Subgroups — #16755100

Order 3328.

2168 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128614	C₂	1	1	yes	maximal, characteristic
2	#13127813	C₂	1	2	yes	maximal, complemented
3	#13127507	C₂	1	2	yes	maximal, complemented
4	#13126654	C₂	1	6	yes	maximal, complemented
5	D₄×#6106	C₂	1	6	yes	maximal, complemented
6	#13126148	C₂	1	3	yes	maximal, complemented
7	#13125774	C₂	1	3	yes	maximal, complemented
8	#13124867	C₂	1	3	yes	maximal, complemented
9	C₂×#11718688	C₂	1	3	yes	maximal, complemented
10	#13123947	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88256	—	2	1	no	—
13	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#554	—	2	3	no	—
17	C₁₃×#554	C₂²	1	3	yes	complemented
18	D₄×Q₈×C₁₃	C₂²	1	3	yes	complemented
19	C₁₃×#533	—	2	3	no	—
20	C₁₃×#533	C₂²	1	3	yes	complemented
21	C₄×C₁₃×#41	—	2	1	no	—
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	complemented
24	C₂²×#6106	C₂²	1	6	yes	complemented
25	#11719282	—	2	1	no	—
26	#11719282	C₂²	1	2	yes	—
27	D₄×D₅₂	—	2	3	no	—
28	D₄×D₅₂	C₂²	1	6	yes	—
29	#11719230	—	2	3	no	—
30	#11719182	C₂²	1	3	yes	—
31	C₂×#88128	C₂²	1	3	yes	—
32	#11718888	C₂²	1	6	yes	complemented
33	#11718749	C₂²	1	6	yes	complemented
34	#11718746	C₂²	1	6	yes	complemented
35	#11718745	C₂²	1	6	yes	complemented
36	#11718744	C₂²	1	6	yes	complemented
37	#11718709	C₂²	1	12	yes	complemented
38	#11718707	C₂²	1	12	yes	complemented
39	#11718688	C₂²	1	3	yes	complemented
40	#11718688	C₂²	1	3	yes	complemented
41	#11718688	C₂²	1	6	yes	complemented
42	#11718688	C₂²	1	6	yes	complemented
43	#11718688	C₂²	1	6	yes	complemented
44	C₄×#6106	C₂²	1	6	yes	complemented
45	C₄×#6106	C₂²	1	6	yes	complemented
46	Q₈×#1055	C₂²	1	2	yes	complemented
47	#11718681	C₂²	1	1	yes	characteristic, complemented
48	#11718681	C₂²	1	3	yes	complemented
49	D₄×#1055	C₂²	1	6	yes	complemented
50	#11718629	C₂²	1	6	yes	complemented
51	C₂×#88049	C₂²	1	6	yes	complemented
52	#11718586	C₂²	1	3	yes	complemented
53	C₂×C₄⋊#1055	C₂²	1	3	yes	complemented
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
56	#88256	—	4	8	no	—
57	C₂×#6131	—	2	2	no	—
58	C₂×D₄×D₁₃	—	2	6	no	—
59	C₂×#6127	—	2	3	no	—
60	C₂²×D₅₂	—	2	3	no	—
61	C₂²×D₅₂	—	2	3	no	—
62	C₂²×D₅₂	C₂³	1	6	yes	—
63	C₁₃×C₄⋊Q₈	—	2	3	no	—
64	C₁₃×C₄⋊Q₈	—	2	3	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×#125	—	2	3	no	—
68	C₁₃×#125	—	2	3	no	—
69	C₁₃×#125	—	2	3	no	—
70	C₁₃×C₂²⋊Q₈	—	2	3	no	—
71	C₁₃×C₂²⋊Q₈	—	2	6	no	—
72	C₁₃×C₂²⋊Q₈	—	2	6	no	—
73	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
74	C₄×Q₈×C₁₃	—	2	1	no	—
75	C₄×Q₈×C₁₃	—	2	1	no	—
76	C₄×Q₈×C₁₃	—	2	3	no	—
77	C₄×Q₈×C₁₃	—	2	3	no	—
78	C₄×Q₈×C₁₃	—	2	3	no	—
79	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
