Subgroups — #15832570

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123947	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123877	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113715	C₂	1	2	yes	maximal, complemented
4	#13113701	C₂	1	2	yes	maximal, complemented
5	#13113680	C₂	1	2	yes	maximal, complemented
6	#13113666	C₂	1	2	yes	maximal, complemented
7	#13113588	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113218	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113123	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#442	C₄	1	2	yes	—
16	C₁₃×#440	C₄	1	2	yes	—
17	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₄×C₁₃×D₈	C₂²	1	2	yes	—
19	C₁₃×#428	C₄	1	1	yes	characteristic
20	C₁₃×#418	C₄	1	1	yes	characteristic
21	C₁₃×#417	C₄	1	1	yes	characteristic
22	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	#11718868	—	2	2	no	—
24	Q₈×#1055	C₂²	1	2	yes	complemented
25	#11718673	—	2	1	no	—
26	#11718673	—	2	1	no	—
27	#11718673	C₂²	1	2	yes	—
28	#11718673	C₂²	1	2	yes	—
29	D₄×#1055	—	2	2	no	—
30	D₄×#1055	C₂²	1	2	yes	complemented
31	#11718586	—	2	1	no	—
32	#11718586	C₂²	1	1	yes	characteristic
33	#11718586	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	—	2	1	no	—
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
38	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
39	D₄⋊#1055	C₂²	1	2	yes	—
40	D₄⋊#1055	C₂²	1	2	yes	—
41	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
43	#11718050	C₂²	1	2	yes	complemented
44	#11718049	C₂²	1	2	yes	complemented
45	#11718046	C₂²	1	2	yes	complemented
46	#11718046	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₃	C₂³	1	2	yes	—
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	—	2	2	no	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	1	no	—
75	C₂²×#1055	—	2	2	no	—
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×#103	C₂×C₄	1	2	yes	—
79	C₁₃×#102	C₂×C₄	1	2	yes	—
80	C₁₃×#102	C₂×C₄	1	2	yes	—
81	C₁₃×#102	C₂×C₄	1	2	yes	—
82	C₁₃×#97	C₂×C₄	1	2	yes	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	C₂²⋊#1055	—	2	1	no	—
85	C₂²⋊#1055	—	2	2	no	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	—	2	2	no	—
88	C₂²⋊#1055	D₄	1	2	yes	—
89	C₄⋊#1055	—	2	1	no	—
90	C₄⋊#1055	—	2	2	no	—
91	C₄⋊#1055	D₄	1	1	yes	characteristic
92	C₄⋊#1055	D₄	1	1	yes	characteristic
93	C₄⋊#1055	C₂³	1	2	yes	—
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄×#1055	—	2	1	no	—
97	C₄×#1055	—	2	1	no	—
98	C₄×#1055	—	2	2	no	—
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	2	yes	—
102	#17875	—	13	1	no	maximal, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₁₃×#41	—	2	2	no	—
105	C₁₃×#41	M₁₆	1	4	yes	complemented
106	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	8	1	no	—
120	C₂²×C₄×C₁₃	—	8	1	no	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₁₃×SD₁₆	—	2	4	no	—
125	C₁₃×D₈	—	2	4	no	—
126	C₁₃×M₁₆	—	2	2	no	—
127	C₁₃×M₁₆	—	2	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	C₂²×C₄	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	2	no	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃	#41	1	1	yes	characteristic
147	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
148	#6099	—	8	2	no	—
149	#6099	—	8	2	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	4	2	no	—
156	C₂×#1055	—	8	2	no	—
157	C₂×#1055	—	8	1	no	—
158	C₂×#1055	C₂×D₄	1	2	yes	—
159	C₂×#1055	C₂×D₄	1	2	yes	—
160	#2988	—	13	1	no	—
161	#2975	—	13	1	no	—
162	C₄×AGL(1,ℤ/8)	D₁₃	1	1	yes	characteristic
163	#1588	—	13	2	no	—
