Subgroups — C₄×#11719106 #16797408

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719106	C₂	1	2	yes	maximal
2	C₄×Q₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×#261	C₂	1	1	yes	maximal, characteristic
4	#13130652	C₂	1	2	yes	maximal, complemented
5	C₄×#88102	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130609	C₂	1	2	yes	maximal, complemented
7	#13130607	C₂	1	2	yes	maximal
8	C₄×#88117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88115	C₂	1	1	yes	maximal, characteristic
10	C₄×#88100	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×SD₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#261	C₂²	1	2	yes	—
13	C₂×D₄×#261	C₂²	1	2	yes	—
14	C₂²×C₄×#261	—	2	1	no	—
15	C₂×SD₁₆×D₁₃	C₂²	1	1	yes	characteristic
16	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
17	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
18	C₂×#88117	C₂²	1	2	yes	—
19	C₂×#88115	C₂²	1	2	yes	—
20	C₄×C₂²⋊#261	—	2	1	no	—
21	#11719106	C₄	1	16	yes	direct product factor
22	C₂×#88102	C₂²	1	2	yes	—
23	C₂×#88100	C₂²	1	2	yes	—
24	C₂×#88100	C₂²	1	2	yes	—
25	C₄⋊C₄×#261	—	2	2	no	—
26	C₄⋊C₄×#261	C₂²	1	2	yes	—
27	C₄⋊C₄×#261	C₂²	1	2	yes	—
28	C₂²⋊C₄×#261	—	2	2	no	—
29	C₄×C₄⋊#261	—	2	1	no	—
30	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
32	C₄²×#261	—	2	1	no	—
33	C₄²×#261	C₂²	1	1	yes	characteristic
34	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×SD₁₆	C₄	1	1	yes	characteristic, complemented
36	SD₁₆×Dic₁₃	C₄	1	1	yes	characteristic, complemented
37	C₄×#6106	C₄	1	1	yes	characteristic, complemented
38	C₄×#6105	C₄	1	1	yes	characteristic, complemented
39	D₁₃×#106	C₂²	1	1	yes	characteristic
40	#11718513	C₄	1	1	yes	characteristic, complemented
41	D₁₃×#103	C₂²	1	1	yes	characteristic
42	#11718449	C₄	1	1	yes	characteristic, complemented
43	D₁₃×#102	C₂²	1	1	yes	characteristic
44	#11718419	C₄	1	1	yes	characteristic, complemented
45	C₄×#6095	C₄	1	1	yes	characteristic, complemented
46	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
47	#11718265	C₂²	1	2	yes	—
48	#11718246	C₂²	1	2	yes	—
49	#11718246	C₂²	1	2	yes	—
50	C₂³×#261	—	2	2	no	—
51	C₂×Q₈×D₁₃	C₂³	1	1	yes	characteristic
52	C₂×D₄×D₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₄×D₁₃	—	2	1	no	—
54	C₂×C₂²⋊#261	—	2	2	no	—
55	Q₈×#261	—	2	4	no	—
56	Q₈×#261	C₂×C₄	1	8	yes	complemented
57	D₄×#261	—	2	4	no	—
58	D₄×#261	C₂×C₄	1	8	yes	—
59	C₂×C₄⋊#261	—	2	2	no	—
60	C₂×C₄⋊#261	C₂³	1	2	yes	—
61	C₂×C₄⋊#261	C₂³	1	2	yes	—
62	C₂×C₄×#261	—	2	2	no	—
63	C₂×C₄×#261	—	2	2	no	—
64	C₂×C₄×#261	—	2	2	no	—
65	C₂×C₄×#261	—	2	1	no	—
66	C₂×C₄×#261	—	2	1	no	—
67	C₂×C₄×#261	—	4	4	no	—
68	C₂×C₄×#261	D₄	1	1	yes	characteristic
69	C₂×C₄×#261	D₄	1	1	yes	characteristic
70	C₂×C₄×#261	D₄	1	2	yes	—