82	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
83	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₁₃	—	2	3	no	—
86	C₄×D₄×C₁₃	—	2	3	no	—
87	C₄×D₄×C₁₃	D₄	1	3	yes	—
88	C₄×D₄×C₁₃	C₂³	1	3	yes	—
89	C₁₃×#117	—	2	3	no	—
90	C₁₃×#117	D₄	1	3	yes	—
91	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
93	C₂×C₄²×C₁₃	—	2	3	no	—
94	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
95	C₂×#6106	—	4	12	no	—
96	C₂×#6106	C₂³	1	6	yes	—
97	C₂×#6106	C₂³	1	6	yes	—
98	C₂×#6106	C₂³	1	12	yes	—
99	#88184	—	2	3	no	—
100	#88184	C₂³	1	6	yes	—
101	C₂²×#1055	C₂³	1	6	yes	—
102	#88149	—	2	6	no	—
103	#88149	—	2	6	no	—
104	#88136	—	2	12	no	—
105	#88129	—	2	3	no	—
106	#88128	—	2	3	no	—
107	#88128	—	2	3	no	—
108	#88128	C₂³	1	3	yes	—
109	#88128	C₂³	1	6	yes	—
110	C₄×D₅₂	—	2	3	no	—
111	C₄×D₅₂	C₂³	1	6	yes	—
112	#88123	C₂³	1	1	yes	characteristic
113	#88075	C₂³	1	2	yes	—
114	#88075	C₂³	1	6	yes	—
115	C₂²⋊#1055	C₂³	1	6	yes	—
116	#88049	C₂³	1	6	yes	—
117	#88049	C₂³	1	6	yes	—
118	#88049	C₂³	1	12	yes	—
119	#88048	C₂³	1	2	yes	—
120	#88048	C₂³	1	6	yes	—
121	C₄⋊#1055	C₂³	1	6	yes	—
122	C₄⋊#1055	C₂³	1	3	yes	—
123	C₄⋊#1055	C₂³	1	1	yes	characteristic
124	C₄×#1055	C₂³	1	6	yes	—
125	#61951	—	13	1	no	maximal, Sylow
126	C₂³×D₁₃	—	2	6	no	—
127	C₁₃×#41	SD₁₆	1	8	yes	complemented
128	C₂×Q₈×C₁₃	—	2	3	no	—
129	C₂×Q₈×C₁₃	—	2	3	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	4	3	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
134	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
136	C₂²×C₄×C₁₃	—	2	3	no	—
137	C₂²×C₄×C₁₃	—	2	3	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
141	C₂×C₂²⋊D₁₃	—	2	6	no	—
142	#6131	—	4	8	no	—
143	D₄×D₁₃	—	4	24	no	—
144	#6127	—	4	12	no	—
145	C₂×D₅₂	—	2	3	no	—
146	C₂×D₅₂	—	2	3	no	—
147	C₂×D₅₂	—	2	6	no	—
148	C₂×D₅₂	—	2	6	no	—
149	C₂×D₅₂	—	2	6	no	—
150	C₂×D₅₂	—	4	6	no	—
151	C₂×D₅₂	—	4	6	no	—
152	C₂×D₅₂	—	4	12	no	—
153	C₂×D₅₂	—	8	6	no	—
154	C₂×D₅₂	C₂⁴	1	6	yes	—
155	C₂×C₄×D₁₃	—	2	6	no	—
156	C₂×Dic₂₆	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	3	no	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	6	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
170	C₁₃×C₂²⋊C₄	—	2	6	no	—
171	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	3	no	—
174	C₄²×C₁₃	—	2	3	no	—
175	C₄²×C₁₃	—	2	3	no	—
176	C₄²×C₁₃	C₂×D₄	1	3	yes	—
177	C₄²×C₁₃	C₂×D₄	1	3	yes	—
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₄²×C₁₃	C₂⁴	1	3	yes	—
180	#6106	—	2	12	no	—
181	#6106	—	4	12	no	—
182	#6106	—	4	6	no	—
183	#6103	—	2	6	no	—
184	#6103	—	2	6	no	—
185	C₄⋊Dic₁₃	—	2	1	no	—
186	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
187	C₂×#1055	—	4	6	no	—
188	C₂×#1055	C₂⁴	1	2	yes	—
189	C₂×#1055	C₂⁴	1	6	yes	—
