Subgroups — #16807425

Order 3328.

484 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131253	C₂	1	1	yes	maximal, characteristic, complemented
2	#13131252	C₂	1	1	yes	maximal, characteristic, complemented
3	#13131222	C₂	1	1	yes	maximal, characteristic, complemented
4	#13131221	C₂	1	1	yes	maximal, characteristic, complemented
5	#13131219	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131218	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131218	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131217	C₂	1	1	yes	maximal, characteristic, complemented
9	#13131204	C₂	1	1	yes	maximal, characteristic, complemented
10	#13131201	C₂	1	1	yes	maximal, characteristic, complemented
11	#13131200	C₂	1	1	yes	maximal, characteristic, complemented
12	#13131172	C₂	1	1	yes	maximal, characteristic, complemented
13	#13131171	C₂	1	1	yes	maximal, characteristic, complemented
14	#13131169	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123809	C₂	1	1	yes	maximal, characteristic
16	#11719233	C₄	1	1	yes	characteristic
17	C₂×#88106	C₂²	1	1	yes	characteristic
18	C₂²×#6092	C₂²	1	1	yes	characteristic
19	C₂×#88098	C₂²	1	1	yes	characteristic
20	C₂×#88098	C₂²	1	1	yes	characteristic
21	C₂×#88098	C₂²	1	1	yes	characteristic
22	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₁₃×#433	C₄	1	1	yes	characteristic
24	#11718658	C₂²	1	1	yes	characteristic
25	#11718497	C₄	1	1	yes	characteristic
26	#11718495	C₂²	1	1	yes	characteristic
27	#11718491	C₂²	1	1	yes	characteristic
28	#11718489	C₄	1	1	yes	characteristic
29	#11718390	C₄	1	1	yes	characteristic
30	#11718389	C₄	1	1	yes	characteristic
31	#11718386	C₂²	1	1	yes	characteristic
32	#11718386	C₂²	1	1	yes	characteristic
33	#11718369	C₂²	1	1	yes	characteristic
34	#11718366	C₄	1	1	yes	characteristic
35	#11718351	C₄	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	C₂²⋊#6092	C₂²	1	1	yes	characteristic
38	C₂²⋊#6092	C₂²	1	1	yes	characteristic
39	#11718260	C₂²	1	1	yes	characteristic
40	#11718260	C₂²	1	1	yes	characteristic
41	#11718260	C₂²	1	1	yes	characteristic
42	#11718260	C₂²	1	1	yes	characteristic
43	#11718259	C₂²	1	1	yes	characteristic
44	#11718259	C₂²	1	1	yes	characteristic
45	#11718259	C₂²	1	1	yes	characteristic
46	#11718259	C₂²	1	1	yes	characteristic
47	#11718258	C₂²	1	1	yes	characteristic
48	#11718258	C₂²	1	1	yes	characteristic
49	#11718258	C₂²	1	1	yes	characteristic
50	#11718257	C₂²	1	1	yes	characteristic
51	#11718231	C₂²	1	1	yes	characteristic
52	C₄⋊#6092	C₂²	1	1	yes	characteristic
53	C₄⋊#6092	C₂²	1	1	yes	characteristic
54	C₄⋊#6092	C₂²	1	1	yes	characteristic
55	C₄⋊#6092	C₂²	1	1	yes	characteristic
56	C₄⋊#6092	C₂²	1	1	yes	characteristic
57	C₄⋊#6092	C₂²	1	1	yes	characteristic
58	C₄×#6092	C₂²	1	1	yes	characteristic
