Subgroups — C₄×Q₈×D₅₂ #16022788

Order 3328.

3148 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×D₁₃	C₂	1	2	yes	maximal, complemented
3	#13117894	C₂	1	3	yes	maximal, complemented
4	#13117843	C₂	1	6	yes	maximal, complemented
5	Q₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₄×D₅₂	C₂	1	3	yes	maximal
7	Q₈×#6103	C₂	1	2	yes	maximal, complemented
8	C₄×#88123	C₂	1	3	yes	maximal, complemented
9	C₄×#88151	C₂	1	6	yes	maximal, complemented
10	C₄²×D₅₂	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×D₁₃	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	—
17	Q₈×D₅₂	C₄	1	16	yes	direct product factor
18	C₄×Q₈×D₁₃	—	2	16	no	—
19	C₂×#88151	C₂²	1	6	yes	—
20	C₂×C₄⋊C₄×D₁₃	C₂²	1	6	yes	—
21	C₂×#88141	C₂²	1	6	yes	—
22	C₂×C₄×D₅₂	C₂²	1	3	yes	—
23	C₂×C₄×D₅₂	C₂²	1	3	yes	—
24	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
25	C₂×C₄²×D₁₃	C₂²	1	6	yes	—
26	C₂×#88123	C₂²	1	3	yes	—
27	C₂×C₄×Dic₂₆	C₂²	1	6	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
31	C₄³×C₁₃	C₂²	1	3	yes	—
32	#11718648	C₂²	1	6	yes	—
33	#11718646	C₂²	1	6	yes	—
34	#11718635	C₂²	1	6	yes	—
35	C₄×#6103	C₂²	1	6	yes	—
36	C₄×#6103	C₂²	1	6	yes	—
37	C₄×#6103	C₂²	1	6	yes	—
38	#11718596	C₂²	1	3	yes	—
39	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
40	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
41	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
42	C₄×C₄⋊Dic₁₃	C₂²	1	6	yes	—
43	#11718590	C₂²	1	6	yes	—
44	#11718589	C₂²	1	6	yes	—
45	#11718589	C₂²	1	6	yes	—
46	#11718329	C₂²	1	12	yes	—
47	#11718314	C₂²	1	12	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×Q₈×D₁₃	—	2	8	no	—
50	C₂×Q₈×D₁₃	—	2	8	no	—
51	C₂×Q₈×D₁₃	C₂×C₄	1	16	yes	complemented
52	C₂²×D₅₂	C₂³	1	1	yes	characteristic
53	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
54	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
55	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
56	C₂²×Dic₂₆	C₂³	1	6	yes	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
59	C₄×Q₈×C₁₃	D₄	1	8	yes	complemented
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
65	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	Q₈×Dic₁₃	—	2	8	no	—
71	C₂×#6103	C₂³	1	6	yes	—
72	C₂×#6103	C₂³	1	6	yes	—
73	C₂×#6103	C₂³	1	2	yes	—
74	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
75	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
76	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
77	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
78	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
79	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂×#6101	C₂³	1	12	yes	—
81	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
82	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
83	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
84	#88151	C₂×C₄	1	48	yes	complemented
85	C₄⋊C₄×D₁₃	—	2	24	no	—
86	#88141	—	2	24	no	—
87	C₄×D₅₂	—	2	12	no	—
88	C₄×D₅₂	C₂×C₄	1	24	yes	—
89	C₄×D₅₂	Q₈	1	8	yes	direct product factor
90	C₄²×D₁₃	—	2	24	no	—
91	#88123	C₂×C₄	1	24	yes	complemented