190	#3498	—	13	1	no	—
191	Q₈×#41	D₁₃	1	1	yes	characteristic, complemented
192	#3392	—	13	2	no	—
193	#3362	—	13	2	no	—
194	#3295	—	13	6	no	—
195	D₄×SD₁₆	—	13	6	no	—
196	#3246	—	13	3	no	—
197	#3208	—	13	3	no	—
198	#3103	—	13	3	no	—
199	C₂×#460	—	13	3	no	—
200	#2988	—	13	1	no	—
201	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
202	C₂²×D₁₃	—	2	6	no	—
203	C₂²×D₁₃	—	4	12	no	—
204	C₂²×D₁₃	—	8	6	no	—
205	C₂²×D₁₃	—	8	6	no	—
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	—	2	3	no	—
208	Q₈×C₁₃	—	2	3	no	—
209	Q₈×C₁₃	—	4	6	no	—
210	Q₈×C₁₃	—	8	3	no	—
211	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	complemented
212	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
213	D₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	3	no	—
216	C₂×C₄×C₁₃	—	2	3	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	3	no	—
219	C₂×C₄×C₁₃	—	2	3	no	—
220	C₂×C₄×C₁₃	—	4	3	no	—
221	C₂×C₄×C₁₃	—	4	6	no	—
222	C₂×C₄×C₁₃	—	8	3	no	—
223	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
230	C₂²⋊D₁₃	—	4	12	no	—
231	C₂×Dic₁₃	—	2	2	no	—
232	D₅₂	—	2	6	no	—
233	D₅₂	—	2	6	no	—
234	D₅₂	—	4	6	no	—
235	D₅₂	—	4	6	no	—
236	D₅₂	—	4	12	no	—
237	D₅₂	—	8	6	no	—
238	D₅₂	—	8	6	no	—
239	C₄×D₁₃	—	4	12	no	—
240	Dic₂₆	—	4	2	no	—
241	#1055	—	2	6	no	—
242	#1055	—	2	2	no	—
243	C₂×H(5,𝔽₂)	—	26	1	no	—
244	C₂²×SD₁₆	—	13	6	no	—
245	Q₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
246	#557	—	2	1	no	—
247	#557	C₂×D₁₃	1	1	yes	characteristic, complemented
248	#554	—	2	3	no	—
249	#554	C₂×D₁₃	1	3	yes	complemented
250	#550	—	13	2	no	—
251	#550	—	26	1	no	—
252	D₄×Q₈	C₂×D₁₃	1	3	yes	complemented
253	D₄²	—	13	6	no	—
254	D₄²	—	26	3	no	—
255	#535	—	26	3	no	—
256	#533	—	2	3	no	—
257	#533	C₂×D₁₃	1	3	yes	complemented
258	#532	—	13	3	no	—
259	C₂×#127	—	13	3	no	—
260	C₄×#41	—	2	1	no	—
261	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂×D₁₃	1	3	yes	complemented
263	#492	—	13	6	no	—
264	#486	—	13	6	no	—
265	#481	—	13	6	no	—
266	#476	—	13	6	no	—
267	#475	—	13	1	no	—
268	#475	—	13	3	no	—
269	#465	—	13	12	no	—
270	#461	—	13	6	no	—
271	#460	—	13	3	no	—
272	#460	—	13	3	no	—
273	#460	—	13	6	no	—
274	#460	—	13	6	no	—
275	#460	—	13	6	no	—
276	#450	—	13	12	no	—
277	#448	—	13	6	no	—
278	C₈×Q₈	—	13	2	no	—
279	C₄×SD₁₆	—	13	6	no	—
280	C₄×SD₁₆	—	13	6	no	—
281	C₈×D₄	—	13	6	no	—
282	#431	—	13	3	no	—
283	C₂×C₄⋊C₈	—	13	3	no	—
284	C₂×#102	—	13	6	no	—
285	C₂²×C₁₃	—	2	3	no	—
286	C₂²×C₁₃	—	2	3	no	—
287	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₂×D₁₃	—	4	6	no	—
290	C₂×D₁₃	—	4	6	no	—
291	C₂×D₁₃	—	4	6	no	—
292	C₂×D₁₃	—	16	12	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	3	no	—
295	C₄×C₁₃	—	2	3	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	3	no	—