164	#1586	—	13	2	no	—
165	#1583	—	13	2	no	—
166	#1581	—	13	2	no	—
167	#1565	—	13	1	no	—
168	#1476	—	13	1	no	—
169	C₂×D₄⋊C₈	—	13	1	no	—
170	#1451	—	13	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	8	1	no	—
175	C₂³×C₁₃	—	8	1	no	—
176	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
177	Q₈×C₁₃	—	2	1	no	—
178	Q₈×C₁₃	C₂×M₁₆	1	2	yes	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	2	1	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	8	1	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	8	1	no	—
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₁₃	#131	1	2	yes	—
205	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	2	2	no	—
210	#1055	—	2	2	no	—
211	#1055	—	2	2	no	—
212	#1055	—	2	2	no	—
213	#1055	—	4	1	no	—
214	#1055	—	4	2	no	—
215	#1055	—	4	1	no	—
216	#1055	—	4	1	no	—
217	C₂×AGL(1,ℤ/8)	Dic₁₃	1	1	yes	characteristic
218	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
220	C₈×Q₈	—	13	2	no	—
221	#442	Dic₁₃	1	2	yes	—
222	#440	Dic₁₃	1	2	yes	—
223	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
224	C₄×D₈	C₂×D₁₃	1	2	yes	—
225	#436	—	13	2	no	—
226	#436	—	13	2	no	—
227	#436	—	26	1	no	—
228	#436	—	26	1	no	—
229	C₈×D₄	—	13	2	no	—
230	C₈×D₄	—	26	2	no	—
231	#431	—	13	1	no	—
232	#431	—	13	1	no	—
233	#431	—	26	1	no	—
234	#428	Dic₁₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	13	1	no	—
236	C₂×C₄⋊C₈	—	26	1	no	—
237	#418	Dic₁₃	1	1	yes	characteristic
238	#417	Dic₁₃	1	1	yes	characteristic
239	#407	—	26	2	no	—
240	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
241	C₂×C₄×C₈	—	13	1	no	—
242	#335	—	13	2	no	—
243	#334	—	13	2	no	—
244	Q₈⋊C₈	—	13	1	no	—
245	Q₈⋊C₈	—	13	1	no	—
246	D₄⋊C₈	—	13	1	no	—
247	D₄⋊C₈	—	13	2	no	—
248	D₄⋊C₈	—	13	1	no	—
249	D₄⋊C₈	—	13	2	no	—
250	#322	—	13	2	no	—
251	#322	—	13	2	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	8	4	no	—
261	C₂²×C₁₃	#435	1	2	yes	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	1	no	—
270	C₄×C₁₃	#435	1	2	yes	—
271	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
272	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
273	C₄×C₁₃	#576	1	1	yes	characteristic
274	C₄×C₁₃	#577	1	1	yes	characteristic
275	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
276	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	AGL(1,ℤ/8)	—	2	4	no	—
279	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
280	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
281	C₂×M₁₆	—	26	2	no	—
282	C₂×M₁₆	—	26	2	no	—
283	C₂×M₁₆	C₂×Dic₁₃	1	1	yes	characteristic
284	C₂×M₁₆	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂²×C₈	—	26	2	no	—
286	C₂²×C₈	—	26	1	no	—
287	C₂²×C₈	—	26	1	no	—
288	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
295	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
296	C₄×D₄	C₂²×D₁₃	1	2	yes	—
297	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	C₂×Dic₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	#107	C₂×Dic₁₃	1	2	yes	—
305	#106	C₂×Dic₁₃	1	2	yes	—
306	C₄⋊C₈	—	13	1	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	2	no	—
309	C₄⋊C₈	—	13	1	no	—
310	C₄⋊C₈	—	13	1	no	—
311	C₄⋊C₈	—	26	2	no	—
312	C₄⋊C₈	—	26	1	no	—
313	#103	C₂×Dic₁₃	1	2	yes	—
314	#102	C₂×Dic₁₃	1	2	yes	—
315	#102	C₂×Dic₁₃	1	2	yes	—
316	#102	C₂×Dic₁₃	1	2	yes	—
317	C₂²⋊C₈	—	13	2	no	—
318	C₂²⋊C₈	—	26	2	no	—
319	C₂²⋊C₈	—	26	2	no	—
320	C₂²⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	—	26	1	no	—
322	#97	C₂×Dic₁₃	1	2	yes	—
323	C₄×C₈	—	13	2	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	26	2	no	—
