Subgroups — #13128631

Order 1664.

1100 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
3	C₂×#88200	C₂	1	2	yes	maximal, complemented
4	#11719435	C₂	1	2	yes	maximal, complemented
5	#11719434	C₂	1	2	yes	maximal, complemented
6	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719341	C₂	1	4	yes	maximal, complemented
9	#11719340	C₂	1	2	yes	maximal, complemented
10	#11719339	C₂	1	4	yes	maximal, complemented
11	D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
12	#11719284	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719250	C₂	1	2	yes	maximal
15	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
16	#11719248	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719244	C₂	1	2	yes	maximal, complemented
18	C₂²×Q₈×C₁₃	C₂²	1	2	yes	complemented
19	C₂×Q₈×D₁₃	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	#88200	C₂²	1	2	yes	—
30	#88200	C₂²	1	4	yes	—
31	#88200	C₂²	1	1	yes	characteristic
32	#88200	C₂²	1	2	yes	complemented
33	#88200	C₂²	1	4	yes	complemented
34	#88200	C₂²	1	4	yes	complemented
35	#88200	C₂²	1	2	yes	complemented
36	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
37	#88198	C₂²	1	4	yes	complemented
38	#88198	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
40	D₄×Dic₁₃	C₂²	1	2	yes	—
41	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
42	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
43	C₂×#6103	C₂²	1	4	yes	—
44	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
45	#88178	C₂²	1	4	yes	complemented
46	#88178	C₂²	1	2	yes	complemented
47	C₂×#6101	C₂²	1	4	yes	complemented
48	#88151	C₂²	1	2	yes	—
49	#88151	C₂²	1	1	yes	characteristic
50	#88151	C₂²	1	4	yes	complemented
51	#88150	C₂²	1	4	yes	—
52	#88150	C₂²	1	2	yes	—
53	#88150	C₂²	1	4	yes	complemented
54	#88150	C₂²	1	4	yes	complemented
55	#88147	C₂²	1	2	yes	—
56	#88147	C₂²	1	1	yes	characteristic
57	#88146	C₂²	1	2	yes	—
58	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
59	C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
60	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
61	#88144	C₂²	1	2	yes	complemented
62	#88144	C₂²	1	2	yes	complemented
63	#88143	C₂²	1	4	yes	complemented
64	#88143	C₂²	1	2	yes	complemented
65	#88142	C₂²	1	2	yes	complemented
66	#88142	C₂²	1	1	yes	characteristic, complemented
67	#88141	C₂²	1	2	yes	complemented
68	#88135	C₂²	1	2	yes	—
69	#88135	C₂²	1	4	yes	—
70	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
72	#88132	C₂²	1	4	yes	complemented
73	#88132	C₂²	1	4	yes	complemented
74	#88132	C₂²	1	4	yes	complemented
75	C₄×D₅₂	C₂²	1	1	yes	characteristic
76	C₄×D₅₂	C₂²	1	2	yes	—
77	#88126	C₂²	1	2	yes	—
78	C₄²×D₁₃	C₂²	1	1	yes	characteristic
79	#88124	C₂²	1	2	yes	complemented