299	C₄×C₁₃	—	4	3	no	—
300	C₄×C₁₃	C₂²×SD₁₆	1	2	yes	—
301	C₄×C₁₃	C₂²×SD₁₆	1	6	yes	—
302	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₄×C₁₃	#585	1	1	yes	characteristic
304	Dic₁₃	—	4	2	no	—
305	H(5,𝔽₂)	—	52	8	no	—
306	C₂×#41	—	26	2	no	—
307	C₂×#41	—	26	3	no	—
308	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
309	C₂²×Q₈	C₂²×D₁₃	1	3	yes	—
310	C₂²×D₄	—	13	6	no	—
311	C₂²×D₄	—	26	6	no	—
312	C₂²×D₄	—	26	3	no	—
313	C₂²×D₄	—	26	3	no	—
314	C₂×SD₁₆	—	13	6	no	—
315	C₂×SD₁₆	—	13	12	no	—
316	C₂×SD₁₆	—	13	6	no	—
317	C₂×SD₁₆	—	52	12	no	—
318	C₂²×C₈	—	13	6	no	—
319	C₄⋊Q₈	—	2	3	no	—
320	C₄⋊Q₈	—	2	3	no	—
321	C₄⋊Q₈	—	13	1	no	—
322	C₄⋊Q₈	C₂²×D₁₃	1	3	yes	—
323	C₄⋊Q₈	C₂²×D₁₃	1	3	yes	—
324	#127	—	13	3	no	—
325	#127	—	13	6	no	—
326	#127	—	26	3	no	—
327	#127	—	26	3	no	—
328	#125	—	2	3	no	—
329	#125	—	2	3	no	—
330	#125	—	2	3	no	—
331	#124	—	26	3	no	—
332	C₂²⋊Q₈	—	2	3	no	—
333	C₂²⋊Q₈	—	2	6	no	—
334	C₂²⋊Q₈	—	2	6	no	—
335	C₂²⋊Q₈	C₂²×D₁₃	1	6	yes	—
336	#121	—	13	6	no	—
337	#121	—	26	3	no	—
338	#121	—	26	6	no	—
339	#121	—	26	6	no	—
340	#120	—	26	12	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	3	no	—
344	C₄×Q₈	—	2	3	no	—
345	C₄×Q₈	—	2	3	no	—
346	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
347	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
348	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
349	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
350	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
351	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	13	6	no	—
355	C₄×D₄	—	26	3	no	—
356	C₄×D₄	C₂²⋊D₁₃	1	3	yes	—
357	C₄×D₄	C₂²×D₁₃	1	3	yes	—
358	#117	—	2	3	no	—
359	#117	C₂²⋊D₁₃	1	3	yes	—
360	C₂×C₄⋊C₄	—	2	3	no	—
361	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
362	C₂×C₄²	—	2	3	no	—
363	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
364	#106	—	13	2	no	—
365	#106	—	13	6	no	—
366	C₄⋊C₈	—	13	3	no	—
367	C₄⋊C₈	—	13	6	no	—
368	C₄⋊C₈	—	13	1	no	—
369	#103	—	13	2	no	—
370	#103	—	13	6	no	—
371	#102	—	13	6	no	—
372	#102	—	13	12	no	—
373	#102	—	13	6	no	—
374	C₂²⋊C₈	—	13	6	no	—
375	C₄×C₈	—	13	6	no	—
376	C₂×C₁₃	—	2	6	no	—
377	C₂×C₁₃	#3488	1	1	yes	characteristic
378	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
379	C₂×C₁₃	#3585	1	1	yes	characteristic
380	D₁₃	—	8	6	no	—
381	C₂⁴	—	26	6	no	—
382	#41	—	52	8	no	—
383	#41	—	52	12	no	—
384	#41	#6106	1	8	yes	complemented
385	C₂×Q₈	—	2	3	no	—
386	C₂×Q₈	—	2	3	no	—
387	C₂×Q₈	—	2	6	no	—
388	C₂×Q₈	—	4	3	no	—
389	C₂×Q₈	—	26	1	no	—
390	C₂×Q₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂×Q₈	C₂³×D₁₃	1	3	yes	—
392	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
393	C₂×D₄	—	13	6	no	—
