Subgroups — #15884714

Order 3328.

926 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	C₂×#11718748	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
3	#13115798	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115594	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115566	C₂	1	2	yes	maximal, complemented
6	#13115407	C₂	1	2	yes	maximal, complemented
7	#13115082	C₂	1	2	yes	maximal
8	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88049	C₂	1	2	yes	maximal
10	C₄×#88049	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄⋊C₄×D₁₃	—	2	1	no	—
15	C₂×C₄×D₅₂	C₂²	1	2	yes	—
16	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
17	C₁₃×#391	—	2	1	no	—
18	C₁₃×#389	C₂²	1	2	yes	—
19	C₁₃×#387	—	2	2	no	—
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	#11718748	C₄	1	8	yes	complemented
24	#11718648	—	2	1	no	—
25	C₂×#88049	C₂²	1	1	yes	characteristic
26	C₂×#88049	C₂²	1	2	yes	—
27	C₂×#88049	C₂²	1	1	yes	characteristic
28	C₂×#88047	C₂²	1	2	yes	—
29	C₂×#88047	C₂²	1	2	yes	—
30	#11718596	C₂²	1	1	yes	characteristic
31	#11718589	C₂²	1	2	yes	—
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	C₂×C₄×#1055	C₂²	1	2	yes	—
35	#11718329	—	2	2	no	—
36	#11718121	C₂²	1	1	yes	characteristic
37	#11718121	C₂²	1	2	yes	—
38	#11718121	C₂²	1	2	yes	—
39	#11718121	C₂²	1	2	yes	—
40	#11718121	C₂²	1	1	yes	characteristic
41	#11718116	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₅₂	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	—	2	1	no	—
45	C₂²×C₄×D₁₃	—	2	2	no	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
48	C₄×Q₈×C₁₃	—	4	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×#6103	—	2	1	no	—
61	C₂×#6103	—	2	2	no	—
62	C₂×C₄⋊Dic₁₃	—	2	1	no	—
63	C₂×C₄⋊Dic₁₃	—	2	1	no	—
64	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂×#6101	—	2	2	no	—
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	2	yes	—
69	C₂²×#1055	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×D₁₃	—	4	4	no	—
71	C₄×D₅₂	—	2	2	no	—
72	C₄×D₅₂	—	2	4	no	—
73	C₄×D₅₂	—	4	2	no	—
74	C₄×D₅₂	C₂×C₄	1	4	yes	—
75	C₁₃×#95	—	2	1	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	D₄	1	2	yes	—
79	#88071	—	2	2	no	—
80	#88049	—	2	2	no	—
81	#88049	C₂×C₄	1	8	yes	—
82	#88049	Q₈	1	4	yes	complemented
83	#88047	—	4	2	no	—
84	#88047	C₂×C₄	1	8	yes	complemented
85	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
86	C₄×#1055	—	2	2	no	—
87	C₄×#1055	—	4	2	no	—
88	#22962	—	13	1	no	maximal, Sylow
89	C₂³×D₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₁₃	—	2	1	no	—
102	C₂²×Dic₁₃	—	2	2	no	—
103	C₂×D₅₂	—	2	1	no	—
104	C₂×D₅₂	—	2	1	no	—
105	C₂×D₅₂	—	2	1	no	—
106	C₂×D₅₂	C₂²×C₄	1	2	yes	—
107	C₂×D₅₂	C₂×Q₈	1	2	yes	—
108	C₂×D₅₂	#41	1	2	yes	—
109	C₂×C₄×D₁₃	—	2	4	no	—
110	C₂×C₄×D₁₃	—	4	2	no	—
111	C₂×C₄×D₁₃	—	4	2	no	—
112	C₂×C₄×D₁₃	—	4	4	no	—
113	C₂×C₄×D₁₃	—	4	4	no	—
114	C₂×C₄×D₁₃	—	8	2	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	4	4	no	—