80	#88123	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₃	—	4	4	no	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
92	C₂²×Dic₁₃	C₂³	1	2	yes	—
93	C₂²×Dic₁₃	C₂³	1	4	yes	—
94	Q₈×D₁₃	—	4	4	no	—
95	D₄×D₁₃	Q₈	1	8	yes	complemented
96	C₂×D₅₂	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₃	—	4	4	no	—
98	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂³	1	2	yes	—
100	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂³	1	4	yes	—
102	C₂×C₄×D₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₃	C₂³	1	4	yes	—
104	C₂×C₄×D₁₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
107	C₂×Dic₂₆	C₂³	1	2	yes	—
108	C₂×Dic₂₆	C₂³	1	2	yes	—
109	C₂×Dic₂₆	C₂³	1	4	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
122	#6103	C₂³	1	2	yes	—
123	#6103	C₂³	1	2	yes	—
124	#6103	C₂³	1	2	yes	—
125	#6103	C₂³	1	4	yes	—
126	#6103	C₂³	1	4	yes	—
127	#6103	C₂³	1	2	yes	—
128	#6103	C₂³	1	4	yes	—
129	C₄⋊Dic₁₃	C₂³	1	2	yes	—
130	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₁₃	C₂³	1	2	yes	—
132	C₄⋊Dic₁₃	C₂³	1	2	yes	—
133	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₃	C₂³	1	4	yes	—
135	C₄⋊Dic₁₃	C₂³	1	4	yes	—
136	#6101	C₂³	1	2	yes	—
137	#6101	C₂³	1	2	yes	—
138	#6101	C₂³	1	2	yes	—
139	#6101	C₂³	1	4	yes	—
140	#6101	C₂³	1	4	yes	—
141	#6101	C₂³	1	2	yes	—
142	#6101	C₂³	1	2	yes	—
143	#6101	C₂³	1	4	yes	—
144	#6101	C₂³	1	4	yes	—
145	#6101	C₂³	1	4	yes	—
146	#6101	C₂³	1	2	yes	—
147	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂³	1	2	yes	—
149	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂³	1	4	yes	—
152	#3501	—	13	1	no	maximal, Sylow
153	C₂³×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₃	—	4	2	no	—
155	C₂²×D₁₃	—	4	2	no	—
156	C₂²×D₁₃	C₂×Q₈	1	8	yes	complemented
157	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×D₁₃	C₂⁴	1	2	yes	—
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	2	2	no	—
161	Q₈×C₁₃	—	4	4	no	—
162	D₄×C₁₃	C₂×Q₈	1	4	yes	complemented
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₃	C₂×Q₈	1	8	yes	complemented
173	C₂×Dic₁₃	—	4	2	no	—
174	C₂×Dic₁₃	—	4	4	no	—
175	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂⁴	1	2	yes	—
178	C₂×Dic₁₃	C₂⁴	1	2	yes	—
179	C₂×Dic₁₃	C₂⁴	1	4	yes	—
180	C₂×Dic₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
182	D₅₂	C₂×Q₈	1	4	yes	complemented
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	4	no	—
185	C₄×D₁₃	—	4	2	no	—
186	C₄×D₁₃	—	4	2	no	—
187	C₄×D₁₃	—	4	1	no	—
188	C₄×D₁₃	—	4	4	no	—
189	C₄×D₁₃	—	4	4	no	—
190	C₄×D₁₃	C₂×Q₈	1	4	yes	complemented
191	Dic₂₆	—	2	2	no	—
192	Dic₂₆	—	4	2	no	—
193	Dic₂₆	—	4	2	no	—
194	Dic₂₆	—	4	4	no	—
195	#554	—	13	2	no	—
196	#554	—	13	2	no	—
197	#554	—	13	4	no	—
198	#554	—	13	1	no	—
199	#554	—	13	2	no	—
200	#554	—	13	1	no	—
201	D₄×Q₈	—	13	2	no	—
202	D₄×Q₈	—	13	1	no	—
203	D₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
