Subgroups — #15875228

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123771	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123480	C₂	1	1	yes	maximal, characteristic
3	#13115781	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115585	C₂	1	2	yes	maximal, complemented
6	#13115542	C₂	1	2	yes	maximal
7	#13115486	C₂	1	2	yes	maximal
8	#13115437	C₂	1	2	yes	maximal, complemented
9	#13114856	C₂	1	1	yes	maximal, characteristic
10	#13114701	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₁₃×#479	C₄	1	2	yes	complemented
15	C₁₃×#478	C₄	1	2	yes	complemented
16	C₁₃×#477	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#476	C₄	1	1	yes	characteristic, complemented
18	C₁₃×#475	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#474	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#427	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₁₃×#416	C₂²	1	2	yes	—
23	C₂×#88077	C₂²	1	2	yes	—
24	#11718895	C₂²	1	1	yes	characteristic
25	#11718895	C₂²	1	1	yes	characteristic
26	C₂×#88059	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
28	#11718685	—	2	1	no	—
29	#11718685	—	2	1	no	—
30	Q₈×#1055	—	2	1	no	—
31	Q₈×#1055	—	2	1	no	—
32	#11718661	—	2	1	no	—
33	#11718661	—	2	1	no	—
34	#11718660	C₂²	1	1	yes	characteristic
35	#11718660	C₂²	1	2	yes	—
36	#11718660	C₂²	1	1	yes	characteristic
37	#11718658	C₂²	1	2	yes	—
38	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	#11718586	—	2	1	no	—
40	#11718586	—	2	1	no	—
41	#11718585	C₂²	1	1	yes	characteristic
42	C₄×#6099	C₂²	1	1	yes	characteristic
43	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
44	#11718144	C₂²	1	2	yes	—
45	#11718142	C₂²	1	2	yes	—
46	#11718124	C₂²	1	2	yes	—
47	#11718124	C₂²	1	2	yes	—
48	#11718124	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#125	C₂×C₄	1	2	yes	—
54	C₁₃×C₂²⋊Q₈	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	—	2	1	no	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#117	—	2	1	no	—
65	C₁₃×#117	C₂³	1	2	yes	—
66	C₁₃×#117	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊Dic₁₃	—	2	1	no	—
70	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
71	C₂×#6099	C₂³	1	1	yes	characteristic
72	C₂×#6099	C₂³	1	2	yes	—
73	C₂×#6099	C₂³	1	1	yes	characteristic
74	C₂²×#1055	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#107	C₂×C₄	1	2	yes	—
78	C₁₃×#106	C₂×C₄	1	2	yes	—
79	C₁₃×#106	C₂×C₄	1	2	yes	—
80	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
83	C₁₃×#103	C₂×C₄	1	2	yes	—
84	C₁₃×#103	C₂×C₄	1	2	yes	—
85	C₁₃×#102	C₂×C₄	1	2	yes	—
86	C₁₃×#102	C₂×C₄	1	2	yes	—
87	#88077	—	4	2	no	—
88	#88071	—	2	1	no	—
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	C₂²⋊#1055	—	2	1	no	—
92	C₂²⋊#1055	—	2	1	no	—
93	#88059	—	4	2	no	—
94	C₈×Dic₁₃	—	4	2	no	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	—	2	1	no	—
99	C₄⋊#1055	—	2	1	no	—
100	C₄⋊#1055	—	2	1	no	—
101	C₄⋊#1055	—	2	2	no	—
102	C₄⋊#1055	—	2	2	no	—
103	#88043	—	2	1	no	—
104	#88043	—	2	2	no	—
105	C₄×#1055	—	2	1	no	—
106	C₄×#1055	—	2	2	no	—
107	C₄×#1055	D₄	1	1	yes	characteristic
108	C₄×#1055	D₄	1	1	yes	characteristic
109	C₄×#1055	D₄	1	1	yes	characteristic
110	C₄×#1055	D₄	1	1	yes	characteristic
111	#22130	—	13	1	no	maximal, Sylow
112	C₁₃×#41	—	2	1	no	—
113	C₁₃×#41	—	2	1	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂²×Dic₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄⋊Dic₁₃	—	2	4	no	—
155	C₄×Dic₁₃	—	2	2	no	—
156	C₄×Dic₁₃	—	2	2	no	—
157	#6099	—	2	2	no	—
158	#6099	—	2	1	no	—
159	#6099	—	2	1	no	—
160	#6099	—	2	1	no	—
161	#6099	—	2	2	no	—
162	#6099	—	2	1	no	—
163	C₂×#1055	—	2	1	no	—
164	C₂×#1055	—	2	1	no	—
165	C₂×#1055	—	2	1	no	—
166	C₂×#1055	—	2	1	no	—
167	C₂×#1055	—	2	1	no	—
168	C₂×#1055	—	2	1	no	—
169	C₂×#1055	—	2	2	no	—
170	C₂×#1055	C₂×D₄	1	1	yes	characteristic