394	C₂×D₄	—	26	6	no	—
395	C₂×D₄	—	26	3	no	—
396	C₂×D₄	—	26	6	no	—
397	C₂×D₄	—	26	3	no	—
398	C₂×D₄	—	26	6	no	—
399	C₂×D₄	—	26	6	no	—
400	C₂×D₄	—	52	6	no	—
401	C₂×D₄	—	52	6	no	—
402	C₂×D₄	—	52	24	no	—
403	C₂×D₄	—	52	12	no	—
404	C₂×D₄	—	104	6	no	—
405	C₂×D₄	C₂×C₂²⋊D₁₃	1	3	yes	—
406	C₂²×C₄	—	2	3	no	—
407	C₂²×C₄	—	2	3	no	—
408	C₂²×C₄	—	26	6	no	—
409	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
410	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
411	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
412	SD₁₆	—	26	12	no	—
413	SD₁₆	—	52	12	no	—
414	SD₁₆	—	52	6	no	—
415	C₂×C₈	—	13	2	no	—
416	C₂×C₈	—	13	6	no	—
417	C₂×C₈	—	52	6	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	3	no	—
420	C₄⋊C₄	—	2	3	no	—
421	C₄⋊C₄	—	2	3	no	—
422	C₄⋊C₄	—	2	3	no	—
423	C₄⋊C₄	—	2	3	no	—
424	C₄⋊C₄	—	2	3	no	—
425	C₄⋊C₄	—	2	3	no	—
426	C₄⋊C₄	—	2	6	no	—
427	C₄⋊C₄	—	13	2	no	—
428	C₄⋊C₄	—	26	1	no	—
429	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
430	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
431	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
432	C₄⋊C₄	C₂³×D₁₃	1	3	yes	—
433	C₂²⋊C₄	—	2	6	no	—
434	C₂²⋊C₄	—	26	6	no	—
435	C₂²⋊C₄	—	26	6	no	—
436	C₂²⋊C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	3	no	—
439	C₄²	—	2	3	no	—
440	C₄²	—	2	3	no	—
441	C₄²	C₂×C₂²⋊D₁₃	1	3	yes	—
442	C₄²	C₂×C₂²⋊D₁₃	1	3	yes	—
443	C₄²	C₂³×D₁₃	1	3	yes	—
444	C₄²	C₂³×D₁₃	1	1	yes	characteristic
445	C₁₃	#61951	1	1	yes	characteristic, complemented, Sylow
446	C₂³	—	26	6	no	—
447	C₂³	—	52	12	no	—
448	C₂³	—	104	6	no	—
449	C₂³	—	104	6	no	—
450	C₂³	C₂²×C₂²⋊D₁₃	1	3	yes	—
451	Q₈	—	2	1	no	—
452	Q₈	—	2	3	no	—
453	Q₈	—	2	3	no	—
454	Q₈	—	4	6	no	—
455	Q₈	—	8	3	no	—
456	Q₈	—	52	2	no	—
457	Q₈	C₂×#6106	1	4	yes	complemented
458	Q₈	#88256	1	2	yes	complemented
459	D₄	—	26	6	no	—
460	D₄	—	26	6	no	—
461	D₄	—	52	6	no	—
462	D₄	—	52	12	no	—
463	D₄	—	52	12	no	—
464	D₄	—	52	6	no	—
465	D₄	—	104	6	no	—
466	D₄	—	104	6	no	—
467	D₄	C₂×#6106	1	12	yes	complemented
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	3	no	—
470	C₂×C₄	—	2	3	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	4	3	no	—
475	C₂×C₄	—	4	6	no	—
476	C₂×C₄	—	8	3	no	—
477	C₂×C₄	—	26	2	no	—
478	C₂×C₄	—	52	12	no	—
479	C₂×C₄	C₂×#6106	1	12	yes	complemented
480	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₂²⋊D₁₃	1	3	yes	—
482	C₂×C₄	C₂²×C₂²⋊D₁₃	1	3	yes	—
483	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₂²⋊D₁₃	1	3	yes	—
485	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
486	C₈	—	26	6	no	—
487	C₈	—	26	2	no	—
488	C₂²	—	2	3	no	—
489	C₂²	—	2	3	no	—
490	C₂²	—	52	6	no	—
491	C₂²	—	52	6	no	—
492	C₂²	—	52	6	no	—
493	C₂²	—	208	12	no	—
494	C₂²	C₂²×#6106	1	6	yes	—
