Subgroups — #15833842

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124867	C₂	1	1	yes	maximal, characteristic
2	#13123582	C₂	1	1	yes	maximal, characteristic
3	#13113726	C₂	1	2	yes	maximal, complemented
4	#13113679	C₂	1	2	yes	maximal, complemented
5	#13113670	C₂	1	2	yes	maximal, complemented
6	C₈×#6106	C₂	1	2	yes	maximal, complemented
7	#13113608	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113286	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88161	—	2	1	no	—
14	#11719182	C₂²	1	1	yes	characteristic
15	C₁₃×#446	—	2	2	no	—
16	C₁₃×#446	C₂²	1	2	yes	—
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#423	—	2	1	no	—
19	C₁₃×#423	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	—	2	1	no	—
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	#11718888	C₄	1	2	yes	—
23	#11718790	—	2	1	no	—
24	#11718688	C₄	1	1	yes	characteristic
25	#11718688	C₄	1	1	yes	characteristic
26	C₄×#6106	C₂²	1	2	yes	—
27	C₄×#6106	C₂²	1	2	yes	—
28	#11718681	C₄	1	1	yes	characteristic
29	#11718681	C₄	1	1	yes	characteristic
30	#11718629	C₄	1	2	yes	—
31	#11718586	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	#11718367	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	—
36	C₈×D₅₂	C₂²	1	2	yes	—
37	Q₈⋊#1055	C₂²	1	1	yes	characteristic
38	Q₈⋊#1055	C₂²	1	1	yes	characteristic
39	Q₈⋊#1055	C₂²	1	1	yes	characteristic
40	Q₈⋊#1055	C₂²	1	1	yes	characteristic
41	#11718075	C₂²	1	2	yes	—
42	#11718075	C₂²	1	2	yes	—
43	#11718072	C₂²	1	2	yes	—
44	#11718072	C₂²	1	2	yes	—
45	#11718047	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×#6127	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×#6106	C₂×C₄	1	2	yes	—
63	C₂×#6106	C₂×C₄	1	2	yes	—
64	#88184	—	2	1	no	—
65	#88184	C₂×C₄	1	2	yes	—
66	C₂²×#1055	—	2	1	no	—
67	C₂²×#1055	—	2	1	no	—
68	#88161	—	4	4	no	—
69	C₂×#6094	—	2	2	no	—
70	C₂×C₈×D₁₃	—	2	2	no	—
71	#88129	—	2	1	no	—
72	#88128	C₂×C₄	1	1	yes	characteristic
73	C₄×D₅₂	—	2	1	no	—
74	C₄×D₅₂	C₂³	1	2	yes	—
75	#88123	C₂×C₄	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₃×#97	—	2	2	no	—
81	C₁₃×#97	D₄	1	2	yes	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	#88075	C₂×C₄	1	2	yes	—
85	#88075	C₂×C₄	1	2	yes	—
86	C₂²⋊#1055	C₂×C₄	1	2	yes	—
87	#88060	—	2	2	no	—
88	#88060	—	2	2	no	—
89	#88049	C₂×C₄	1	2	yes	—
90	#88049	C₂×C₄	1	2	yes	—
91	#88048	C₂×C₄	1	2	yes	—
92	#88048	C₂×C₄	1	2	yes	—
93	C₄⋊#1055	—	2	1	no	—
94	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	1	yes	characteristic
97	C₄⋊#1055	C₂³	1	1	yes	characteristic
98	C₄×#1055	—	2	1	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	#17997	—	13	1	no	maximal, Sylow
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	4	1	no	—
106	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	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	—	4	2	no	—
115	#6127	—	4	2	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	—	2	2	no	—
122	C₁₃×M₁₆	—	4	2	no	—
123	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
124	C₂×C₈×C₁₃	—	2	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	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	#41	1	1	yes	characteristic
141	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
142	#6106	—	2	4	no	—
143	#6106	—	4	2	no	—
144	#6103	—	2	2	no	—
145	#6103	—	2	2	no	—
146	C₄⋊Dic₁₃	—	2	1	no	—
147	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	4	2	no	—
153	C₂×#1055	—	4	2	no	—
154	C₂×#1055	C₂²×C₄	1	2	yes	—
155	C₂×#1055	C₂²×C₄	1	2	yes	—
156	#6094	—	4	4	no	—
157	C₈×D₁₃	—	4	4	no	—
158	#3103	—	13	1	no	—
159	Q₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
160	#2935	—	13	1	no	—
161	#1590	—	13	2	no	—
162	#1583	—	13	2	no	—
163	#1582	—	13	2	no	—
164	C₈×SD₁₆	—	13	2	no	—
165	#1570	—	13	1	no	—