92	C₄×Dic₂₆	—	2	24	no	—
93	C₁₃×#95	C₂³	1	6	yes	—
94	#88071	C₂³	1	6	yes	—
95	#88071	C₂³	1	6	yes	—
96	#88071	C₂³	1	12	yes	—
97	#88071	C₂³	1	6	yes	—
98	C₄×D₄×Q₈	—	13	1	no	maximal, Sylow
99	C₂³×D₁₃	C₂⁴	1	2	yes	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₁₃	#41	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
111	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
112	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
113	Q₈×D₁₃	—	2	64	no	—
114	C₂×D₅₂	C₂²×C₄	1	4	yes	—
115	C₂×D₅₂	C₂×Q₈	1	4	yes	—
116	C₂×D₅₂	#41	1	4	yes	—
117	C₂×C₄×D₁₃	—	2	4	no	—
118	C₂×C₄×D₁₃	—	2	12	no	—
119	C₂×C₄×D₁₃	—	2	12	no	—
120	C₂×C₄×D₁₃	—	2	4	no	—
121	C₂×C₄×D₁₃	—	2	12	no	—
122	C₂×C₄×D₁₃	—	2	12	no	—
123	C₂×C₄×D₁₃	—	4	6	no	—
124	C₂×C₄×D₁₃	C₂²×C₄	1	24	yes	—
125	C₂×C₄×D₁₃	C₂×Q₈	1	8	yes	complemented
126	C₂×Dic₂₆	—	2	12	no	—
127	C₂×Dic₂₆	—	2	12	no	—
128	C₂×Dic₂₆	C₂²×C₄	1	24	yes	—
129	C₁₃×C₄⋊C₄	—	2	6	no	—
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
131	C₁₃×C₄⋊C₄	C₂×D₄	1	12	yes	—
132	C₄²×C₁₃	—	2	6	no	—
133	C₄²×C₁₃	—	2	6	no	—
134	C₄²×C₁₃	—	2	6	no	—
135	C₄²×C₁₃	—	4	3	no	—
136	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
137	C₄²×C₁₃	C₂×D₄	1	12	yes	—
138	C₄²×C₁₃	C₂×Q₈	1	4	yes	complemented
139	#6103	—	2	12	no	—
140	#6103	C₂²×C₄	1	24	yes	—
141	#6103	C₂×Q₈	1	8	yes	complemented
142	C₄⋊Dic₁₃	—	2	12	no	—
143	C₄⋊Dic₁₃	—	2	6	no	—
144	C₄⋊Dic₁₃	—	4	6	no	—
145	C₄⋊Dic₁₃	C₂²×C₄	1	12	yes	—
146	C₄⋊Dic₁₃	C₂²×C₄	1	24	yes	—
147	C₄⋊Dic₁₃	C₂×Q₈	1	4	yes	complemented
148	#6101	—	2	24	no	—
149	C₄×Dic₁₃	—	2	12	no	—
150	C₄×Dic₁₃	—	2	12	no	—
151	C₄×Dic₁₃	—	2	12	no	—
152	C₂×D₄×Q₈	—	13	1	no	—
153	C₂²×C₄×Q₈	—	13	2	no	—
154	#2365	—	13	3	no	—
155	#2360	—	13	6	no	—
156	Q₈×C₄⋊C₄	—	13	1	no	—
157	D₄×C₄⋊C₄	—	13	3	no	—
158	Q₈×C₂²⋊C₄	—	13	2	no	—
159	C₄×C₄⋊Q₈	—	13	3	no	—
160	C₄×C₂²⋊Q₈	—	13	6	no	—
161	C₄²×Q₈	D₁₃	1	1	yes	characteristic, complemented
162	C₄²×D₄	—	13	3	no	—
163	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
164	C₂²×D₁₃	—	2	2	no	—
165	C₂²×D₁₃	—	2	2	no	—
166	C₂²×D₁₃	—	2	2	no	—
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
169	C₂²×D₁₃	C₂²×Q₈	1	4	yes	—
170	C₂²×D₁₃	C₂×#41	1	4	yes	—
171	Q₈×C₁₃	C₄×D₄	1	16	yes	complemented
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	3	no	—
174	C₂×C₄×C₁₃	—	2	3	no	—
175	C₂×C₄×C₁₃	—	2	3	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	3	no	—
178	C₂×C₄×C₁₃	—	2	3	no	—
179	C₂×C₄×C₁₃	—	2	3	no	—
180	C₂×C₄×C₁₃	—	2	3	no	—
181	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
182	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
183	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
191	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	—	2	6	no	—
195	C₂×Dic₁₃	—	2	6	no	—
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	6	no	—
198	C₂×Dic₁₃	—	2	6	no	—
199	C₂×Dic₁₃	—	2	6	no	—
200	C₂×Dic₁₃	C₂³×C₄	1	12	yes	—
201	C₂×Dic₁₃	C₂²×Q₈	1	4	yes	—
202	D₅₂	C₄×Q₈	1	16	yes	direct product factor
203	C₄×D₁₃	—	2	48	no	—
204	C₄×D₁₃	—	2	16	no	—
205	C₄×D₁₃	—	4	24	no	—