122	C₁₃×C₄⋊C₄	D₈	1	4	yes	—
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
124	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	4	4	no	—
128	C₄²×C₁₃	—	4	2	no	—
129	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₃	#41	1	2	yes	—
131	#6103	—	2	4	no	—
132	#6103	—	4	4	no	—
133	C₄⋊Dic₁₃	—	2	1	no	—
134	C₄⋊Dic₁₃	—	2	2	no	—
135	C₄⋊Dic₁₃	—	2	2	no	—
136	C₄⋊Dic₁₃	—	4	2	no	—
137	C₄⋊Dic₁₃	—	8	1	no	—
138	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
139	#6101	—	4	4	no	—
140	C₂×#1055	—	2	1	no	—
141	C₂×#1055	—	2	1	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	—	2	1	no	—
147	C₂×#1055	C₂²×C₄	1	4	yes	—
148	C₂×#1055	C₂×Q₈	1	2	yes	—
149	C₂×#474	—	13	1	no	—
150	#2365	D₁₃	1	1	yes	characteristic, complemented
151	D₄×C₄⋊C₄	—	13	1	no	—
152	#1990	—	13	1	no	—
153	#1947	—	13	1	no	—
154	#1942	—	13	2	no	—
155	#1918	—	13	2	no	—
156	#1862	—	13	2	no	—
157	C₈×C₄⋊C₄	—	13	1	no	—
158	C₄×#102	—	13	1	no	—
159	C₄×#102	—	13	2	no	—
160	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₂²×D₁₃	—	2	2	no	—
162	C₂²×D₁₃	—	2	2	no	—
163	C₂²×D₁₃	—	2	2	no	—
164	C₂²×D₁₃	—	4	1	no	—
165	C₂²×D₁₃	—	4	1	no	—
166	C₂²×D₁₃	—	4	1	no	—
167	C₂²×D₁₃	—	4	1	no	—
168	Q₈×C₁₃	—	4	8	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₁₃	C₂×D₈	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×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	4	1	no	—
198	C₂×Dic₁₃	—	4	1	no	—
199	C₂×Dic₁₃	—	4	2	no	—
200	C₂×Dic₁₃	—	4	2	no	—
201	C₂×Dic₁₃	—	4	2	no	—
202	D₅₂	—	2	2	no	—
203	D₅₂	—	2	2	no	—
204	D₅₂	—	2	2	no	—
205	D₅₂	C₄×Q₈	1	4	yes	complemented
206	C₄×D₁₃	—	4	8	no	—
207	C₄×D₁₃	—	8	8	no	—
208	#1055	—	2	4	no	—
209	#1055	—	2	2	no	—
210	#1055	—	4	1	no	—
211	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
212	C₂×C₄×Q₈	—	2	1	no	—
213	C₂×C₄×D₄	—	13	1	no	—
214	C₂×C₄×D₄	—	13	2	no	—
215	C₂²×C₄⋊C₄	—	26	1	no	—
216	#474	—	13	8	no	—
217	C₂×#107	—	13	2	no	—
218	C₂×#107	—	13	2	no	—
219	C₂×C₄⋊C₈	—	13	1	no	—
220	C₂×#102	—	13	2	no	—
221	C₂×#102	—	13	1	no	—
222	C₂×#102	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	2	no	—
225	#391	—	2	1	no	—
226	#389	—	13	2	no	—
227	#389	C₂×D₁₃	1	2	yes	—
228	#387	—	2	2	no	—
229	#385	—	26	2	no	—
230	#384	—	13	1	no	—
231	#380	—	26	1	no	—
232	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
233	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
235	#340	—	13	2	no	—
236	#340	—	13	1	no	—
237	#340	—	13	2	no	—
238	#340	—	13	1	no	—
239	#340	—	13	2	no	—
240	#336	—	13	2	no	—
241	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₁₃	#546	1	1	yes	characteristic
243	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
244	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
246	C₂²×C₁₃	#577	1	1	yes	characteristic
247	C₂²×C₁₃	#578	1	1	yes	characteristic
248	C₂×D₁₃	—	2	4	no	—
249	C₂×D₁₃	—	4	2	no	—
250	C₂×D₁₃	—	4	2	no	—
251	C₂×D₁₃	—	4	2	no	—
252	C₂×D₁₃	—	4	2	no	—
253	C₂×D₁₃	—	4	2	no	—
254	C₂×D₁₃	—	4	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	8	1	no	—