166	#1492	—	13	1	no	—
167	C₂×Q₈⋊C₈	—	13	1	no	—
168	C₈×M₁₆	—	13	1	no	—
169	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂²×D₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	2	1	no	—
172	Q₈×C₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	2	1	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	#131	1	2	yes	complemented
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	8	1	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₁₃	#135	1	2	yes	—
190	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂²⋊D₁₃	—	4	4	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	D₅₂	—	2	2	no	—
196	D₅₂	—	2	2	no	—
197	D₅₂	—	4	2	no	—
198	D₅₂	—	8	1	no	—
199	C₄×D₁₃	—	4	2	no	—
200	C₄×D₁₃	—	4	2	no	—
201	Dic₂₆	—	4	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	2	no	—
204	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
205	#1055	—	2	2	no	—
206	#1055	—	2	2	no	—
207	#1055	—	2	2	no	—
208	#1055	—	4	1	no	—
209	#1055	—	4	1	no	—
210	#1055	—	4	1	no	—
211	C₂×#131	—	26	1	no	—
212	#532	—	13	1	no	—
213	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
214	#481	—	13	2	no	—
215	#475	—	13	1	no	—
216	#475	—	13	1	no	—
217	#460	—	13	1	no	—
218	#460	—	13	1	no	—
219	#448	—	13	2	no	—
220	#446	—	2	2	no	—
221	#446	C₂×D₁₃	1	2	yes	—
222	C₈×Q₈	C₂×D₁₃	1	2	yes	—
223	C₄×SD₁₆	—	13	2	no	—
224	C₄×SD₁₆	—	13	2	no	—
225	#436	—	13	2	no	—
226	#435	—	26	2	no	—
227	C₈×D₄	—	13	2	no	—
228	#431	—	13	1	no	—
229	#423	—	2	1	no	—
230	#423	C₂×D₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	13	1	no	—
232	#408	—	26	1	no	—
233	C₄×M₁₆	—	2	1	no	—
234	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
235	C₂×C₄×C₈	—	13	1	no	—
236	#334	—	13	2	no	—
237	#334	—	13	2	no	—
238	Q₈⋊C₈	—	13	1	no	—
239	Q₈⋊C₈	—	13	1	no	—
240	Q₈⋊C₈	—	13	1	no	—
241	Q₈⋊C₈	—	13	1	no	—
242	D₄⋊C₈	—	13	2	no	—
243	D₄⋊C₈	—	13	2	no	—
244	#322	—	13	2	no	—
245	C₈²	—	13	2	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₁₃	—	4	2	no	—
251	C₂×D₁₃	—	4	2	no	—
252	C₂×D₁₃	—	4	2	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
261	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
262	C₄×C₁₃	#568	1	1	yes	characteristic
263	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
264	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
265	Dic₁₃	—	4	2	no	—
266	C₂×#41	—	26	1	no	—
267	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
268	C₂×SD₁₆	—	13	2	no	—
269	C₂×SD₁₆	—	13	2	no	—
270	#131	—	52	4	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	26	2	no	—
273	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
274	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
275	C₂²×C₈	—	26	1	no	—
276	C₂²×C₈	—	26	1	no	—
277	C₂²×C₈	—	26	2	no	—
278	C₄⋊Q₈	—	13	1	no	—
279	#127	—	13	1	no	—
280	#124	—	26	1	no	—
281	#121	—	13	2	no	—
282	#121	—	26	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
286	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
287	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
288	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
289	C₄×D₄	—	13	2	no	—
290	C₄×D₄	—	26	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
295	#106	—	13	2	no	—
296	#106	—	13	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	13	1	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	1	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	26	1	no	—
305	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
306	#103	—	13	2	no	—
307	#103	—	13	2	no	—
308	#102	—	13	2	no	—
309	#102	—	13	2	no	—
310	C₂²⋊C₈	—	13	2	no	—
311	C₂²⋊C₈	—	26	2	no	—
312	C₂²⋊C₈	—	26	2	no	—
313	#97	—	2	2	no	—
314	#97	C₂²⋊D₁₃	1	2	yes	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	—	13	2	no	—
317	C₄×C₈	—	13	1	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	—	26	1	no	—