206	Dic₂₆	—	2	48	no	—
207	C₂³×Q₈	—	13	2	no	—
208	D₄×Q₈	—	13	16	no	—
209	C₂×C₄⋊Q₈	—	13	3	no	—
210	C₂×C₂²⋊Q₈	—	13	6	no	—
211	C₂×C₄×Q₈	—	13	2	no	—
212	C₂×C₄×Q₈	—	13	6	no	—
213	C₂×C₄×Q₈	—	13	6	no	—
214	C₂×C₄×Q₈	—	26	16	no	—
215	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
218	C₂×C₄×D₄	—	13	3	no	—
219	C₂×C₄×D₄	—	13	1	no	—
220	C₂×C₄×D₄	—	13	3	no	—
221	C₂²×C₄⋊C₄	—	13	6	no	—
222	C₂²×C₄²	—	13	6	no	—
223	#391	—	13	6	no	—
224	#391	—	13	6	no	—
225	#389	—	13	6	no	—
226	#389	—	13	6	no	—
227	#389	—	13	6	no	—
228	#387	—	13	12	no	—
229	#385	—	13	12	no	—
230	#384	—	13	3	no	—
231	#380	—	13	6	no	—
232	C₄×C₄⋊C₄	—	13	3	no	—
233	C₄×C₄⋊C₄	—	13	6	no	—
234	C₄×C₄⋊C₄	—	13	3	no	—
235	C₄×C₄⋊C₄	—	13	3	no	—
236	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
237	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
238	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
239	C₄×C₂²⋊C₄	—	13	6	no	—
240	C₄×C₂²⋊C₄	—	13	6	no	—
241	C₄×C₂²⋊C₄	—	13	6	no	—
242	C₄³	C₂×D₁₃	1	3	yes	—
243	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
244	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
245	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
246	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
247	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
249	C₂²×C₁₃	#585	1	1	yes	characteristic
250	C₂×D₁₃	—	2	4	no	—
251	C₂×D₁₃	—	2	4	no	—
252	C₂×D₁₃	—	2	4	no	—
253	C₂×D₁₃	—	2	4	no	—
254	C₂×D₁₃	—	2	4	no	—
255	C₂×D₁₃	—	2	4	no	—
256	C₂×D₁₃	C₂×C₄×Q₈	1	8	yes	complemented
257	C₄×C₁₃	—	2	6	no	—
258	C₄×C₁₃	—	2	6	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	3	no	—
261	C₄×C₁₃	C₂×C₄×D₄	1	12	yes	—
262	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	complemented
263	C₄×C₁₃	D₄×Q₈	1	4	yes	complemented
264	Dic₁₃	—	2	12	no	—
265	Dic₁₃	—	2	4	no	—
266	Dic₁₃	—	4	6	no	—
267	C₂²×Q₈	—	13	16	no	—
268	C₂²×Q₈	—	13	6	no	—
269	C₂²×Q₈	—	26	8	no	—
270	C₂²×Q₈	—	26	8	no	—
271	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
272	C₂²×D₄	—	13	1	no	—
273	C₂³×C₄	—	13	6	no	—
274	C₂³×C₄	—	13	2	no	—
275	C₂³×C₄	—	13	6	no	—
276	C₄⋊Q₈	—	13	24	no	—
277	C₂²⋊Q₈	—	13	48	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	26	8	no	—
280	C₄×Q₈	—	26	24	no	—
281	C₄×Q₈	—	26	24	no	—
282	C₄×Q₈	C₄×D₁₃	1	8	yes	complemented
283	C₄×Q₈	D₅₂	1	8	yes	direct product factor
284	C₄×D₄	—	13	24	no	—
285	C₄×D₄	—	13	8	no	—
286	C₄×D₄	—	26	12	no	—
287	C₂×C₄⋊C₄	—	13	3	no	—
288	C₂×C₄⋊C₄	—	13	1	no	—
289	C₂×C₄⋊C₄	—	13	6	no	—
290	C₂×C₄⋊C₄	—	13	12	no	—
291	C₂×C₄⋊C₄	—	13	6	no	—
292	C₂×C₄⋊C₄	—	13	3	no	—
293	C₂×C₄⋊C₄	—	13	6	no	—
294	C₂×C₄⋊C₄	—	26	24	no	—
295	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
296	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
297	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
298	C₂×C₂²⋊C₄	—	13	6	no	—
299	C₂×C₂²⋊C₄	—	13	2	no	—
300	C₂×C₂²⋊C₄	—	13	6	no	—
301	C₂×C₄²	—	13	6	no	—
302	C₂×C₄²	—	13	6	no	—
303	C₂×C₄²	—	13	6	no	—
304	C₂×C₄²	—	26	24	no	—
305	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