59	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×#6099	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂³	1	1	yes	characteristic
64	C₂×#6094	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
68	#88152	C₈	1	1	yes	characteristic
69	#88150	C₈	1	1	yes	characteristic
70	#88148	C₈	1	1	yes	characteristic
71	#88143	C₈	1	1	yes	characteristic
72	#88139	C₈	1	1	yes	characteristic
73	#88138	C₈	1	1	yes	characteristic
74	#88137	C₈	1	1	yes	characteristic
75	#88133	C₈	1	1	yes	characteristic
76	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
77	#88126	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
80	#88106	—	4	1	no	—
81	C₂×#6092	—	4	1	no	—
82	C₂×#6092	C₂³	1	1	yes	characteristic
83	C₂×#6092	C₂³	1	1	yes	characteristic
84	C₂×#6092	C₂³	1	1	yes	characteristic
85	C₂×#6092	C₂³	1	1	yes	characteristic
86	C₂×#6092	C₂³	1	1	yes	characteristic
87	C₂×#6092	C₂³	1	1	yes	characteristic
88	C₂×#6092	C₂³	1	1	yes	characteristic
89	C₂×#6092	C₂³	1	1	yes	characteristic
90	#88098	—	4	1	no	—
91	#88098	—	4	1	no	—
92	#88098	—	4	1	no	—
93	D₁₃⋊C₁₆	—	4	1	no	—
94	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
100	#88060	C₂×C₄	1	1	yes	characteristic
101	#88060	C₂×C₄	1	1	yes	characteristic
102	#88060	C₂×C₄	1	1	yes	characteristic
103	#88060	C₂×C₄	1	1	yes	characteristic
104	#88055	C₂×C₄	1	1	yes	characteristic
105	#88054	C₂×C₄	1	1	yes	characteristic
106	#88054	C₂×C₄	1	1	yes	characteristic
107	#88054	C₂×C₄	1	1	yes	characteristic
108	#88054	C₂×C₄	1	1	yes	characteristic
109	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
111	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
112	#88043	C₂×C₄	1	1	yes	characteristic
113	#88043	C₂×C₄	1	1	yes	characteristic
114	C₄×#1055	C₂³	1	1	yes	characteristic
115	C₄×#1055	C₂³	1	1	yes	characteristic
116	#33509	—	13	1	no	maximal, Sylow
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
120	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
131	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
134	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
138	#6103	C₂×C₈	1	1	yes	characteristic
139	#6103	C₂×C₈	1	1	yes	characteristic
140	#6103	C₂×C₈	1	1	yes	characteristic
141	#6103	C₂×C₈	1	1	yes	characteristic
142	#6103	C₂×C₈	1	1	yes	characteristic
143	#6103	C₂×C₈	1	1	yes	characteristic
144	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
145	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
146	#6101	C₂×C₈	1	1	yes	characteristic
147	#6101	C₂×C₈	1	1	yes	characteristic
148	#6101	C₂×C₈	1	1	yes	characteristic
149	#6101	C₂×C₈	1	1	yes	characteristic
150	#6101	C₂×C₈	1	1	yes	characteristic
151	#6101	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
156	#6099	—	4	1	no	—
157	C₂×#1055	—	2	1	no	—
158	C₂×#1055	—	2	1	no	—
159	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
162	C₂×#1055	C₂⁴	1	1	yes	characteristic
