Subgroups — C₄×#11718821 #15869793

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718821	C₂	1	1	yes	maximal, characteristic
2	C₄×#88186	C₂	1	2	yes	maximal, complemented
3	C₄×#88155	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115747	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115619	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115495	C₂	1	2	yes	maximal, complemented
7	#13115347	C₂	1	2	yes	maximal, complemented
8	#13114901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88059	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88073	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂×#88186	C₂²	1	2	yes	—
15	C₂×#88155	C₂²	1	1	yes	characteristic
16	C₂×#88155	C₂²	1	1	yes	characteristic
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×D₈	—	2	1	no	—
19	C₄×C₁₃×D₈	—	2	1	no	—
20	C₄×C₁₃×D₈	—	2	1	no	—
21	C₄×C₁₃×D₈	—	2	1	no	—
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×#88073	C₂²	1	2	yes	—
26	C₂×#88073	C₂²	1	2	yes	—
27	#11718876	C₂²	1	2	yes	—
28	#11718821	C₄	1	8	yes	direct product factor
29	C₂×#88059	C₂²	1	1	yes	characteristic
30	C₂×#88059	C₂²	1	1	yes	characteristic
31	#11718762	C₂²	1	1	yes	characteristic
32	#11718762	C₂²	1	1	yes	characteristic
33	#11718679	—	2	2	no	—
34	C₄×#6105	—	2	2	no	—
35	#11718675	—	2	2	no	—
36	C₄×#6104	—	2	2	no	—
37	#11718627	C₂²	1	2	yes	—
38	#11718625	C₂²	1	2	yes	—
39	C₄×#6099	C₂²	1	1	yes	characteristic
40	C₄×#6099	C₂²	1	2	yes	—
41	#11718350	—	2	1	no	—
42	#11718350	—	2	1	no	—
43	C₄×#6094	—	2	1	no	—
44	C₄×C₈×D₁₃	—	2	1	no	—
45	#11718144	C₂²	1	2	yes	—
46	#11718122	C₂²	1	2	yes	—
47	#11718122	C₂²	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂×#6127	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×D₈	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	1	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×#6105	—	2	2	no	—
65	#88186	—	2	4	no	—
66	#88186	C₂×C₄	1	8	yes	complemented
67	C₂×#6104	—	2	2	no	—
68	C₄×C₂²⋊D₁₃	—	2	1	no	—
69	C₄×C₂²⋊D₁₃	—	2	1	no	—
70	#88180	C₂³	1	1	yes	characteristic
71	C₂×#6099	C₂³	1	2	yes	—
72	C₂×#6099	C₂³	1	2	yes	—
73	C₂×#6099	C₂³	1	1	yes	characteristic
74	C₂×#6099	C₂³	1	1	yes	characteristic
75	#88155	—	2	2	no	—
76	#88155	—	2	2	no	—
77	#88155	—	2	2	no	—
78	#88155	C₂×C₄	1	4	yes	complemented
79	C₂×#6094	—	2	1	no	—
80	C₂×#6094	—	2	1	no	—
81	C₂×C₈×D₁₃	—	2	1	no	—
82	C₂×C₈×D₁₃	—	2	1	no	—
83	C₄×D₅₂	D₄	1	1	yes	characteristic
84	C₄×D₅₂	D₄	1	1	yes	characteristic
85	#88126	—	2	1	no	—
86	C₄²×D₁₃	—	2	1	no	—
87	C₄×Dic₂₆	D₄	1	1	yes	characteristic
88	C₄×Dic₂₆	D₄	1	1	yes	characteristic
89	C₁₃×#107	—	2	1	no	—
90	C₁₃×#107	—	2	1	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
96	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
97	#88073	—	2	4	no	—
98	#88073	C₂×C₄	1	8	yes	complemented
99	#88072	—	2	2	no	—
100	#88072	—	2	2	no	—
101	#88059	—	2	2	no	—
102	#88059	C₂×C₄	1	4	yes	complemented
103	#88055	—	2	1	no	—
104	#88055	—	2	1	no	—
105	C₈×Dic₁₃	—	2	1	no	—
106	C₈×Dic₁₃	—	2	1	no	—
107	#88050	—	2	2	no	—
108	#88049	—	2	2	no	—
109	#88048	—	2	2	no	—
110	#88047	—	2	2	no	—
111	#88043	—	2	2	no	—
112	#88043	—	2	1	no	—
113	C₄×#1055	—	2	2	no	—
114	C₄×#1055	—	2	1	no	—
115	C₄×#472	—	13	1	no	maximal, Sylow
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	—	8	4	no	—
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	—	2	1	no	—
131	#6127	—	2	1	no	—