171	C₂×#1055	C₂×D₄	1	1	yes	characteristic
172	C₂×#1055	C₂×D₄	1	1	yes	characteristic
173	C₂×#1055	C₂×D₄	1	1	yes	characteristic
174	#3076	D₁₃	1	1	yes	characteristic
175	#2960	—	13	1	no	—
176	#2922	—	13	1	no	—
177	#1986	—	13	1	no	—
178	#1950	—	13	1	no	—
179	#1945	—	13	2	no	—
180	#1937	—	13	2	no	—
181	#1929	—	13	2	no	—
182	#1922	—	13	2	no	—
183	#1806	—	13	1	no	—
184	C₈×C₄⋊C₄	—	13	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	1	no	—
188	Q₈×C₁₃	—	2	1	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	2	1	no	—
192	D₄×C₁₃	—	2	1	no	—
193	D₄×C₁₃	—	4	1	no	—
194	D₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
216	C₂×Dic₁₃	—	2	4	no	—
217	C₂×Dic₁₃	—	4	2	no	—
218	C₂×Dic₁₃	—	4	2	no	—
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	—	2	2	no	—
221	#1055	—	2	1	no	—
222	#1055	—	2	1	no	—
223	#1055	—	2	1	no	—
224	#1055	—	2	1	no	—
225	#1055	—	4	1	no	—
226	#1055	—	4	1	no	—
227	#1055	—	4	2	no	—
228	#533	C₂×D₁₃	1	1	yes	characteristic
229	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
230	#479	Dic₁₃	1	2	yes	complemented
231	#478	Dic₁₃	1	2	yes	complemented
232	#477	Dic₁₃	1	1	yes	characteristic, complemented
233	#476	Dic₁₃	1	1	yes	characteristic, complemented
234	#475	Dic₁₃	1	1	yes	characteristic, complemented
235	#474	Dic₁₃	1	1	yes	characteristic, complemented
236	#446	—	26	1	no	—
237	#446	—	26	1	no	—
238	C₈×Q₈	—	26	1	no	—
239	C₈×Q₈	—	26	1	no	—
240	#433	—	26	1	no	—
241	#433	—	26	1	no	—
242	#431	—	26	1	no	—
243	#431	—	26	1	no	—
244	C₂×#108	—	13	2	no	—
245	#427	C₂×D₁₃	1	2	yes	—
246	#424	—	13	1	no	—
247	#424	—	13	1	no	—
248	#424	—	13	2	no	—
249	#423	—	13	1	no	—
250	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
251	C₂×#104	—	13	2	no	—
252	#416	C₂×D₁₃	1	2	yes	—
253	#408	—	13	1	no	—
254	#408	—	13	1	no	—
255	#405	—	13	2	no	—
256	C₄×M₁₆	—	13	1	no	—
257	C₂×C₄×C₈	—	13	1	no	—
258	C₂×C₄×C₈	—	13	2	no	—
259	C₄×C₄⋊C₄	—	13	1	no	—
260	#341	—	13	2	no	—
261	#339	—	13	2	no	—
262	#339	—	13	2	no	—
263	#339	—	13	2	no	—
264	#336	—	13	2	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	—	4	1	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₁₃	#541	1	1	yes	characteristic
272	C₂²×C₁₃	#542	1	1	yes	characteristic
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	#443	1	2	yes	—
282	C₄×C₁₃	#519	1	1	yes	characteristic
283	C₄×C₁₃	#520	1	1	yes	characteristic
284	C₄×C₁₃	#536	1	1	yes	characteristic
285	C₄×C₁₃	#537	1	1	yes	characteristic
286	Dic₁₃	—	4	4	no	—
287	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
288	C₂×M₁₆	—	13	1	no	—
289	C₂×M₁₆	—	13	1	no	—
290	C₂×M₁₆	—	13	2	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	13	1	no	—
293	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
294	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
296	#125	C₂×Dic₁₃	1	2	yes	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
302	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	C₂²×D₁₃	1	1	yes	characteristic
309	#117	C₂²×D₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	—	26	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	13	2	no	—
313	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
314	#108	—	52	2	no	—
315	#107	C₂×Dic₁₃	1	2	yes	—
316	#107	C₂×Dic₁₃	1	2	yes	—
317	#106	C₂×Dic₁₃	1	2	yes	—
318	#106	C₂×Dic₁₃	1	2	yes	—
319	C₄⋊C₈	—	26	1	no	—
320	C₄⋊C₈	—	26	1	no	—
321	C₄⋊C₈	—	26	1	no	—
322	C₄⋊C₈	—	26	1	no	—
323	C₄⋊C₈	—	26	2	no	—
324	C₄⋊C₈	—	26	2	no	—
325	C₄⋊C₈	—	26	1	no	—
326	C₄⋊C₈	—	26	1	no	—
327	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
328	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
329	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
330	#104	—	52	2	no	—
331	#103	C₂×Dic₁₃	1	2	yes	—
332	#103	C₂×Dic₁₃	1	2	yes	—
333	#102	C₂×Dic₁₃	1	2	yes	—
334	#102	C₂×Dic₁₃	1	2	yes	—