163	#6094	—	4	1	no	—
164	C₈×D₁₃	—	2	1	no	—
165	C₈×D₁₃	—	2	1	no	—
166	C₈×D₁₃	—	2	1	no	—
167	C₈×D₁₃	—	2	1	no	—
168	C₈×D₁₃	—	4	1	no	—
169	#6092	—	2	1	no	—
170	#6092	—	2	1	no	—
171	#6092	—	2	1	no	—
172	#6092	—	2	1	no	—
173	#6092	—	2	1	no	—
174	#6092	—	2	1	no	—
175	#6092	—	2	1	no	—
176	#6092	—	2	1	no	—
177	#2966	—	13	1	no	—
178	#2183	—	13	1	no	—
179	#2183	—	13	1	no	—
180	#2169	—	13	1	no	—
181	#2169	—	13	1	no	—
182	#2168	—	13	1	no	—
183	#2168	—	13	1	no	—
184	#2168	—	13	1	no	—
185	#2168	—	13	1	no	—
186	#2164	—	13	1	no	—
187	#2164	—	13	1	no	—
188	#2163	—	13	1	no	—
189	#2151	—	13	1	no	—
190	#2151	—	13	1	no	—
191	#2150	—	13	1	no	—
192	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
193	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂²⋊D₁₃	—	4	1	no	—
204	C₂²⋊D₁₃	—	4	1	no	—
205	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
210	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
211	D₅₂	—	4	1	no	—
212	C₄×D₁₃	—	2	1	no	—
213	C₄×D₁₃	—	2	1	no	—
214	C₄×D₁₃	—	2	1	no	—
215	C₄×D₁₃	—	2	1	no	—
216	C₄×D₁₃	—	4	1	no	—
217	C₄×D₁₃	—	4	1	no	—
218	Dic₂₆	—	4	1	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	2	1	no	—
221	C₈×C₁₃	—	2	1	no	—
222	C₈×C₁₃	—	2	1	no	—
223	#1055	—	2	1	no	—
224	#1055	—	2	1	no	—
225	#1055	—	2	1	no	—
226	#1055	H(5,𝔽₂)	1	1	yes	characteristic
227	#1055	2₋¹⁺⁴	1	1	yes	characteristic
228	#529	—	13	1	no	—
229	C₂×M₃₂	—	13	1	no	—
230	C₂×M₃₂	—	13	1	no	—
231	C₂×M₃₂	—	13	1	no	—
232	C₂×M₃₂	—	13	1	no	—
233	C₂²×C₁₆	—	13	1	no	—
234	C₂²×C₁₆	—	13	1	no	—
235	#446	—	13	1	no	—
236	C₈×Q₈	—	13	1	no	—
237	#436	—	13	1	no	—
238	#435	—	13	1	no	—
239	#435	—	13	1	no	—
240	C₈×D₄	—	13	1	no	—
241	C₈×D₄	—	13	1	no	—
242	C₈×D₄	—	13	1	no	—
243	#433	—	13	1	no	—
244	#433	#261	1	1	yes	characteristic
245	#432	—	13	1	no	—
246	#405	—	13	1	no	—
247	#405	—	13	1	no	—
248	C₂×C₄×C₈	—	13	1	no	—
249	C₄⋊C₁₆	—	13	1	no	—
250	C₄⋊C₁₆	—	13	1	no	—
251	C₄⋊C₁₆	—	13	1	no	—
252	C₄⋊C₁₆	—	13	1	no	—
253	C₄⋊C₁₆	—	13	1	no	—
254	C₄⋊C₁₆	—	13	1	no	—
255	C₄⋊C₁₆	—	13	1	no	—
256	C₄⋊C₁₆	—	13	1	no	—
257	C₄⋊C₁₆	—	13	1	no	—
258	C₄⋊C₁₆	—	13	1	no	—
259	C₂²⋊C₁₆	—	13	1	no	—
260	C₂²⋊C₁₆	—	13	1	no	—
261	C₂²⋊C₁₆	—	13	1	no	—
262	C₂²⋊C₁₆	—	13	1	no	—
263	C₂²⋊C₁₆	—	13	1	no	—
264	C₂²⋊C₁₆	—	13	1	no	—
265	#346	—	13	1	no	—
266	#346	—	13	1	no	—
267	#346	—	13	1	no	—
268	#346	—	13	1	no	—
269	C₄×C₁₆	—	13	1	no	—
270	C₄×C₁₆	—	13	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
275	C₂×D₁₃	—	2	1	no	—
276	C₂×D₁₃	—	2	1	no	—
277	C₂×D₁₃	—	2	1	no	—
278	C₂×D₁₃	—	2	1	no	—
279	C₂×D₁₃	—	2	1	no	—
280	C₂×D₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	#520	1	1	yes	characteristic
287	C₄×C₁₃	#568	1	1	yes	characteristic
288	Dic₁₃	—	2	1	no	—
289	Dic₁₃	—	2	1	no	—
290	Dic₁₃	—	2	1	no	—
291	Dic₁₃	—	2	1	no	—
292	Dic₁₃	—	2	1	no	—
293	Dic₁₃	—	2	1	no	—