495	C₂²	C₂³×C₂²⋊D₁₃	1	1	yes	characteristic
496	C₄	—	2	3	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	3	no	—
500	C₄	—	4	3	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	3	no	—
503	C₄	—	52	2	no	—
504	C₄	C₂²×#6106	1	6	yes	—
505	C₄	C₂²×#6106	1	2	yes	—
506	C₄	C₂×#88256	1	1	yes	characteristic
507	C₄	#11719648	1	1	yes	characteristic
508	C₂	—	2	6	no	—
509	C₂	—	104	6	no	—
510	C₂	#13128505	1	1	yes	characteristic
511	C₂	C₂³×#6106	1	1	yes	characteristic
512	C₂	#13129615	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	Q₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	#13128614	C₂
hypercenter	Q₈×#41	D₁₃
hypocenter	C₁₃	#61951
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. #13127813	C₂	semidirect
3. #13127507	C₂	semidirect
4. #13126654	C₂	semidirect
5. D₄×#6106	C₂	semidirect
6. #13126148	C₂	semidirect
7. #13125774	C₂	semidirect
8. #13124867	C₂	semidirect
9. C₂×#11718688	C₂	semidirect
10. #13123947	C₂	semidirect
11. Q₈×C₁₃×#41	C₂	semidirect
13. Q₈²×C₁₃	C₂²	semidirect
15. C₁₃×#557	C₂²	semidirect
17. C₁₃×#554	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#533	C₂²	semidirect
23. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
24. C₂²×#6106	C₂²	semidirect
32. #11718888	C₂²	semidirect
33. #11718749	C₂²	semidirect
34. #11718746	C₂²	semidirect
35. #11718745	C₂²	semidirect
36. #11718744	C₂²	semidirect
37. #11718709	C₂²	semidirect
38. #11718707	C₂²	semidirect
39. #11718688	C₂²	semidirect
40. #11718688	C₂²	semidirect
41. #11718688	C₂²	semidirect
42. #11718688	C₂²	semidirect
43. #11718688	C₂²	semidirect
44. C₄×#6106	C₂²	semidirect
45. C₄×#6106	C₂²	semidirect
46. Q₈×#1055	C₂²	semidirect
47. #11718681	C₂²	semidirect
48. #11718681	C₂²	semidirect
49. D₄×#1055	C₂²	semidirect
50. #11718629	C₂²	semidirect
51. C₂×#88049	C₂²	semidirect
52. #11718586	C₂²	semidirect
53. C₂×C₄⋊#1055	C₂²	semidirect
127. C₁₃×#41	SD₁₆	semidirect
191. Q₈×#41	D₁₃	semidirect
211. Q₈×C₁₃	C₂×SD₁₆	semidirect
212. Q₈×C₁₃	H(5,𝔽₂)	semidirect
213. D₄×C₁₃	C₂×SD₁₆	semidirect
223. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
245. Q₈²	C₂×D₁₃	semidirect
247. #557	C₂×D₁₃	semidirect
249. #554	C₂×D₁₃	semidirect
252. D₄×Q₈	C₂×D₁₃	semidirect
257. #533	C₂×D₁₃	semidirect
262. C₂×C₄×Q₈	C₂×D₁₃	semidirect
384. #41	#6106	semidirect
445. C₁₃	#61951	semidirect
457. Q₈	C₂×#6106	semidirect
458. Q₈	#88256	semidirect
467. D₄	C₂×#6106	semidirect
479. C₂×C₄	C₂×#6106	semidirect

Maximal subgroups

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

subgroup	index
#13128614	2
#13127813	2
#13127507	2
#13126654	2
D₄×#6106	2
#13126148	2
#13125774	2
#13124867	2
C₂×#11718688	2
#13123947	2
Q₈×C₁₃×#41	2
#61951	13