306	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
307	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
308	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
309	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
310	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
311	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
312	#95	—	13	6	no	—
313	#95	—	13	6	no	—
314	#95	—	13	6	no	—
315	#95	—	13	12	no	—
316	#95	C₂²×D₁₃	1	6	yes	—
317	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
318	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
319	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
321	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
322	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
323	C₂×C₁₃	#3482	1	1	yes	characteristic
324	D₁₃	—	2	8	no	—
325	C₂⁴	—	13	2	no	—
326	C₂×Q₈	—	13	24	no	—
327	C₂×Q₈	—	26	64	no	—
328	C₂×Q₈	—	26	12	no	—
329	C₂×Q₈	—	26	12	no	—
330	C₂×Q₈	C₂×C₄×D₁₃	1	4	yes	—
331	C₂×Q₈	C₂×D₅₂	1	4	yes	—
332	C₂×Q₈	#6127	1	4	yes	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	4	no	—
335	C₂×D₄	—	13	4	no	—
336	C₂²×C₄	—	13	2	no	—
337	C₂²×C₄	—	13	6	no	—
338	C₂²×C₄	—	13	24	no	—
339	C₂²×C₄	—	13	8	no	—
340	C₂²×C₄	—	13	6	no	—
341	C₂²×C₄	—	26	12	no	—
342	C₂²×C₄	—	26	4	no	—
343	C₂²×C₄	—	26	12	no	—
344	C₂²×C₄	—	26	12	no	—
345	C₂²×C₄	—	26	4	no	—
346	C₂²×C₄	—	26	12	no	—
347	C₂²×C₄	—	52	6	no	—
348	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
349	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
350	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
351	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
353	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
355	C₄⋊C₄	—	2	6	no	—
356	C₄⋊C₄	—	13	12	no	—
357	C₄⋊C₄	—	13	24	no	—
358	C₄⋊C₄	—	13	4	no	—
359	C₄⋊C₄	—	26	24	no	—
360	C₄⋊C₄	—	26	12	no	—
361	C₄⋊C₄	—	26	6	no	—
362	C₄⋊C₄	—	52	6	no	—
363	C₄⋊C₄	C₂×C₄×D₁₃	1	12	yes	—
364	C₄⋊C₄	C₂×D₅₂	1	12	yes	—
365	C₂²⋊C₄	—	13	24	no	—
366	C₂²⋊C₄	—	13	8	no	—
367	C₂²⋊C₄	—	26	12	no	—
368	C₄²	—	2	6	no	—
369	C₄²	—	2	6	no	—
370	C₄²	—	2	6	no	—
371	C₄²	—	4	3	no	—
372	C₄²	—	26	12	no	—
373	C₄²	—	26	12	no	—
374	C₄²	—	26	12	no	—
375	C₄²	C₂×C₄×D₁₃	1	12	yes	—
376	C₄²	C₂×D₅₂	1	12	yes	—
377	C₄²	Q₈×D₁₃	1	4	yes	complemented
378	C₁₃	C₄×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	13	4	no	—
380	C₂³	—	13	4	no	—
381	C₂³	—	13	4	no	—
382	C₂³	—	26	2	no	—
383	C₂³	—	26	2	no	—
384	C₂³	—	26	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
387	Q₈	—	26	48	no	—
388	Q₈	C₄×D₅₂	1	16	yes	direct product factor
389	D₄	—	13	16	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	3	no	—
392	C₂×C₄	—	2	3	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	2	3	no	—
396	C₂×C₄	—	2	3	no	—
397	C₂×C₄	—	2	3	no	—
398	C₂×C₄	—	2	3	no	—
399	C₂×C₄	—	13	12	no	—
400	C₂×C₄	—	13	4	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	6	no	—
403	C₂×C₄	—	26	6	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	48	no	—
406	C₂×C₄	—	26	16	no	—
407	C₂×C₄	—	26	6	no	—
408	C₂×C₄	—	26	6	no	—
409	C₂×C₄	—	26	6	no	—