71	C₂×C₄×#261	C₂³	1	2	yes	—
72	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
73	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
75	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×#6106	C₂×C₄	1	1	yes	characteristic
78	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×#6105	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	—	2	1	no	—
81	SD₁₆×D₁₃	C₂×C₄	1	8	yes	—
82	C₂×#6095	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
85	#88147	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₄×D₁₃	—	2	1	no	—
87	C₄⋊C₄×D₁₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×D₁₃	C₂³	1	1	yes	characteristic
89	#88141	—	2	1	no	—
90	#88141	C₂×C₄	1	1	yes	characteristic, complemented
91	#88135	—	2	1	no	—
92	C₂²⋊C₄×D₁₃	—	2	1	no	—
93	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
94	C₄²×D₁₃	—	2	1	no	—
95	C₄²×D₁₃	C₂³	1	1	yes	characteristic
96	C₄×Dic₂₆	—	2	1	no	—
97	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic, complemented
98	#88117	C₂×C₄	1	8	yes	complemented
99	#88115	C₂×C₄	1	8	yes	—
100	(C₂×#261)⋊C₄	—	2	2	no	—
101	(C₂×#261)⋊C₄	—	2	2	no	—
102	(C₂×#261)⋊C₄	—	2	1	no	—
103	(C₂×#261)⋊C₄	—	2	1	no	—
104	C₄×#1057	—	2	1	no	—
105	C₄×#1057	—	2	1	no	—
106	#88102	C₂×C₄	1	8	yes	complemented
107	#88100	—	2	4	no	—
108	#88100	C₂×C₄	1	8	yes	complemented
109	C₁₃×#106	C₂×C₄	1	1	yes	characteristic, complemented
110	C₁₃×#103	C₂×C₄	1	1	yes	characteristic, complemented
111	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
112	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
113	#88075	C₂×C₄	1	1	yes	characteristic, complemented
114	#88072	C₂×C₄	1	1	yes	characteristic
115	#88061	C₂×C₄	1	1	yes	characteristic
116	#88057	C₂×C₄	1	1	yes	characteristic, complemented
117	#88056	C₂×C₄	1	1	yes	characteristic, complemented
118	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
119	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
120	#88050	C₂×C₄	1	1	yes	characteristic, complemented
121	#88049	C₂×C₄	1	1	yes	characteristic
122	#88048	C₂×C₄	1	1	yes	characteristic, complemented
123	#88048	C₂×C₄	1	1	yes	characteristic, complemented
124	C₄×#1055	C₂×C₄	1	1	yes	characteristic, complemented
125	C₄×#440	—	13	1	no	maximal, Sylow
126	C₂³×D₁₃	—	2	1	no	—
127	C₂²×#261	—	2	2	no	—
128	C₂²×#261	—	2	2	no	—
129	C₂²×#261	—	2	8	no	—
130	C₂²×#261	—	4	4	no	—
131	C₂²×#261	—	4	4	no	—
132	C₂²×#261	C₂×D₄	1	2	yes	—
133	C₂²×#261	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂×C₂²⋊D₁₃	—	2	1	no	—
138	C₂²×Dic₁₃	—	2	1	no	—
139	Q₈×D₁₃	—	2	2	no	—
140	Q₈×D₁₃	C₂²×C₄	1	4	yes	—
141	D₄×D₁₃	—	2	2	no	—
142	D₄×D₁₃	C₂²×C₄	1	4	yes	—
143	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×D₁₃	—	2	1	no	—
145	C₂×C₄×D₁₃	—	2	1	no	—