132	#6127	—	2	1	no	—
133	#6127	C₂²×C₄	1	2	yes	—
134	#6127	#41	1	2	yes	—
135	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	—	2	1	no	—
137	C₂×C₄×D₁₃	—	2	1	no	—
138	C₂×C₄×D₁₃	—	2	1	no	—
139	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
140	C₁₃×D₈	—	2	4	no	—
141	C₁₃×D₈	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	#41	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	2	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊Dic₁₃	—	2	1	no	—
159	#6105	—	2	8	no	—
160	#6104	—	2	8	no	—
161	#6103	—	2	1	no	—
162	#6103	—	2	1	no	—
163	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
165	#6101	—	2	1	no	—
166	#6101	—	2	1	no	—
167	C₄×Dic₁₃	—	2	1	no	—
168	C₄×Dic₁₃	—	2	1	no	—
169	C₄×Dic₁₃	—	2	1	no	—
170	#6099	—	2	1	no	—
171	#6099	—	2	1	no	—
172	#6099	—	2	2	no	—
173	#6099	—	2	2	no	—
174	#6099	—	2	2	no	—
175	#6099	C₂²×C₄	1	2	yes	—
176	#6099	C₂²×C₄	1	4	yes	—
177	#6099	#41	1	2	yes	—
178	C₂×#1055	—	2	1	no	—
179	C₂×#1055	—	2	1	no	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	#6094	—	2	4	no	—
183	#6094	—	2	4	no	—
184	C₈×D₁₃	—	2	4	no	—
185	C₈×D₁₃	—	2	4	no	—
186	C₂×#472	—	13	1	no	—
187	C₄×AGL(1,ℤ/8)	—	13	2	no	—
188	C₂×C₄×D₈	D₁₃	1	1	yes	characteristic, complemented
189	C₄×#131	—	13	1	no	—
190	#1978	—	13	1	no	—
191	#1952	—	13	1	no	—
192	#1931	—	13	2	no	—
193	#1907	—	13	2	no	—
194	#1816	—	13	1	no	—
195	C₄×#108	—	13	1	no	—
196	C₄×#100	—	13	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	8	2	no	—
201	C₂³×C₁₃	—	8	2	no	—
202	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂²×D₁₃	—	2	1	no	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	2	4	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	8	4	no	—
213	C₂×C₄×C₁₃	—	8	2	no	—
214	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂²⋊D₁₃	—	2	2	no	—
225	C₂²⋊D₁₃	—	2	2	no	—
226	C₂×Dic₁₃	—	2	1	no	—
227	C₂×Dic₁₃	—	2	1	no	—
228	C₂×Dic₁₃	—	2	1	no	—
229	D₅₂	—	2	1	no	—
230	D₅₂	C₄×D₄	1	2	yes	—
231	C₄×D₁₃	—	2	2	no	—
232	C₄×D₁₃	—	2	2	no	—
233	C₄×D₁₃	—	4	2	no	—
234	C₄×D₁₃	—	4	2	no	—
235	Dic₂₆	—	2	1	no	—
236	Dic₂₆	C₄×D₄	1	2	yes	—
237	C₈×C₁₃	—	2	1	no	—
238	C₈×C₁₃	—	2	1	no	—
239	C₈×C₁₃	C₄×D₄	1	2	yes	—
240	C₈×C₁₃	C₄×D₄	1	2	yes	—
241	#1055	—	2	2	no	—
242	#1055	—	2	4	no	—
243	#1055	—	2	2	no	—
244	#1055	—	4	2	no	—
245	C₂×AGL(1,ℤ/8)	—	13	2	no	—
246	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
247	C₂×#131	—	13	1	no	—
248	C₂×#131	—	13	1	no	—
249	C₄×#41	—	13	1	no	—
250	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
251	#472	—	13	8	no	—
252	#442	—	26	2	no	—
253	#440	—	26	2	no	—
254	C₄×SD₁₆	—	26	2	no	—
255	C₄×D₈	—	2	1	no	—
256	C₄×D₈	—	2	1	no	—
257	C₄×D₈	—	2	1	no	—
258	C₄×D₈	—	2	1	no	—
259	C₄×D₈	—	26	2	no	—
260	C₂×#108	—	13	1	no	—
261	C₂×#108	—	13	1	no	—
262	#428	—	13	2	no	—
263	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
264	#418	—	13	2	no	—
265	#417	—	13	2	no	—
266	C₂×#102	C₂×D₁₃	1	2	yes	—
267	C₂×#100	—	13	2	no	—
268	C₂×#100	—	13	2	no	—
269	#405	—	13	1	no	—
270	#405	—	13	1	no	—
271	#405	—	26	1	no	—
272	#405	—	26	1	no	—
273	C₄×M₁₆	—	13	1	no	—
274	C₄×M₁₆	—	13	2	no	—
275	C₄×M₁₆	—	26	1	no	—
276	C₂×C₄×C₈	—	26	1	no	—
277	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
278	#343	—	13	2	no	—
279	#343	—	13	2	no	—
280	#341	—	13	2	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	8	4	no	—
285	C₂²×C₁₃	—	8	4	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