294	C₂×M₁₆	—	13	1	no	—
295	C₂×M₁₆	—	13	1	no	—
296	C₂²×C₈	—	13	1	no	—
297	C₂²×C₈	—	13	1	no	—
298	C₂²×C₈	—	13	1	no	—
299	C₂²×C₈	—	13	1	no	—
300	#126	—	13	1	no	—
301	#126	—	13	1	no	—
302	#125	—	13	1	no	—
303	#124	—	13	1	no	—
304	#123	—	13	1	no	—
305	#123	—	13	1	no	—
306	C₂²⋊Q₈	—	13	1	no	—
307	#121	—	13	1	no	—
308	C₄×Q₈	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	—	13	1	no	—
312	#117	—	13	1	no	—
313	#117	C₂×#261	1	1	yes	characteristic
314	C₂×C₄²	—	13	1	no	—
315	M₃₂	—	52	1	no	—
316	M₃₂	—	52	1	no	—
317	M₃₂	—	52	1	no	—
318	M₃₂	—	52	1	no	—
319	C₂×C₁₆	—	13	1	no	—
320	C₂×C₁₆	—	13	1	no	—
321	C₂×C₁₆	—	13	1	no	—
322	C₂×C₁₆	—	13	1	no	—
323	C₂×C₁₆	—	13	1	no	—
324	C₂×C₁₆	—	13	1	no	—
325	C₂×C₁₆	—	13	1	no	—
326	C₂×C₁₆	—	13	1	no	—
327	C₂×C₁₆	—	52	1	no	—
328	C₂×C₁₆	—	52	1	no	—
329	C₄⋊C₈	—	13	1	no	—
330	C₄⋊C₈	—	13	1	no	—
331	C₄⋊C₈	—	13	1	no	—
332	C₄⋊C₈	—	13	1	no	—
333	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
334	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
335	C₂²⋊C₈	—	13	1	no	—
336	C₂²⋊C₈	—	13	1	no	—
337	C₂²⋊C₈	—	13	1	no	—
338	C₂²⋊C₈	—	13	1	no	—
339	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
340	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
341	#97	—	13	1	no	—
342	#97	—	13	1	no	—
343	#97	—	13	1	no	—
344	#97	C₂×#261	1	1	yes	characteristic
345	C₄×C₈	—	13	1	no	—
346	C₄×C₈	—	13	1	no	—
347	C₄×C₈	—	13	1	no	—
348	C₄×C₈	—	13	1	no	—
349	C₄×C₈	—	13	1	no	—
350	C₄×C₈	C₂×#261	1	1	yes	characteristic
351	C₂×C₁₃	—	4	1	no	—
352	C₂×C₁₃	#2988	1	1	yes	characteristic
353	C₂×C₁₃	#3407	1	1	yes	characteristic
354	C₂×C₁₃	#3407	1	1	yes	characteristic
355	D₁₃	—	4	1	no	—
356	D₁₃	—	4	1	no	—
357	C₂×Q₈	—	13	1	no	—
358	C₂×D₄	—	13	1	no	—
359	C₂×D₄	—	13	1	no	—
360	C₂×D₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	1	no	—
365	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
366	M₁₆	—	52	1	no	—
367	M₁₆	—	52	1	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	13	1	no	—
371	C₂×C₈	—	13	1	no	—
372	C₂×C₈	—	26	1	no	—
373	C₂×C₈	—	26	1	no	—
374	C₂×C₈	—	26	1	no	—
375	C₂×C₈	—	26	1	no	—
376	C₂×C₈	—	26	1	no	—
377	C₂×C₈	—	26	1	no	—
378	C₂×C₈	—	52	1	no	—
379	C₂×C₈	C₂²×#261	1	1	yes	characteristic
380	C₂×C₈	C₂²×#261	1	1	yes	characteristic
381	C₂×C₈	C₂²×#261	1	1	yes	characteristic
382	C₂×C₈	C₂²×#261	1	1	yes	characteristic
383	C₄⋊C₄	—	13	1	no	—
384	C₄⋊C₄	—	13	1	no	—
385	C₄⋊C₄	—	13	1	no	—
386	C₄⋊C₄	—	13	1	no	—
387	C₄⋊C₄	—	13	1	no	—
388	C₄⋊C₄	—	13	1	no	—
389	C₄⋊C₄	—	13	1	no	—
390	C₄⋊C₄	—	13	1	no	—
391	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
392	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
393	C₂²⋊C₄	—	13	1	no	—
394	C₂²⋊C₄	—	13	1	no	—
395	C₂²⋊C₄	—	13	1	no	—
396	C₂²⋊C₄	—	13	1	no	—
397	C₂²⋊C₄	—	13	1	no	—
398	C₂²⋊C₄	—	13	1	no	—
399	C₂²⋊C₄	—	13	1	no	—
400	C₂²⋊C₄	—	13	1	no	—