204	#544	—	13	2	no	—
205	#543	—	13	4	no	—
206	#533	—	13	1	no	—
207	#533	—	13	1	no	—
208	C₂×C₂²⋊Q₈	—	13	2	no	—
209	C₂×C₂²⋊Q₈	—	13	2	no	—
210	#518	—	13	2	no	—
211	C₂×C₄×D₄	—	13	1	no	—
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	C₂²×Q₈	1	4	yes	—
215	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	1	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	2	1	no	—
220	C₂×D₁₃	—	4	8	no	—
221	C₂×D₁₃	C₂²×Q₈	1	2	yes	—
222	C₂×D₁₃	C₂²×Q₈	1	4	yes	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	C₂²×Q₈	1	2	yes	—
229	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
230	Dic₁₃	—	2	2	no	—
231	Dic₁₃	—	2	2	no	—
232	Dic₁₃	—	2	1	no	—
233	Dic₁₃	—	2	1	no	—
234	Dic₁₃	—	2	4	no	—
235	Dic₁₃	—	2	2	no	—
236	Dic₁₃	C₂²×Q₈	1	2	yes	—
237	C₂²×Q₈	—	13	2	no	—
238	C₂²×Q₈	C₂×D₁₃	1	2	yes	complemented
239	C₂²×D₄	—	13	1	no	—
240	C₂³×C₄	—	13	2	no	—
241	C₄⋊Q₈	—	13	1	no	—
242	C₄⋊Q₈	—	13	4	no	—
243	C₄⋊Q₈	—	13	1	no	—
244	C₄⋊Q₈	—	13	2	no	—
245	C₄⋊Q₈	—	13	1	no	—
246	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
247	C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
248	#125	—	13	2	no	—
249	#125	—	13	2	no	—
250	#125	—	13	4	no	—
251	#125	—	13	2	no	—
252	#125	—	13	2	no	—
253	C₂²⋊Q₈	—	13	2	no	—
254	C₂²⋊Q₈	—	13	1	no	—
255	C₂²⋊Q₈	—	13	4	no	—
256	C₂²⋊Q₈	—	13	2	no	—
257	C₂²⋊Q₈	—	13	2	no	—
258	C₂²⋊Q₈	—	13	4	no	—
259	C₂²⋊Q₈	—	13	4	no	—
260	C₂²⋊Q₈	—	13	2	no	—
261	C₂²⋊Q₈	—	13	4	no	—
262	C₂²⋊Q₈	—	13	1	no	—
263	C₂²⋊Q₈	—	13	4	no	—
264	C₂²⋊Q₈	—	13	2	no	—
265	C₂²⋊Q₈	—	13	2	no	—
266	C₂²⋊Q₈	—	13	4	no	—
267	C₂²⋊Q₈	—	13	4	no	—
268	C₂²⋊Q₈	—	13	4	no	—
269	C₂²⋊Q₈	—	13	4	no	—
270	C₂²⋊Q₈	—	13	4	no	—
271	C₂²⋊Q₈	—	13	4	no	—
272	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
273	C₂²⋊Q₈	C₂×D₁₃	1	4	yes	complemented
274	C₄×Q₈	—	13	2	no	—
275	C₄×Q₈	—	13	2	no	—
276	C₄×Q₈	—	13	1	no	—
277	C₄×Q₈	—	13	2	no	—
278	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
279	C₄×D₄	—	13	1	no	—
280	C₄×D₄	—	13	2	no	—
281	C₄×D₄	—	13	2	no	—
282	C₄×D₄	—	13	4	no	—
283	C₄×D₄	—	13	1	no	—
284	C₄×D₄	—	13	2	no	—
285	C₄×D₄	—	13	2	no	—
286	C₄×D₄	—	13	4	no	—
287	C₄×D₄	—	13	1	no	—
288	C₄×D₄	—	13	2	no	—
289	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
290	C₄×D₄	C₂×D₁₃	1	2	yes	—
291	#117	—	13	2	no	—
292	#117	—	13	2	no	—
293	C₂×C₄⋊C₄	—	13	4	no	—
294	C₂×C₄⋊C₄	—	13	2	no	—
295	C₂×C₄⋊C₄	—	13	1	no	—
296	C₂×C₄⋊C₄	—	13	4	no	—
297	C₂×C₄⋊C₄	—	13	2	no	—
298	C₂×C₂²⋊C₄	—	13	4	no	—
299	C₂×C₂²⋊C₄	—	13	2	no	—
300	C₂×C₂²⋊C₄	—	13	4	no	—
301	C₂×C₄²	—	13	1	no	—
302	C₂×C₁₃	—	2	4	no	—
303	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
304	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₁₃	#585	1	1	yes	characteristic
306	D₁₃	—	2	2	no	—
307	D₁₃	—	2	4	no	—