146	C₂×C₄×D₁₃	—	2	1	no	—
147	C₂×C₄×D₁₃	—	2	1	no	—
148	C₂×C₄×D₁₃	—	2	1	no	—
149	C₂×C₄×D₁₃	—	4	2	no	—
150	C₂×C₄×D₁₃	—	4	2	no	—
151	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
156	C₂²⋊#261	—	2	8	no	—
157	C₂×#1057	—	2	2	no	—
158	C₄⋊#261	—	2	8	no	—
159	C₄⋊#261	—	2	2	no	—
160	C₄⋊#261	—	2	2	no	—
161	C₄⋊#261	C₂²×C₄	1	4	yes	—
162	C₄⋊#261	C₂²×C₄	1	4	yes	—
163	C₄×#261	—	2	8	no	—
164	C₄×#261	—	2	2	no	—
165	C₄×#261	—	2	2	no	—
166	C₄×#261	—	4	2	no	—
167	C₄×#261	—	4	4	no	—
168	C₄×#261	—	4	4	no	—
169	C₄×#261	—	4	2	no	—
170	C₄×#261	—	4	2	no	—
171	C₄×#261	C₂²×C₄	1	4	yes	—
172	C₄×#261	#41	1	4	yes	—
173	D₁₃⋊C₈	—	2	2	no	—
174	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
175	C₁₃×SD₁₆	C₄²	1	4	yes	complemented
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²⋊Dic₁₃	—	2	1	no	—
185	#6106	C₄²	1	4	yes	complemented
186	#6105	C₄²	1	4	yes	complemented
187	#6103	—	2	1	no	—
188	#6103	—	2	1	no	—
189	C₄⋊Dic₁₃	—	2	1	no	—
190	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
192	#6101	—	2	1	no	—
193	#6101	—	2	1	no	—
194	#6101	—	2	1	no	—
195	#6101	—	2	1	no	—
196	C₄×Dic₁₃	—	2	1	no	—
197	C₄×Dic₁₃	—	2	1	no	—
198	C₄×Dic₁₃	—	2	1	no	—
199	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₁₃	#41	1	1	yes	characteristic
201	C₄×Dic₁₃	#41	1	1	yes	characteristic
202	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
203	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
204	#6095	C₄²	1	4	yes	complemented
205	C₈×D₁₃	—	2	2	no	—
206	C₈×D₁₃	C₂²×C₄	1	4	yes	—
207	C₂×#440	—	13	2	no	—
208	C₂×C₄×SD₁₆	—	13	1	no	—
209	C₄²×Q₈	—	13	1	no	—
210	C₄²×D₄	—	13	1	no	—
211	#1776	—	13	2	no	—
212	C₄×#107	—	13	1	no	—
213	#1763	—	13	2	no	—
214	#1762	—	13	2	no	—
215	C₄×#103	—	13	1	no	—
216	C₄×#102	—	13	1	no	—
217	C₄×#97	—	13	1	no	—
218	C₂³×C₁₃	—	2	1	no	—
219	C₂²×D₁₃	—	2	1	no	—
220	C₂²×D₁₃	—	2	4	no	—
221	C₂²×D₁₃	—	4	1	no	—
222	C₂²×D₁₃	—	4	1	no	—
223	C₂²×D₁₃	—	4	2	no	—
224	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×#261	—	2	2	no	—
226	C₂×#261	—	2	2	no	—
227	C₂×#261	—	2	2	no	—
228	C₂×#261	—	2	2	no	—
229	C₂×#261	—	2	4	no	—
230	C₂×#261	—	2	4	no	—
231	C₂×#261	—	4	16	no	—
232	C₂×#261	—	4	2	no	—
233	C₂×#261	—	4	2	no	—
234	C₂×#261	—	4	2	no	—
235	C₂×#261	—	4	2	no	—
236	C₂×#261	C₄×D₄	1	4	yes	—
237	C₂×#261	C₄×D₄	1	4	yes	—
238	Q₈×C₁₃	—	2	1	no	—
239	Q₈×C₁₃	C₂×C₄²	1	2	yes	complemented
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	C₂×C₄²	1	2	yes	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
249	C₂²⋊D₁₃	—	2	4	no	—
250	C₂×Dic₁₃	—	2	1	no	—
251	C₂×Dic₁₃	—	2	1	no	—
252	C₂×Dic₁₃	—	2	1	no	—
253	C₂×Dic₁₃	—	4	2	no	—
254	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
255	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