261	C₄×C₁₃	C₄×D₈	1	4	yes	—
262	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₄×C₁₃	#520	1	1	yes	characteristic
264	C₄×C₁₃	#552	1	1	yes	characteristic
265	C₄×C₁₃	#554	1	1	yes	characteristic
266	Dic₁₃	—	4	2	no	—
267	Dic₁₃	—	8	2	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	—	13	1	no	—
270	C₂³×C₄	—	26	1	no	—
271	C₂³×C₄	—	26	2	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	C₄×D₁₃	1	4	yes	complemented
277	C₄×Q₈	—	4	4	no	—
278	C₄×D₄	—	13	4	no	—
279	C₄×D₄	—	26	4	no	—
280	C₄×D₄	—	26	2	no	—
281	C₄×D₄	—	52	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	2	no	—
286	C₂×C₄⋊C₄	—	26	2	no	—
287	C₂×C₄⋊C₄	—	26	1	no	—
288	C₂×C₄⋊C₄	—	26	1	no	—
289	C₂×C₄⋊C₄	—	52	4	no	—
290	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	26	1	no	—
296	C₂×C₂²⋊C₄	—	26	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
300	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
301	#107	—	13	8	no	—
302	#107	—	52	2	no	—
303	C₄⋊C₈	—	13	4	no	—
304	#102	—	13	8	no	—
305	#102	—	13	4	no	—
306	#102	—	26	2	no	—
307	C₄×C₈	—	26	2	no	—
308	C₄×C₈	—	52	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	26	2	no	—
313	#95	C₂²⋊D₁₃	1	2	yes	—
314	C₂×C₁₃	#2360	1	1	yes	characteristic
315	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
316	C₂×C₁₃	#2947	1	1	yes	characteristic
317	C₂×C₁₃	#3294	1	1	yes	characteristic
318	C₂×C₁₃	#3302	1	1	yes	characteristic
319	C₂×C₁₃	Q₈×D₈	1	1	yes	characteristic
320	C₂×C₁₃	#3381	1	1	yes	characteristic
321	D₁₃	—	4	4	no	—
322	C₂⁴	—	26	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×D₄	—	13	2	no	—
327	C₂×D₄	—	13	2	no	—
328	C₂×D₄	—	13	2	no	—
329	C₂×D₄	—	26	1	no	—
330	C₂×D₄	—	26	1	no	—
331	C₂×D₄	—	26	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	26	1	no	—
336	C₂²×C₄	—	26	4	no	—
337	C₂²×C₄	—	26	2	no	—
338	C₂²×C₄	—	52	4	no	—
339	C₂²×C₄	—	52	2	no	—
340	C₂²×C₄	—	52	2	no	—
341	C₂²×C₄	—	52	4	no	—
342	C₂²×C₄	—	104	2	no	—
343	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
344	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
346	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
348	C₂×C₈	—	13	4	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	1	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	1	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	13	2	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	—	26	2	no	—
367	C₄⋊C₄	—	26	2	no	—
368	C₄⋊C₄	—	52	4	no	—
369	C₄⋊C₄	—	52	2	no	—
370	C₄⋊C₄	—	104	1	no	—
371	C₄⋊C₄	#6104	1	4	yes	—
372	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
373	C₄⋊C₄	Q₈×D₁₃	1	2	yes	—
374	C₂²⋊C₄	—	26	4	no	—
375	C₂²⋊C₄	—	52	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	4	2	no	—
380	C₄²	C₂×C₄×D₁₃	1	2	yes	—
381	C₄²	#6127	1	2	yes	—
382	C₁₃	#22962	1	1	yes	characteristic, complemented, Sylow
383	C₂³	—	26	2	no	—
384	C₂³	—	26	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	—	52	1	no	—
387	C₂³	—	52	1	no	—
388	C₂³	—	52	1	no	—