308	C₂⁴	—	13	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	13	1	no	—
311	C₂×Q₈	—	13	2	no	—
312	C₂×Q₈	—	13	2	no	—
313	C₂×Q₈	—	13	4	no	—
314	C₂×Q₈	—	52	4	no	—
315	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
316	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×Q₈	C₂²×D₁₃	1	4	yes	—
318	C₂×D₄	—	13	2	no	—
319	C₂×D₄	—	13	8	no	—
320	C₂×D₄	—	13	1	no	—
321	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	4	no	—
324	C₂²×C₄	—	13	2	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	2	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	4	no	—
329	C₂²×C₄	—	13	4	no	—
330	C₂²×C₄	—	13	2	no	—
331	C₂²×C₄	—	13	2	no	—
332	C₂²×C₄	—	52	4	no	—
333	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
334	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
335	C₄⋊C₄	—	13	4	no	—
336	C₄⋊C₄	—	13	2	no	—
337	C₄⋊C₄	—	13	2	no	—
338	C₄⋊C₄	—	13	1	no	—
339	C₄⋊C₄	—	13	2	no	—
340	C₄⋊C₄	—	13	2	no	—
341	C₄⋊C₄	—	13	1	no	—
342	C₄⋊C₄	—	13	4	no	—
343	C₄⋊C₄	—	13	4	no	—
344	C₄⋊C₄	—	13	4	no	—
345	C₄⋊C₄	—	13	4	no	—
346	C₄⋊C₄	—	13	4	no	—
347	C₄⋊C₄	—	13	2	no	—
348	C₄⋊C₄	—	13	2	no	—
349	C₄⋊C₄	—	13	2	no	—
350	C₄⋊C₄	—	13	2	no	—
351	C₄⋊C₄	—	13	4	no	—
352	C₄⋊C₄	—	13	2	no	—
353	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
356	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
359	C₂²⋊C₄	—	13	2	no	—
360	C₂²⋊C₄	—	13	4	no	—
361	C₂²⋊C₄	—	13	4	no	—
362	C₂²⋊C₄	—	13	2	no	—
363	C₂²⋊C₄	—	13	2	no	—
364	C₂²⋊C₄	—	13	2	no	—
365	C₂²⋊C₄	—	13	4	no	—
366	C₂²⋊C₄	—	13	4	no	—
367	C₂²⋊C₄	—	13	2	no	—
368	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
369	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	4	no	—
374	C₄²	—	13	2	no	—
375	C₄²	C₂²×D₁₃	1	1	yes	characteristic
376	C₄²	C₂²×D₁₃	1	2	yes	—
377	C₁₃	#3501	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	13	1	no	—
379	C₂³	—	13	2	no	—
380	C₂³	—	13	8	no	—
381	C₂³	—	52	2	no	—
382	C₂³	—	52	2	no	—
383	C₂³	C₂³×D₁₃	1	2	yes	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	26	2	no	—
388	Q₈	—	52	2	no	—
389	Q₈	—	52	2	no	—
390	Q₈	—	52	4	no	—
391	D₄	—	13	8	no	—
392	D₄	—	13	4	no	—
393	D₄	Q₈×D₁₃	1	4	yes	complemented
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	4	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	4	no	—
401	C₂×C₄	—	13	2	no	—
402	C₂×C₄	—	13	2	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	52	4	no	—
407	C₂×C₄	—	52	1	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	—	52	2	no	—
410	C₂×C₄	—	52	4	no	—
411	C₂×C₄	—	52	4	no	—
412	C₂×C₄	—	52	2	no	—
413	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₁₃	1	4	yes	—
415	C₂×C₄	C₂³×D₁₃	1	2	yes	—
416	C₂×C₄	C₂³×D₁₃	1	2	yes	—
417	C₂×C₄	C₂³×D₁₃	1	2	yes	—
418	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	13	2	no	—
423	C₂²	—	13	4	no	—