320	C₄×C₈	C₂²×D₁₃	1	2	yes	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	#2933	1	1	yes	characteristic
323	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
324	C₂×C₁₃	#2956	1	1	yes	characteristic
325	D₁₃	—	8	2	no	—
326	#41	—	52	2	no	—
327	#41	—	52	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	26	1	no	—
332	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
333	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
334	C₂×D₄	—	13	2	no	—
335	C₂×D₄	—	26	2	no	—
336	C₂×D₄	—	26	1	no	—
337	C₂×D₄	—	26	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	26	2	no	—
341	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
342	C₂²×C₄	#6127	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	SD₁₆	—	26	4	no	—
345	SD₁₆	—	52	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	—	52	4	no	—
349	M₁₆	#6106	1	4	yes	complemented
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	26	1	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	52	2	no	—
358	C₂×C₈	—	52	2	no	—
359	C₂×C₈	—	52	4	no	—
360	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
361	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	13	2	no	—
368	C₄⋊C₄	—	26	1	no	—
369	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
371	C₂²⋊C₄	—	26	2	no	—
372	C₂²⋊C₄	—	26	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₄²	#6127	1	1	yes	characteristic
379	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
380	C₄²	C₂³×D₁₃	1	1	yes	characteristic
381	C₁₃	#17997	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	26	2	no	—
383	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	52	2	no	—
389	Q₈	#88161	1	2	yes	complemented
390	D₄	—	26	2	no	—
391	D₄	—	26	2	no	—
392	D₄	—	52	4	no	—
393	D₄	—	52	2	no	—
394	D₄	—	104	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	52	2	no	—
406	C₂×C₄	—	52	2	no	—
407	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
408	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#6106	1	2	yes	—
411	C₂×C₄	#88204	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#6127	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	26	2	no	—
418	C₈	—	26	2	no	—
419	C₈	—	26	2	no	—
420	C₈	—	52	1	no	—
421	C₈	—	52	1	no	—
422	C₈	—	52	1	no	—
423	C₈	C₂×#6106	1	4	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	52	2	no	—
427	C₂²	—	52	2	no	—
428	C₂²	—	52	2	no	—
429	C₂²	C₄×#6106	1	2	yes	—
430	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	52	2	no	—
439	C₄	C₄×#6106	1	2	yes	—
440	C₄	C₂×#88161	1	1	yes	characteristic
441	C₄	#11719450	1	1	yes	characteristic
442	C₄	C₂²×#6106	1	1	yes	characteristic
443	C₄	C₂×#88204	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	104	2	no	—
446	C₂	#13123561	1	1	yes	characteristic
447	C₂	C₂×C₄×#6106	1	1	yes	characteristic
448	C₂	#13123743	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	Q₈×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11719182	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	Q₈×M₁₆	D₁₃
hypocenter	C₁₃	#17997
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13113726	C₂	semidirect
4. #13113679	C₂	semidirect
5. #13113670	C₂	semidirect
6. C₈×#6106	C₂	semidirect
7. #13113608	C₂	semidirect
9. C₂×Q₈⋊#1055	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
11. Q₈×C₁₃×M₁₆	C₂	semidirect
123. C₁₃×M₁₆	SD₁₆	semidirect
159. Q₈×M₁₆	D₁₃	semidirect
175. Q₈×C₁₃	#131	semidirect
349. M₁₆	#6106	semidirect
381. C₁₃	#17997	semidirect
389. Q₈	#88161	semidirect

Maximal subgroups

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

subgroup	index
#13124867	2
#13123582	2
#13113726	2
#13113679	2
#13113670	2
C₈×#6106	2
#13113608	2
#13113286	2
C₂×Q₈⋊#1055	2
M₁₆×#1055	2
Q₈×C₁₃×M₁₆	2
#17997	13