389	C₂³	—	52	1	no	—
390	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
391	Q₈	—	4	8	no	—
392	D₄	—	13	4	no	—
393	D₄	—	26	2	no	—
394	D₄	—	26	2	no	—
395	D₄	—	26	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	52	1	no	—
414	C₂×C₄	—	52	1	no	—
415	C₂×C₄	—	52	8	no	—
416	C₂×C₄	—	52	2	no	—
417	C₂×C₄	—	52	2	no	—
418	C₂×C₄	—	52	2	no	—
419	C₂×C₄	—	104	8	no	—
420	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
421	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
422	C₂×C₄	C₂×#6104	1	4	yes	—
423	C₂×C₄	C₂×#6104	1	2	yes	—
424	C₂×C₄	#88204	1	2	yes	—
425	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#6127	1	1	yes	characteristic
427	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
428	C₂×C₄	#88254	1	1	yes	characteristic
429	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
430	C₂×C₄	#88256	1	1	yes	characteristic
431	C₈	—	26	4	no	—
432	C₈	—	26	2	no	—
433	C₈	—	52	1	no	—
434	C₂²	—	26	4	no	—
435	C₂²	—	52	2	no	—
436	C₂²	—	52	2	no	—
437	C₂²	—	52	2	no	—
438	C₂²	—	52	2	no	—
439	C₂²	—	52	2	no	—
440	C₂²	—	52	2	no	—
441	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₂²	C₂²×#6104	1	1	yes	characteristic
443	C₂²	Q₈×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₂²	C₂×#88204	1	1	yes	characteristic
445	C₂²	#11719534	1	1	yes	characteristic
446	C₂²	#11719542	1	1	yes	characteristic
447	C₂²	#11719543	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	52	2	no	—
455	C₄	—	104	2	no	—
456	C₄	C₄×#6104	1	4	yes	—
457	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
458	C₄	#11719279	1	1	yes	characteristic
459	C₄	#11719284	1	1	yes	characteristic
460	C₄	#11719286	1	1	yes	characteristic
461	C₂	—	52	4	no	—
462	C₂	#13117837	1	1	yes	characteristic
463	C₂	C₂×C₄×#6104	1	1	yes	characteristic
464	C₂	#13123679	1	1	yes	characteristic
465	C₂	#13126643	1	1	yes	characteristic
466	C₂	#13126747	1	1	yes	characteristic
467	C₂	Q₈×#6104	1	1	yes	characteristic
468	C₂	#13127707	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2365	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₅₂	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2365	D₁₃
hypocenter	C₁₃	#22962
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2365

Complements

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

N	H ≅ G/N	type
3. #13115798	C₂	semidirect
4. #13115594	C₂	semidirect
5. #13115566	C₂	semidirect
6. #13115407	C₂	semidirect
8. C₄⋊C₄×#1055	C₂	semidirect
11. C₁₃×#2365	C₂	semidirect
23. #11718748	C₄	semidirect
47. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
82. #88049	Q₈	semidirect
84. #88047	C₂×C₄	semidirect
85. C₄⋊#1055	C₂×C₄	semidirect
150. #2365	D₁₃	semidirect
205. D₅₂	C₄×Q₈	semidirect
276. C₄⋊Q₈	C₄×D₁₃	semidirect
382. C₁₃	#22962	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718748	2
C₄⋊C₄×D₅₂	2
#13115798	2
#13115594	2
#13115566	2
#13115407	2
#13115082	2
C₄⋊C₄×#1055	2
C₄×#88049	2
C₁₃×#2365	2
#22962	13