424	C₂²	—	26	2	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	26	2	no	—
427	C₂²	—	26	1	no	—
428	C₂²	—	52	8	no	—
429	C₂²	C₂×Q₈×D₁₃	1	4	yes	—
430	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	13	2	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	2	no	—
439	C₄	—	26	2	no	—
440	C₄	—	26	4	no	—
441	C₄	—	26	2	no	—
442	C₄	—	26	1	no	—
443	C₄	#88251	1	2	yes	—
444	C₄	C₂×Q₈×D₁₃	1	2	yes	—
445	C₂	—	2	4	no	—
446	C₂	—	26	2	no	—
447	C₂	—	26	4	no	—
448	C₂	C₂×#88251	1	1	yes	characteristic
449	C₂	C₂²×Q₈×D₁₃	1	1	yes	characteristic
450	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	D₄×Q₈×C₁₃	C₂
prime radical	C₂×D₄×D₁₃	C₂²
hypercenter	D₄×Q₈	D₁₃
hypocenter	C₁₃	#3501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. D₄×Q₈×C₁₃	C₂	semidirect
2. Q₈×C₂²⋊D₁₃	C₂	semidirect
3. C₂×#88200	C₂	semidirect
4. #11719435	C₂	semidirect
5. #11719434	C₂	semidirect
6. #11719433	C₂	semidirect
7. #11719432	C₂	semidirect
8. #11719341	C₂	semidirect
9. #11719340	C₂	semidirect
10. #11719339	C₂	semidirect
11. D₁₃×C₂²⋊Q₈	C₂	semidirect
12. #11719284	C₂	semidirect
13. #11719283	C₂	semidirect
16. #11719248	C₂	semidirect
17. #11719244	C₂	semidirect
18. C₂²×Q₈×C₁₃	C₂²	semidirect
19. C₂×Q₈×D₁₃	C₂²	semidirect
22. C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₁₃	C₂²	semidirect
32. #88200	C₂²	semidirect
33. #88200	C₂²	semidirect
34. #88200	C₂²	semidirect
35. #88200	C₂²	semidirect
36. Q₈×Dic₁₃	C₂²	semidirect
37. #88198	C₂²	semidirect
38. #88198	C₂²	semidirect
44. C₂×C₄⋊Dic₁₃	C₂²	semidirect
45. #88178	C₂²	semidirect
46. #88178	C₂²	semidirect
47. C₂×#6101	C₂²	semidirect
50. #88151	C₂²	semidirect
53. #88150	C₂²	semidirect
54. #88150	C₂²	semidirect
59. C₄⋊C₄×D₁₃	C₂²	semidirect
60. C₄⋊C₄×D₁₃	C₂²	semidirect
61. #88144	C₂²	semidirect
62. #88144	C₂²	semidirect
63. #88143	C₂²	semidirect
64. #88143	C₂²	semidirect
65. #88142	C₂²	semidirect
66. #88142	C₂²	semidirect
67. #88141	C₂²	semidirect
72. #88132	C₂²	semidirect
73. #88132	C₂²	semidirect
74. #88132	C₂²	semidirect
79. #88124	C₂²	semidirect
80. #88123	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
95. D₄×D₁₃	Q₈	semidirect
156. C₂²×D₁₃	C₂×Q₈	semidirect
162. D₄×C₁₃	C₂×Q₈	semidirect
172. C₂²⋊D₁₃	C₂×Q₈	semidirect
182. D₅₂	C₂×Q₈	semidirect
190. C₄×D₁₃	C₂×Q₈	semidirect
203. D₄×Q₈	D₁₃	semidirect
238. C₂²×Q₈	C₂×D₁₃	semidirect
246. C₄⋊Q₈	C₂×D₁₃	semidirect
247. C₄⋊Q₈	C₂×D₁₃	semidirect
272. C₂²⋊Q₈	C₂×D₁₃	semidirect
273. C₂²⋊Q₈	C₂×D₁₃	semidirect
278. C₄×Q₈	C₂×D₁₃	semidirect
377. C₁₃	#3501	semidirect
393. D₄	Q₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×Q₈×C₁₃	2
Q₈×C₂²⋊D₁₃	2
C₂×#88200	2
#11719435	2
#11719434	2
#11719433	2
#11719432	2
#11719341	2
#11719340	2
#11719339	2
D₁₃×C₂²⋊Q₈	2
#11719284	2
#11719283	2
#11719250	2
C₄×D₄×D₁₃	2
#11719248	2
#11719244	2
#3501	13