	#433	—	26	1	no	—
241	#432	—	13	1	no	—
242	#431	C₂×D₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	13	1	no	—
244	C₂×C₂²⋊C₈	—	26	1	no	—
245	#405	—	26	1	no	—
246	C₄×M₁₆	—	13	1	no	—
247	C₂×C₄×C₈	—	13	1	no	—
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	2	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	—	4	1	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	8	4	no	—
265	C₂²×C₁₃	#444	1	2	yes	—
266	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
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	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	#568	1	2	yes	—
276	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₁₃	#575	1	1	yes	characteristic
278	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
281	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
282	C₂×M₁₆	—	26	2	no	—
283	C₂×M₁₆	—	26	2	no	—
284	C₂×M₁₆	—	26	1	no	—
285	C₂×M₁₆	—	26	1	no	—
286	C₂×M₁₆	—	52	4	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	26	1	no	—
290	C₂²×C₈	—	26	1	no	—
291	#126	—	2	1	no	—
292	#125	C₂×Dic₁₃	1	1	yes	characteristic
293	#124	C₂×Dic₁₃	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
296	#121	C₂×Dic₁₃	1	1	yes	characteristic
297	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
302	C₄×D₄	C₂²×D₁₃	1	2	yes	—
303	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
308	#107	C₂×Dic₁₃	1	2	yes	—
309	#106	C₂×Dic₁₃	1	2	yes	—
310	C₄⋊C₈	—	13	1	no	—
311	C₄⋊C₈	—	13	1	no	—
312	C₄⋊C₈	—	13	2	no	—
313	C₄⋊C₈	—	26	1	no	—
314	C₄⋊C₈	—	26	1	no	—
315	C₄⋊C₈	—	26	1	no	—
316	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
317	#103	C₂×Dic₁₃	1	2	yes	—
318	#102	C₂×Dic₁₃	1	2	yes	—
319	#102	C₂×Dic₁₃	1	2	yes	—
320	#102	C₂×Dic₁₃	1	2	yes	—
321	C₂²⋊C₈	—	26	2	no	—
322	C₂²⋊C₈	—	26	2	no	—
323	C₂²⋊C₈	—	26	1	no	—
324	C₂²⋊C₈	—	26	1	no	—
325	C₂²⋊C₈	—	26	1	no	—
326	C₂²⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
327	C₂²⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
328	#97	—	26	1	no	—
329	#97	—	26	1	no	—
330	#97	—	26	1	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	13	1	no	—
334	C₄×C₈	—	13	1	no	—
335	C₄×C₈	—	13	2	no	—
336	C₄×C₈	—	26	1	no	—
337	C₄×C₈	C₂²×D₁₃	1	2	yes	—
338	C₂×C₁₃	—	2	2	no	—
339	C₂×C₁₃	—	8	1	no	—
340	C₂×C₁₃	—	8	2	no	—
341	C₂×C₁₃	#2930	1	1	yes	characteristic
342	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
350	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
358	C₂²×C₄	#6129	1	1	yes	characteristic
359	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
360	SD₁₆	—	4	2	no	—
361	D₈	—	4	2	no	—
362	M₁₆	—	52	4	no	—
363	M₁₆	—	52	4	no	—
364	M₁₆	—	52	2	no	—
365	M₁₆	—	52	2	no	—
366	C₂×C₈	—	13	1	no	—
367	C₂×C₈	—	13	1	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	26	1	no	—
372	C₂×C₈	—	26	1	no	—
373	C₂×C₈	—	26	2	no	—
374	C₂×C₈	—	26	2	no	—
375	C₂×C₈	—	52	2	no	—
376	C₂×C₈	—	52	1	no	—
377	C₂×C₈	—	52	2	no	—
378	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
379	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
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	—	2	1	no	—
385	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
386	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	D₄×D₁₃	1	1	yes	characteristic
397	C₄²	#6129	1	1	yes	characteristic
398	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
399	C₄²	C₂³×D₁₃	1	1	yes	characteristic
400	C₁₃	#17938	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
428	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
429	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×#6129	1	1	yes	characteristic
432	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	13	2	no	—
436	C₈	—	26	1	no	—
437	C₈	—	26	1	no	—
438	C₈	—	26	1	no	—
439	C₈	—	52	2	no	—
440	C₈	—	52	1	no	—
441	C₈	—	52	2	no	—
442	C₈	—	52	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	8	4	no	—
452	C₂²	#11718858	1	2	yes	—
453	C₂²	C₂×D₄×Dic₁₃	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	2	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₄	#11719478	1	1	yes	characteristic
464	C₄	#11719524	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	8	1	no	—
468	C₂	#13123540	1	1	yes	characteristic
469	C₂	AGL(1,ℤ/8)×Dic₁₃	1	1	yes	characteristic
470	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3105	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#447	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3105	D₁₃
hypocenter	C₁₃	#17938
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #13123812	C₂	semidirect
2. C₂×#11718673	C₂	semidirect
3. #13113750	C₂	semidirect
4. #13113739	C₂	semidirect
5. #13113680	C₂	semidirect
6. #13113666	C₂	semidirect
7. #13113621	C₂	semidirect
8. #13113279	C₂	semidirect
9. #13113249	C₂	semidirect
10. #13113126	C₂	semidirect
25. #11718685	C₂²	semidirect
26. Q₈×#1055	C₂²	semidirect
31. #11718673	C₂²	semidirect
34. D₄×#1055	C₂²	semidirect
41. Q₈⋊#1055	C₂²	semidirect
44. D₄⋊#1055	C₂²	semidirect
45. #11718050	C₂²	semidirect
46. #11718049	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. #11718046	C₂²	semidirect
400. C₁₃	#17938	semidirect

Maximal subgroups

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

subgroup	index
#13123812	2
C₂×#11718673	2
#13113750	2
#13113739	2
#13113680	2
#13113666	2
#13113621	2
#13113279	2
#13113249	2
#13113126	2
C₁₃×#3105	2
#17938	13