327	C₄×C₈	—	26	1	no	—
328	C₄×C₈	—	26	1	no	—
329	C₄×C₈	C₂²×D₁₃	1	2	yes	—
330	C₂×C₁₃	—	2	2	no	—
331	C₂×C₁₃	—	4	2	no	—
332	C₂×C₁₃	—	8	2	no	—
333	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
334	C₂×C₁₃	#2946	1	1	yes	characteristic
335	C₂×C₁₃	#2956	1	1	yes	characteristic
336	C₂⁴	—	2	1	no	—
337	#41	—	2	2	no	—
338	#41	#6099	1	4	yes	complemented
339	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
345	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	8	1	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
355	C₂²×C₄	#6129	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
357	SD₁₆	—	2	4	no	—
358	D₈	—	2	4	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	104	2	no	—
362	M₁₆	—	104	2	no	—
363	C₂×C₈	—	13	2	no	—
364	C₂×C₈	—	13	2	no	—
365	C₂×C₈	—	26	1	no	—
366	C₂×C₈	—	26	1	no	—
367	C₂×C₈	—	26	1	no	—
368	C₂×C₈	—	26	2	no	—
369	C₂×C₈	—	26	1	no	—
370	C₂×C₈	—	52	2	no	—
371	C₂×C₈	—	104	2	no	—
372	C₂×C₈	—	104	1	no	—
373	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
374	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	D₄×D₁₃	1	1	yes	characteristic
390	C₄²	#6129	1	1	yes	characteristic
391	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
392	C₄²	C₂³×D₁₃	1	1	yes	characteristic
393	C₁₃	#17875	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×#6099	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	2	no	—
407	D₄	C₂×#6099	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₂×#6099	1	2	yes	—
424	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
426	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
427	C₂×C₄	#88202	1	2	yes	—
428	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#6129	1	1	yes	characteristic
430	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	26	2	no	—
434	C₈	—	26	2	no	—
435	C₈	—	26	2	no	—
436	C₈	—	52	1	no	—
437	C₈	—	52	2	no	—
438	C₈	—	52	1	no	—
439	C₈	—	52	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	#11718672	1	2	yes	—
450	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	1	no	—
458	C₄	#11718672	1	2	yes	—
459	C₄	#11719479	1	1	yes	characteristic
460	C₄	#11719480	1	1	yes	characteristic
461	C₄	C₂²×#6099	1	1	yes	characteristic
462	C₄	C₂×#88202	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₂×#11718672	1	1	yes	characteristic
467	C₂	#13123669	1	1	yes	characteristic
468	C₂	#13123746	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₄×C₁₃×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₁₃
hypocenter	C₁₃	#17875
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #13123947	C₂	semidirect
2. #13123877	C₂	semidirect
3. #13113715	C₂	semidirect
4. #13113701	C₂	semidirect
5. #13113680	C₂	semidirect
6. #13113666	C₂	semidirect
7. #13113588	C₂	semidirect
8. #13113218	C₂	semidirect
9. C₂×D₄⋊#1055	C₂	semidirect
10. #13113123	C₂	semidirect
24. Q₈×#1055	C₂²	semidirect
30. D₄×#1055	C₂²	semidirect
37. Q₈⋊#1055	C₂²	semidirect
38. Q₈⋊#1055	C₂²	semidirect
41. D₄⋊#1055	C₂²	semidirect
42. D₄⋊#1055	C₂²	semidirect
43. #11718050	C₂²	semidirect
44. #11718049	C₂²	semidirect
45. #11718046	C₂²	semidirect
46. #11718046	C₂²	semidirect
105. C₁₃×#41	M₁₆	semidirect
338. #41	#6099	semidirect
393. C₁₃	#17875	semidirect

Maximal subgroups

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

subgroup	index
#13123947	2
#13123877	2
#13113715	2
#13113701	2
#13113680	2
#13113666	2
#13113588	2
#13113218	2
C₂×D₄⋊#1055	2
#13113123	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#17875	13