256	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
257	D₅₂	—	2	1	no	—
258	D₅₂	C₂×C₄²	1	2	yes	—
259	C₄×D₁₃	—	2	4	no	—
260	C₄×D₁₃	—	2	2	no	—
261	C₄×D₁₃	—	4	1	no	—
262	C₄×D₁₃	—	4	1	no	—
263	C₄×D₁₃	—	4	2	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	—	4	2	no	—
266	C₄×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
267	C₄×D₁₃	#137	1	2	yes	—
268	C₄×D₁₃	C₂³×C₄	1	2	yes	—
269	C₄×D₁₃	C₂×#41	1	2	yes	—
270	Dic₂₆	—	2	1	no	—
271	Dic₂₆	—	2	4	no	—
272	Dic₂₆	C₂×C₄²	1	2	yes	complemented
273	#1057	—	2	4	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	C₂×C₄²	1	2	yes	complemented
276	#1055	—	2	1	no	—
277	#1055	C₂×C₄²	1	2	yes	complemented
278	C₂²×SD₁₆	—	13	1	no	—
279	C₂×C₄×Q₈	—	13	2	no	—
280	C₂×C₄×Q₈	—	13	1	no	—
281	C₂×C₄×D₄	—	13	2	no	—
282	C₂×C₄×D₄	—	13	1	no	—
283	C₂²×C₄²	—	26	1	no	—
284	#440	—	13	16	no	—
285	C₄×SD₁₆	—	13	1	no	—
286	C₄×SD₁₆	—	13	1	no	—
287	C₄×SD₁₆	—	13	1	no	—
288	C₄×SD₁₆	—	13	1	no	—
289	C₄×SD₁₆	—	13	1	no	—
290	C₄×SD₁₆	—	13	1	no	—
291	C₄×SD₁₆	—	13	1	no	—
292	C₄×SD₁₆	#261	1	1	yes	characteristic, complemented
293	C₂×#107	—	13	2	no	—
294	C₂×#106	—	13	1	no	—
295	C₂×#103	—	13	2	no	—
296	C₂×#103	—	13	1	no	—
297	C₂×#102	—	13	2	no	—
298	C₂×#102	—	13	1	no	—
299	C₂×#97	—	13	2	no	—
300	C₂×#97	—	13	2	no	—
301	C₂×C₄×C₈	—	13	1	no	—
302	C₂×C₄×C₈	—	13	1	no	—
303	C₄×C₄⋊C₄	—	13	1	no	—
304	C₄×C₄⋊C₄	—	13	1	no	—
305	C₄×C₄⋊C₄	—	13	2	no	—
306	C₄×C₄⋊C₄	—	13	2	no	—
307	C₄×C₄⋊C₄	—	26	1	no	—
308	C₄×C₄⋊C₄	—	26	2	no	—
309	C₄×C₂²⋊C₄	—	26	2	no	—
310	C₄×C₂²⋊C₄	—	26	1	no	—
311	C₄³	—	13	1	no	—
312	C₄³	—	26	1	no	—
313	#340	—	13	2	no	—
314	#340	—	13	2	no	—
315	#340	—	13	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	4	1	no	—
322	C₂×D₁₃	—	4	1	no	—
323	C₂×D₁₃	—	4	4	no	—
324	C₂×D₁₃	—	4	4	no	—
325	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
326	C₂×D₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₂×D₁₃	C₂×#137	1	1	yes	characteristic
328	C₂×D₁₃	#575	1	2	yes	—
329	#261	—	2	4	no	—
330	#261	—	2	4	no	—
331	#261	—	4	4	no	—
332	#261	—	4	4	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	#440	1	2	yes	complemented
338	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
339	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	4	1	no	—
343	Dic₁₃	—	4	1	no	—
344	Dic₁₃	#440	1	2	yes	complemented
345	Dic₁₃	C₄×#41	1	2	yes	—
346	C₂²×Q₈	—	13	1	no	—
347	C₂²×D₄	—	13	1	no	—
348	C₂³×C₄	—	26	1	no	—
349	C₂³×C₄	—	26	2	no	—
350	C₂×SD₁₆	—	13	1	no	—
351	C₂×SD₁₆	—	13	1	no	—
352	C₂×SD₁₆	—	13	8	no	—
353	C₂×SD₁₆	—	13	1	no	—
354	C₂×SD₁₆	C₂×#261	1	1	yes	characteristic
355	C₂²×C₈	—	13	1	no	—
356	C₂²×C₈	—	13	2	no	—
357	C₂²×C₈	—	13	1	no	—
358	C₄×Q₈	—	13	8	no	—
359	C₄×Q₈	—	13	1	no	—
360	C₄×Q₈	—	13	1	no	—
361	C₄×Q₈	—	13	1	no	—
362	C₄×Q₈	—	26	1	no	—