290	C₂²×C₁₃	#529	1	1	yes	characteristic
291	C₂×D₁₃	—	2	2	no	—
292	C₂×D₁₃	—	4	1	no	—
293	C₂×D₁₃	—	4	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	8	2	no	—
298	C₄×C₁₃	#472	1	2	yes	complemented
299	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
300	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
301	C₄×C₁₃	#525	1	1	yes	characteristic
302	C₄×C₁₃	#532	1	1	yes	characteristic
303	Dic₁₃	—	2	2	no	—
304	Dic₁₃	—	4	1	no	—
305	Dic₁₃	—	4	1	no	—
306	C₂×#41	—	13	1	no	—
307	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
308	C₂³×C₄	—	2	2	no	—
309	AGL(1,ℤ/8)	—	13	8	no	—
310	AGL(1,ℤ/8)	—	26	4	no	—
311	C₂×SD₁₆	—	26	2	no	—
312	C₂×D₈	—	2	2	no	—
313	C₂×D₈	—	2	1	no	—
314	C₂×D₈	—	2	1	no	—
315	C₂×D₈	—	26	2	no	—
316	C₂×D₈	C₄×D₁₃	1	4	yes	complemented
317	#131	—	13	4	no	—
318	#131	—	26	2	no	—
319	#131	—	26	2	no	—
320	#131	—	26	2	no	—
321	C₂×M₁₆	—	13	1	no	—
322	C₂×M₁₆	—	13	1	no	—
323	C₂×M₁₆	—	13	2	no	—
324	C₂×M₁₆	—	13	2	no	—
325	C₂×M₁₆	—	26	1	no	—
326	C₂×M₁₆	—	26	1	no	—
327	C₂²×C₈	—	26	1	no	—
328	C₂²×C₈	—	26	1	no	—
329	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
331	C₄×Q₈	—	13	1	no	—
332	C₄×Q₈	—	13	1	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	13	1	no	—
338	C₄×D₄	—	13	1	no	—
339	C₄×D₄	—	26	1	no	—
340	C₄×D₄	—	26	1	no	—
341	#117	—	13	1	no	—
342	#117	—	26	1	no	—
343	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₄²	—	26	1	no	—
346	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
347	#108	—	13	4	no	—
348	#108	—	26	2	no	—
349	#107	—	2	1	no	—
350	#107	—	2	1	no	—
351	#107	—	26	2	no	—
352	#106	—	26	2	no	—
353	#103	—	26	2	no	—
354	#102	—	2	2	no	—
355	#102	—	2	2	no	—
356	#102	—	26	2	no	—
357	#102	—	26	2	no	—
358	#102	—	26	2	no	—
359	#100	—	13	8	no	—
360	#100	—	26	4	no	—
361	#97	—	26	1	no	—
362	#97	—	26	1	no	—
363	#97	—	26	2	no	—
364	#97	—	26	1	no	—
365	C₄×C₈	—	26	1	no	—
366	C₄×C₈	—	26	1	no	—
367	C₄×C₈	—	26	2	no	—
368	C₄×C₈	—	26	1	no	—
369	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
371	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
372	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
373	C₂×C₁₃	—	2	1	no	—
374	C₂×C₁₃	—	2	1	no	—
375	C₂×C₁₃	—	8	4	no	—
376	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
378	C₂×C₁₃	#3067	1	1	yes	characteristic
379	D₁₃	—	4	2	no	—
380	C₂⁴	—	2	2	no	—
381	#41	—	13	2	no	—
382	#41	—	13	2	no	—
383	#41	—	26	1	no	—
384	#41	—	26	1	no	—
385	C₂×Q₈	—	13	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	13	1	no	—
392	C₂×D₄	—	26	1	no	—
393	C₂×D₄	C₂×C₄×D₁₃	1	4	yes	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	8	4	no	—
398	C₂²×C₄	—	26	1	no	—
399	C₂²×C₄	—	26	1	no	—
400	C₂²×C₄	—	26	1	no	—
401	C₂²×C₄	#6129	1	1	yes	characteristic
402	C₂²×C₄	#6129	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
404	SD₁₆	—	26	8	no	—
405	D₈	—	2	4	no	—
406	D₈	—	2	4	no	—
407	D₈	—	26	8	no	—
408	M₁₆	—	13	2	no	—
409	M₁₆	—	13	4	no	—
410	M₁₆	—	13	2	no	—
411	M₁₆	—	26	4	no	—
412	M₁₆	—	26	1	no	—
413	M₁₆	—	26	1	no	—
414	M₁₆	—	26	2	no	—
415	M₁₆	—	26	4	no	—
416	M₁₆	—	26	2	no	—
417	M₁₆	—	26	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	26	4	no	—
421	C₂×C₈	—	26	2	no	—
422	C₂×C₈	—	26	1	no	—
423	C₂×C₈	—	26	1	no	—
424	C₂×C₈	—	26	4	no	—
425	C₂×C₈	—	26	2	no	—
426	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
427	C₂×C₈	#6127	1	2	yes	—
428	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	13	1	no	—