401	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
402	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	C₂²×#261	1	1	yes	characteristic
408	C₄²	C₂²×#261	1	1	yes	characteristic
409	C₁₆	—	26	1	no	—
410	C₁₆	—	26	1	no	—
411	C₁₆	—	26	1	no	—
412	C₁₆	—	26	1	no	—
413	C₁₆	—	26	1	no	—
414	C₁₆	—	26	1	no	—
415	C₁₆	—	26	1	no	—
416	C₁₆	—	26	1	no	—
417	C₁₃	#33509	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	13	1	no	—
419	C₂³	—	13	1	no	—
420	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
421	Q₈	—	52	1	no	—
422	D₄	—	52	1	no	—
423	D₄	—	52	1	no	—
424	D₄	—	52	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	13	1	no	—
428	C₂×C₄	—	13	1	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	26	1	no	—
434	C₂×C₄	—	26	1	no	—
435	C₂×C₄	—	26	1	no	—
436	C₂×C₄	—	26	1	no	—
437	C₂×C₄	—	52	1	no	—
438	C₂×C₄	—	52	1	no	—
439	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
440	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
441	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
442	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
443	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
444	C₂×C₄	C₂³×#261	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	13	1	no	—
450	C₈	—	13	1	no	—
451	C₈	—	26	1	no	—
452	C₈	—	26	1	no	—
453	C₈	—	26	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	26	1	no	—
458	C₂²	—	26	1	no	—
459	C₂²	—	26	1	no	—
460	C₂²	—	26	1	no	—
461	C₂²	—	26	1	no	—
462	C₂²	—	26	1	no	—
463	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	26	1	no	—
470	C₄	—	26	1	no	—
471	C₄	—	26	1	no	—
472	C₄	—	26	1	no	—
473	C₄	—	26	1	no	—
474	C₄	—	26	1	no	—
475	C₄	#11719629	1	1	yes	characteristic
476	C₄	#11719631	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	52	1	no	—
479	C₂	—	52	1	no	—
480	C₂	#13131753	1	1	yes	characteristic
481	C₂	#13131804	1	1	yes	characteristic
482	C₂	#13131804	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#433	C₄
prime radical	#88138	C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#433	#261
hypocenter	C₁₃	#33509
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
1. #13131253	C₂	semidirect
2. #13131252	C₂	semidirect
3. #13131222	C₂	semidirect
4. #13131221	C₂	semidirect
5. #13131219	C₂	semidirect
6. #13131218	C₂	semidirect
7. #13131218	C₂	semidirect
8. #13131217	C₂	semidirect
9. #13131204	C₂	semidirect
10. #13131201	C₂	semidirect
11. #13131200	C₂	semidirect
12. #13131172	C₂	semidirect
13. #13131171	C₂	semidirect
14. #13131169	C₂	semidirect
417. C₁₃	#33509	semidirect

Maximal subgroups

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

subgroup	index
#13131253	2
#13131252	2
#13131222	2
#13131221	2
#13131219	2
#13131218	2
#13131217	2
#13131204	2
#13131201	2
#13131200	2
#13131172	2
#13131171	2
#13131169	2
#13123809	2
#33509	13