363	C₄×Q₈	—	26	1	no	—
364	C₄×Q₈	—	26	4	no	—
365	C₄×Q₈	C₂×#261	1	1	yes	characteristic, complemented
366	C₄×D₄	—	13	8	no	—
367	C₄×D₄	—	13	1	no	—
368	C₄×D₄	—	13	1	no	—
369	C₄×D₄	—	13	1	no	—
370	C₄×D₄	—	26	1	no	—
371	C₄×D₄	—	26	1	no	—
372	C₄×D₄	—	26	4	no	—
373	C₄×D₄	C₂×#261	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	13	2	no	—
375	C₂×C₄⋊C₄	—	13	2	no	—
376	C₂×C₄⋊C₄	—	13	1	no	—
377	C₂×C₄⋊C₄	—	13	1	no	—
378	C₂×C₄⋊C₄	—	26	1	no	—
379	C₂×C₄⋊C₄	—	26	2	no	—
380	C₂×C₂²⋊C₄	—	26	1	no	—
381	C₂×C₂²⋊C₄	—	26	2	no	—
382	C₂×C₄²	—	13	2	no	—
383	C₂×C₄²	—	13	1	no	—
384	C₂×C₄²	—	13	1	no	—
385	C₂×C₄²	—	13	1	no	—
386	C₂×C₄²	—	13	2	no	—
387	C₂×C₄²	—	26	1	no	—
388	C₂×C₄²	—	26	2	no	—
389	C₂×C₄²	—	26	1	no	—
390	C₂×C₄²	—	26	2	no	—
391	C₂×C₄²	—	26	1	no	—
392	C₂×C₄²	—	26	2	no	—
393	C₂×C₄²	—	52	4	no	—
394	#107	—	13	8	no	—
395	#106	—	13	1	no	—
396	#106	—	13	1	no	—
397	#106	—	13	1	no	—
398	#106	C₂×#261	1	1	yes	characteristic, complemented
399	#103	—	13	8	no	—
400	#103	—	13	1	no	—
401	#103	—	13	1	no	—
402	#103	—	13	1	no	—
403	#103	C₂×#261	1	1	yes	characteristic, complemented
404	#102	—	13	8	no	—
405	#102	—	13	1	no	—
406	#102	—	13	1	no	—
407	#102	—	13	1	no	—
408	#102	C₂×#261	1	1	yes	characteristic
409	#97	—	13	8	no	—
410	#97	—	26	4	no	—
411	C₄×C₈	—	13	1	no	—
412	C₄×C₈	—	13	1	no	—
413	C₄×C₈	—	13	1	no	—
414	C₄×C₈	—	26	1	no	—
415	C₄×C₈	—	26	1	no	—
416	C₄×C₈	C₂×#261	1	1	yes	characteristic, complemented
417	#95	—	26	2	no	—
418	#95	—	26	1	no	—
419	#95	—	26	2	no	—
420	#95	—	26	1	no	—
421	C₂×C₁₃	—	4	2	no	—
422	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
424	C₂×C₁₃	#2943	1	1	yes	characteristic
425	D₁₃	—	4	2	no	—
426	D₁₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
427	D₁₃	C₄×#137	1	2	yes	—
428	C₂⁴	—	26	1	no	—
429	C₂×Q₈	—	13	4	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×Q₈	—	26	1	no	—
432	C₂×Q₈	—	26	2	no	—
433	C₂×Q₈	C₂²×#261	1	1	yes	characteristic
434	C₂×D₄	—	13	4	no	—
435	C₂×D₄	—	13	1	no	—
436	C₂×D₄	—	26	2	no	—
437	C₂×D₄	—	26	1	no	—
438	C₂×D₄	C₂²×#261	1	1	yes	characteristic
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	13	1	no	—
441	C₂²×C₄	—	13	1	no	—
442	C₂²×C₄	—	13	2	no	—
443	C₂²×C₄	—	13	2	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	—	26	1	no	—
446	C₂²×C₄	—	26	1	no	—
447	C₂²×C₄	—	26	1	no	—
448	C₂²×C₄	—	26	1	no	—
449	C₂²×C₄	—	26	1	no	—
450	C₂²×C₄	—	26	8	no	—
451	C₂²×C₄	—	26	2	no	—
452	C₂²×C₄	—	26	2	no	—
453	C₂²×C₄	—	26	1	no	—
454	C₂²×C₄	—	52	2	no	—
455	C₂²×C₄	—	52	2	no	—
456	C₂²×C₄	—	52	4	no	—
457	C₂²×C₄	—	52	4	no	—
458	SD₁₆	—	13	4	no	—
459	SD₁₆	—	13	4	no	—
460	SD₁₆	—	13	4	no	—
461	SD₁₆	C₄×#261	1	4	yes	complemented
462	C₂×C₈	—	13	1	no	—
463	C₂×C₈	—	13	4	no	—
464	C₂×C₈	—	13	4	no	—
465	C₂×C₈	—	13	1	no	—