335	C₂²⋊C₈	—	26	1	no	—
336	C₂²⋊C₈	—	26	1	no	—
337	C₂²⋊C₈	—	26	1	no	—
338	C₂²⋊C₈	—	26	1	no	—
339	#97	—	26	2	no	—
340	#97	—	26	1	no	—
341	C₄×C₈	—	13	1	no	—
342	C₄×C₈	—	13	1	no	—
343	C₄×C₈	—	13	1	no	—
344	C₄×C₈	—	13	1	no	—
345	C₄×C₈	—	26	2	no	—
346	C₄×C₈	—	26	1	no	—
347	C₄×C₈	—	52	2	no	—
348	#95	—	26	1	no	—
349	C₂×C₁₃	—	2	1	no	—
350	C₂×C₁₃	—	2	1	no	—
351	C₂×C₁₃	—	8	1	no	—
352	C₂×C₁₃	#2323	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
354	C₂×C₁₃	#2955	1	1	yes	characteristic
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	26	2	no	—
368	C₂²×C₄	#6129	1	1	yes	characteristic
369	C₂²×C₄	#6129	1	1	yes	characteristic
370	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
371	M₁₆	—	26	1	no	—
372	M₁₆	—	26	1	no	—
373	M₁₆	—	26	2	no	—
374	M₁₆	—	26	2	no	—
375	M₁₆	—	26	1	no	—
376	M₁₆	—	26	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	26	1	no	—
384	C₂×C₈	—	26	1	no	—
385	C₂×C₈	—	26	1	no	—
386	C₂×C₈	—	26	1	no	—
387	C₂×C₈	—	26	1	no	—
388	C₂×C₈	—	26	1	no	—
389	C₂×C₈	—	26	2	no	—
390	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
391	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	26	4	no	—
399	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
400	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
401	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	26	2	no	—
412	C₄²	—	26	2	no	—
413	C₄²	D₄×D₁₃	1	1	yes	characteristic
414	C₄²	D₄×D₁₃	1	1	yes	characteristic
415	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
416	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
417	C₁₃	#22130	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	2	1	no	—
419	C₂³	C₂×#6129	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	26	4	no	—
440	C₂×C₄	—	52	2	no	—
441	C₂×C₄	—	52	2	no	—
442	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
443	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
445	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
447	C₂×C₄	#88254	1	1	yes	characteristic
448	C₂×C₄	#88254	1	1	yes	characteristic
449	C₂×C₄	#88256	1	1	yes	characteristic
450	C₂×C₄	#88257	1	1	yes	characteristic
451	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	26	1	no	—
455	C₈	—	26	1	no	—
456	C₈	—	26	1	no	—
457	C₈	—	26	1	no	—
458	C₈	—	52	1	no	—
459	C₈	—	52	1	no	—
460	C₈	—	52	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	#11719330	1	1	yes	characteristic
467	C₂²	#11719348	1	1	yes	characteristic
468	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	52	4	no	—
478	C₄	#11718857	1	2	yes	—
479	C₄	#11719333	1	1	yes	characteristic
480	C₄	#11719334	1	1	yes	characteristic
481	C₄	#11719517	1	1	yes	characteristic
482	C₄	#11719532	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	#13117520	1	1	yes	characteristic
487	C₂	C₂×#11718857	1	1	yes	characteristic
488	C₂	#13123739	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#3076	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3076	D₁₃
hypocenter	C₁₃	#22130
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #13123771	C₂	semidirect
3. #13115781	C₂	semidirect
4. #13115612	C₂	semidirect
5. #13115585	C₂	semidirect
8. #13115437	C₂	semidirect
10. #13114701	C₂	semidirect
14. C₁₃×#479	C₄	semidirect
15. C₁₃×#478	C₄	semidirect
16. C₁₃×#477	C₄	semidirect
17. C₁₃×#476	C₄	semidirect
18. C₁₃×#475	C₄	semidirect
19. C₁₃×#474	C₄	semidirect
230. #479	Dic₁₃	semidirect
231. #478	Dic₁₃	semidirect
232. #477	Dic₁₃	semidirect
233. #476	Dic₁₃	semidirect
234. #475	Dic₁₃	semidirect
235. #474	Dic₁₃	semidirect
417. C₁₃	#22130	semidirect

Maximal subgroups

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

subgroup	index
#13123771	2
#13123480	2
#13115781	2
#13115612	2
#13115585	2
#13115542	2
#13115486	2
#13115437	2
#13114856	2
#13114701	2
C₁₃×#3076	2
#22130	13