435	C₄⋊C₄	—	13	1	no	—
436	C₄⋊C₄	—	26	1	no	—
437	C₄⋊C₄	—	26	1	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	26	1	no	—
441	C₂²⋊C₄	—	26	1	no	—
442	C₂²⋊C₄	—	26	1	no	—
443	C₄²	—	26	1	no	—
444	C₄²	—	26	1	no	—
445	C₄²	—	26	1	no	—
446	C₄²	D₄×D₁₃	1	1	yes	characteristic
447	C₄²	D₄×D₁₃	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
450	C₁₃	C₄×#472	1	1	yes	characteristic, complemented, Sylow
451	C₂³	—	2	4	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	26	1	no	—
457	C₂³	C₂×#6129	1	1	yes	characteristic
458	Q₈	—	13	2	no	—
459	Q₈	—	26	1	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	13	2	no	—
465	D₄	—	26	2	no	—
466	D₄	—	26	2	no	—
467	D₄	—	26	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	26	1	no	—
475	C₂×C₄	—	26	2	no	—
476	C₂×C₄	—	26	2	no	—
477	C₂×C₄	—	26	1	no	—
478	C₂×C₄	—	26	1	no	—
479	C₂×C₄	—	52	2	no	—
480	C₂×C₄	—	52	2	no	—
481	C₂×C₄	#88192	1	1	yes	characteristic
482	C₂×C₄	#88192	1	1	yes	characteristic
483	C₂×C₄	#88192	1	1	yes	characteristic
484	C₂×C₄	#88192	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂×#6127	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
488	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
489	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	—	26	2	no	—
494	C₈	—	26	4	no	—
495	C₈	—	26	2	no	—
496	C₈	—	52	2	no	—
497	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
498	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	4	no	—
503	C₂²	—	8	4	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	26	2	no	—
507	C₂²	—	52	1	no	—
508	C₂²	—	52	1	no	—
509	C₂²	C₄×#6129	1	1	yes	characteristic
510	C₂²	#11719262	1	1	yes	characteristic
511	C₂²	C₂×#88192	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	26	2	no	—
517	C₄	—	52	1	no	—
518	C₄	—	52	1	no	—
519	C₄	#11718821	1	2	yes	direct product factor
520	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
521	C₄	#11719253	1	1	yes	characteristic
522	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
523	C₄	#11719533	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	8	4	no	—
527	C₂	—	52	2	no	—
528	C₂	C₄×#88192	1	1	yes	characteristic
529	C₂	C₂×#11718821	1	1	yes	characteristic
530	C₂	#13124552	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88192
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	C₂×#11718821	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×D₈	D₁₃
hypocenter	C₁₃	C₄×#472
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×#88186	C₂	semidirect
3. C₄×#88155	C₂	semidirect
4. #13115747	C₂	semidirect
5. #13115619	C₂	semidirect
6. #13115495	C₂	semidirect
7. #13115347	C₂	semidirect
8. #13114901	C₂	semidirect
9. C₄×#88059	C₂	semidirect
10. C₄×#88073	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
28. #11718821	C₄	direct (N × H)
54. C₂×C₁₃×D₈	C₂×C₄	semidirect
66. #88186	C₂×C₄	semidirect
78. #88155	C₂×C₄	semidirect
98. #88073	C₂×C₄	semidirect
102. #88059	C₂×C₄	semidirect
188. C₂×C₄×D₈	D₁₃	semidirect
298. C₄×C₁₃	#472	semidirect
316. C₂×D₈	C₄×D₁₃	semidirect
450. C₁₃	C₄×#472	semidirect
519. C₄	#11718821	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11718821	2
C₄×#88186	2
C₄×#88155	2
#13115747	2
#13115619	2
#13115495	2
#13115347	2
#13114901	2
C₄×#88059	2
C₄×#88073	2
C₂×C₄×C₁₃×D₈	2
C₄×#472	13

Subgroups — C4×#11718821 #15869793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718821 #15869793