466	C₂×C₈	—	26	2	no	—
467	C₂×C₈	—	26	2	no	—
468	C₂×C₈	—	26	2	no	—
469	C₂×C₈	C₂²×#261	1	1	yes	characteristic
470	C₂×C₈	C₂²×#261	1	1	yes	characteristic
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	13	4	no	—
473	C₄⋊C₄	—	13	4	no	—
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	26	1	no	—
477	C₄⋊C₄	—	26	1	no	—
478	C₄⋊C₄	—	26	1	no	—
479	C₄⋊C₄	—	26	1	no	—
480	C₄⋊C₄	—	26	2	no	—
481	C₄⋊C₄	—	26	2	no	—
482	C₄⋊C₄	—	26	8	no	—
483	C₄⋊C₄	—	26	1	no	—
484	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	26	1	no	—
488	C₂²⋊C₄	—	26	1	no	—
489	C₂²⋊C₄	—	26	8	no	—
490	C₂²⋊C₄	—	26	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	13	4	no	—
493	C₄²	—	13	4	no	—
494	C₄²	—	13	1	no	—
495	C₄²	—	13	1	no	—
496	C₄²	—	13	1	no	—
497	C₄²	—	26	1	no	—
498	C₄²	—	26	1	no	—
499	C₄²	—	26	2	no	—
500	C₄²	—	26	2	no	—
501	C₄²	—	26	8	no	—
502	C₄²	—	26	1	no	—
503	C₄²	—	52	2	no	—
504	C₄²	—	52	2	no	—
505	C₄²	—	52	2	no	—
506	C₄²	—	52	4	no	—
507	C₄²	—	52	4	no	—
508	C₄²	C₂²×#261	1	1	yes	characteristic
509	C₁₃	C₄×#440	1	1	yes	characteristic, complemented, Sylow
510	C₂³	—	2	1	no	—
511	C₂³	—	13	1	no	—
512	C₂³	—	26	4	no	—
513	C₂³	—	26	1	no	—
514	C₂³	—	52	1	no	—
515	C₂³	—	52	1	no	—
516	C₂³	—	52	2	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	13	2	no	—
519	Q₈	—	26	4	no	—
520	Q₈	—	26	1	no	—
521	Q₈	C₂×C₄×#261	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	13	2	no	—
524	D₄	—	26	4	no	—
525	D₄	—	26	1	no	—
526	D₄	C₂×C₄×#261	1	2	yes	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	13	1	no	—
532	C₂×C₄	—	13	1	no	—
533	C₂×C₄	—	13	2	no	—
534	C₂×C₄	—	13	2	no	—
535	C₂×C₄	—	13	2	no	—
536	C₂×C₄	—	13	2	no	—
537	C₂×C₄	—	13	4	no	—
538	C₂×C₄	—	13	4	no	—
539	C₂×C₄	—	13	1	no	—
540	C₂×C₄	—	26	4	no	—
541	C₂×C₄	—	26	2	no	—
542	C₂×C₄	—	26	2	no	—
543	C₂×C₄	—	26	2	no	—
544	C₂×C₄	—	26	2	no	—
545	C₂×C₄	—	26	2	no	—
546	C₂×C₄	—	26	1	no	—
547	C₂×C₄	—	26	4	no	—
548	C₂×C₄	—	26	4	no	—
549	C₂×C₄	—	26	1	no	—
550	C₂×C₄	—	26	1	no	—
551	C₂×C₄	—	52	2	no	—
552	C₂×C₄	—	52	1	no	—
553	C₂×C₄	—	52	2	no	—
554	C₂×C₄	—	52	1	no	—
555	C₂×C₄	—	52	2	no	—
556	C₂×C₄	—	52	16	no	—
557	C₂×C₄	—	52	2	no	—
558	C₂×C₄	—	52	2	no	—
559	C₂×C₄	—	52	2	no	—
560	C₂×C₄	—	52	2	no	—
561	C₂×C₄	—	52	2	no	—
562	C₂×C₄	D₄×#261	1	1	yes	characteristic
563	C₂×C₄	D₄×#261	1	1	yes	characteristic
564	C₂×C₄	C₂³×#261	1	1	yes	characteristic
565	C₈	—	2	1	no	—
566	C₈	—	13	2	no	—
567	C₈	—	26	4	no	—
568	C₈	—	26	1	no	—
569	C₈	C₂×C₄×#261	1	2	yes	complemented
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	13	2	no	—
574	C₂²	—	13	1	no	—
575	C₂²	—	13	1	no	—
576	C₂²	—	13	2	no	—
577	C₂²	—	26	2	no	—
578	C₂²	—	52	4	no	—
579	C₂²	—	52	4	no	—
580	C₂²	—	52	1	no	—
581	C₂²	—	52	1	no	—
582	C₂²	C₂×D₄×#261	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	13	2	no	—