410	C₂×C₄	—	52	24	no	—
411	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
412	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
413	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
414	C₂×C₄	C₂²×D₅₂	1	6	yes	—
415	C₂×C₄	C₂²×D₅₂	1	6	yes	—
416	C₂×C₄	C₂²×D₅₂	1	2	yes	—
417	C₂×C₄	C₂×#6127	1	6	yes	—
418	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
419	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
420	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
421	C₂×C₄	#41×D₁₃	1	2	yes	—
422	C₂×C₄	#88257	1	2	yes	—
423	C₂²	—	13	8	no	—
424	C₂²	—	26	4	no	—
425	C₂²	—	26	4	no	—
426	C₂²	—	26	4	no	—
427	C₂²	—	26	4	no	—
428	C₂²	—	26	4	no	—
429	C₂²	—	26	4	no	—
430	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
431	C₂²	C₂³×D₅₂	1	1	yes	characteristic
432	C₂²	C₂²×#6127	1	1	yes	characteristic
433	C₂²	C₂²×Q₈×D₁₃	1	1	yes	characteristic
434	C₂²	C₂×#41×D₁₃	1	1	yes	characteristic
435	C₂²	C₂×#88257	1	1	yes	characteristic
436	C₂²	#11719648	1	1	yes	characteristic
437	C₄	—	2	6	no	—
438	C₄	—	2	6	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	3	no	—
441	C₄	—	26	12	no	—
442	C₄	—	26	4	no	—
443	C₄	—	52	6	no	—
444	C₄	C₂×C₄×D₅₂	1	12	yes	—
445	C₄	C₄×Q₈×D₁₃	1	4	yes	complemented
446	C₄	Q₈×D₅₂	1	4	yes	direct product factor
447	C₂	—	26	8	no	—
448	C₂	C₂²×C₄×D₅₂	1	1	yes	characteristic
449	C₂	C₂×C₄×Q₈×D₁₃	1	1	yes	characteristic
450	C₂	C₄×#88257	1	1	yes	characteristic
451	C₂	C₂×Q₈×D₅₂	1	1	yes	characteristic
452	C₂	#41×D₅₂	1	1	yes	characteristic
453	C₂	Q₈×#6127	1	1	yes	characteristic
454	C₂	#13128458	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₄²×Q₈×C₁₃	C₂
socle, cosocle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₅₂	C₂³
hypercenter	C₄²×Q₈	D₁₃
hypocenter	C₁₃	C₄×D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×D₁₃	C₂	semidirect
3. #13117894	C₂	semidirect
4. #13117843	C₂	semidirect
5. Q₈×C₄⋊Dic₁₃	C₂	semidirect
7. Q₈×#6103	C₂	semidirect
8. C₄×#88123	C₂	semidirect
9. C₄×#88151	C₂	semidirect
11. C₄²×Q₈×C₁₃	C₂	semidirect
17. Q₈×D₅₂	C₄	direct (N × H)
51. C₂×Q₈×D₁₃	C₂×C₄	semidirect
58. C₄×Q₈×C₁₃	C₂×C₄	semidirect
59. C₄×Q₈×C₁₃	D₄	semidirect
84. #88151	C₂×C₄	semidirect
89. C₄×D₅₂	Q₈	direct (N × H)
91. #88123	C₂×C₄	semidirect
125. C₂×C₄×D₁₃	C₂×Q₈	semidirect
138. C₄²×C₁₃	C₂×Q₈	semidirect
141. #6103	C₂×Q₈	semidirect
147. C₄⋊Dic₁₃	C₂×Q₈	semidirect
161. C₄²×Q₈	D₁₃	semidirect
171. Q₈×C₁₃	C₄×D₄	semidirect
202. D₅₂	C₄×Q₈	direct (N × H)
256. C₂×D₁₃	C₂×C₄×Q₈	semidirect
262. C₄×C₁₃	C₂×C₄×Q₈	semidirect
263. C₄×C₁₃	D₄×Q₈	semidirect
282. C₄×Q₈	C₄×D₁₃	semidirect
283. C₄×Q₈	D₅₂	direct (N × H)
377. C₄²	Q₈×D₁₃	semidirect
378. C₁₃	C₄×D₄×Q₈	semidirect
388. Q₈	C₄×D₅₂	direct (N × H)
445. C₄	C₄×Q₈×D₁₃	semidirect
446. C₄	Q₈×D₅₂	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×Q₈×D₅₂	2
C₂×C₄×Q₈×D₁₃	2
#13117894	2
#13117843	2
Q₈×C₄⋊Dic₁₃	2
C₄⋊C₄×D₅₂	2
Q₈×#6103	2
C₄×#88123	2
C₄×#88151	2
C₄²×D₅₂	2
C₄²×Q₈×C₁₃	2
C₄×D₄×Q₈	13

Subgroups — C4×Q8×D52 #16022788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×D₅₂ #16022788