588	C₄	—	13	2	no	—
589	C₄	—	26	4	no	—
590	C₄	—	26	4	no	—
591	C₄	—	26	2	no	—
592	C₄	—	26	1	no	—
593	C₄	—	52	4	no	—
594	C₄	—	52	4	no	—
595	C₄	—	52	1	no	—
596	C₄	—	52	1	no	—
597	C₄	#11719106	1	2	yes	direct product factor
598	C₄	C₂²×C₄×#261	1	1	yes	characteristic
599	C₄	#41×#261	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	13	2	no	—
602	C₂	—	13	2	no	—
603	C₂	—	52	2	no	—
604	C₂	C₄×D₄×#261	1	1	yes	characteristic
605	C₂	C₂×#11719106	1	1	yes	characteristic
606	C₂	#13131590	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₄×C₁₃×SD₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₄×D₁₃	C₂³
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₄×SD₁₆	#261
hypocenter	C₁₃	C₄×#440
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#261	C₂	semidirect
4. #13130652	C₂	semidirect
5. C₄×#88102	C₂	semidirect
6. #13130609	C₂	semidirect
8. C₄×#88117	C₂	semidirect
10. C₄×#88100	C₂	semidirect
21. #11719106	C₄	direct (N × H)
35. C₄×C₁₃×SD₁₆	C₄	semidirect
36. SD₁₆×Dic₁₃	C₄	semidirect
37. C₄×#6106	C₄	semidirect
38. C₄×#6105	C₄	semidirect
40. #11718513	C₄	semidirect
42. #11718449	C₄	semidirect
44. #11718419	C₄	semidirect
45. C₄×#6095	C₄	semidirect
56. Q₈×#261	C₂×C₄	semidirect
74. C₄×Q₈×C₁₃	C₂×C₄	semidirect
76. Q₈×Dic₁₃	C₂×C₄	semidirect
90. #88141	C₂×C₄	semidirect
97. C₄×Dic₂₆	C₂×C₄	semidirect
98. #88117	C₂×C₄	semidirect
106. #88102	C₂×C₄	semidirect
108. #88100	C₂×C₄	semidirect
109. C₁₃×#106	C₂×C₄	semidirect
110. C₁₃×#103	C₂×C₄	semidirect
112. C₄×C₈×C₁₃	C₂×C₄	semidirect
113. #88075	C₂×C₄	semidirect
116. #88057	C₂×C₄	semidirect
117. #88056	C₂×C₄	semidirect
118. C₈×Dic₁₃	C₂×C₄	semidirect
119. C₈×Dic₁₃	C₂×C₄	semidirect
120. #88050	C₂×C₄	semidirect
122. #88048	C₂×C₄	semidirect
123. #88048	C₂×C₄	semidirect
124. C₄×#1055	C₂×C₄	semidirect
175. C₁₃×SD₁₆	C₄²	semidirect
185. #6106	C₄²	semidirect
186. #6105	C₄²	semidirect
204. #6095	C₄²	semidirect
239. Q₈×C₁₃	C₂×C₄²	semidirect
272. Dic₂₆	C₂×C₄²	semidirect
275. C₈×C₁₃	C₂×C₄²	semidirect
277. #1055	C₂×C₄²	semidirect
292. C₄×SD₁₆	#261	semidirect
337. C₄×C₁₃	#440	semidirect
344. Dic₁₃	#440	semidirect
365. C₄×Q₈	C₂×#261	semidirect
398. #106	C₂×#261	semidirect
403. #103	C₂×#261	semidirect
416. C₄×C₈	C₂×#261	semidirect
461. SD₁₆	C₄×#261	semidirect
509. C₁₃	C₄×#440	semidirect
521. Q₈	C₂×C₄×#261	semidirect
569. C₈	C₂×C₄×#261	semidirect
597. C₄	#11719106	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×#11719106	2
C₄×Q₈×#261	2
C₄×D₄×#261	2
#13130652	2
C₄×#88102	2
#13130609	2
#13130607	2
C₄×#88117	2
C₄×#88115	2
C₄×#88100	2
C₄×SD₁₆×D₁₃	2
C₄×#440	13

Subgroups — C4×#11719106 #16797408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719106 #16797408