Subgroups — #12070722

Order 1280.

794 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	#10611271	C₂	1	2	yes	maximal, complemented
3	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601674	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601655	C₂	1	2	yes	maximal, complemented
6	#10599362	C₂	1	1	yes	maximal, characteristic, complemented
7	#10599349	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598965	C₂	1	2	yes	maximal, complemented
9	#10598946	C₂	1	2	yes	maximal, complemented
10	C₈×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₅×D₈	C₄	1	1	yes	characteristic
13	C₂×D₅×M₁₆	—	2	2	no	—
14	C₄×D₄×D₅	C₂²	1	2	yes	—
15	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₅×#436	C₂²	1	2	yes	complemented
17	D₈×Dic₅	C₄	1	1	yes	characteristic
18	#65416	—	2	2	no	—
19	C₄×#686	C₂²	1	2	yes	—
20	#65301	C₂²	1	2	yes	complemented
21	D₅×#107	C₄	1	1	yes	characteristic
22	#65161	C₄	1	1	yes	characteristic
23	#65126	C₂²	1	2	yes	—
24	#65123	C₂²	1	2	yes	complemented
25	D₅×#102	C₄	1	2	yes	—
26	#65045	C₄	1	2	yes	—
27	#65017	—	2	2	no	—
28	#65015	—	2	2	no	—
29	C₄×D₄₀	C₂²	1	1	yes	characteristic
30	C₄×#676	C₂²	1	1	yes	characteristic
31	C₈×D₂₀	C₂²	1	2	yes	complemented
32	#64974	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₅×#335	C₂²	1	1	yes	characteristic, complemented
35	C₅×D₄⋊C₈	C₂²	1	2	yes	complemented
36	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
37	D₄⋊#168	C₂²	1	2	yes	complemented
38	#64703	C₂²	1	2	yes	complemented
39	#64699	C₂²	1	2	yes	complemented
40	#64679	C₂²	1	2	yes	complemented
41	#64678	C₂²	1	1	yes	characteristic, complemented
42	#64675	C₂²	1	1	yes	characteristic, complemented
43	#64674	C₂²	1	1	yes	characteristic, complemented
44	C₈×#168	C₂²	1	1	yes	characteristic, complemented
45	M₁₆×D₈	—	5	1	no	maximal, Sylow
46	C₂×D₄×D₅	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₅	—	2	2	no	—
48	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₄×C₅×D₄	C₂³	1	2	yes	—
51	D₄×Dic₅	C₂×C₄	1	2	yes	—
52	C₂×#686	C₂×C₄	1	2	yes	—
53	C₄×C₂²⋊D₅	—	2	2	no	—
54	C₂×#681	—	2	2	no	—
55	D₅×D₈	—	2	4	no	—
56	D₅×M₁₆	—	4	8	no	—
57	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
58	C₂×#676	—	2	2	no	—
59	C₂×#676	D₄	1	1	yes	characteristic
60	C₂×#676	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅	—	2	2	no	—
62	C₂×C₈×D₅	—	2	2	no	—
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	#4039	C₂×C₄	1	2	yes	—
66	D₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	#4027	—	2	2	no	—
68	D₅×C₂²⋊C₄	—	2	2	no	—
69	C₄×D₂₀	C₂³	1	2	yes	—
70	C₄²×D₅	C₂³	1	1	yes	characteristic
71	C₅×#107	C₂×C₄	1	1	yes	characteristic
72	C₅×C₄⋊C₈	C₂³	1	2	yes	—
73	C₅×#102	C₂×C₄	1	2	yes	—
74	C₅×C₂²⋊C₈	—	2	2	no	—
75	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	#3964	C₂×C₄	1	2	yes	—
79	C₂²⋊#168	—	2	2	no	—
80	#3953	C₂×C₄	1	2	yes	—
81	#3952	—	2	1	no	—
82	#3952	—	2	2	no	—
83	#3952	—	2	2	no	—
84	#3950	C₂×C₄	1	1	yes	characteristic
85	#3947	D₄	1	1	yes	characteristic
86	#3947	D₄	1	1	yes	characteristic
87	#3946	—	2	2	no	—
88	#3946	—	2	1	no	—
89	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
91	#3941	C₂×C₄	1	2	yes	—
92	#3939	C₂×C₄	1	2	yes	—
93	C₄⋊#168	C₂³	1	2	yes	—
94	C₄×#168	C₂³	1	1	yes	characteristic
95	C₄×#168	C₂³	1	1	yes	characteristic
96	C₄×#168	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₈	—	5	1	no	—
98	D₄×M₁₆	—	5	2	no	—
99	#1589	—	5	1	no	—
100	#1589	D₅	1	1	yes	characteristic, complemented
101	#1581	—	5	2	no	—
102	#1581	—	5	2	no	—
103	C₈×D₈	—	5	1	no	—
104	C₈×D₈	—	5	1	no	—
105	#1567	—	5	1	no	—
106	#1486	—	5	2	no	—
107	C₈×M₁₆	—	5	1	no	—
108	C₂³×D₅	—	2	2	no	—
109	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂×C₂²⋊D₅	—	2	2	no	—
112	C₂²×Dic₅	—	2	2	no	—
113	D₄×D₅	—	2	4	no	—
114	D₄×D₅	—	4	2	no	—
115	C₂×D₂₀	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₅	—	2	2	no	—
117	C₂×C₄×D₅	—	2	2	no	—
118	C₂×C₄×D₅	—	2	2	no	—
119	C₂×C₄×D₅	—	4	4	no	—
120	C₂×C₄×D₅	—	4	4	no	—
121	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₅	#41	1	1	yes	characteristic
124	C₅×D₈	—	2	2	no	—
125	C₅×M₁₆	—	4	4	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
132	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
133	C₅×C₂²⋊C₄	—	2	2	no	—
134	C₄²×C₅	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₅	—	2	2	no	—
136	#686	—	2	4	no	—
137	#685	—	2	2	no	—
138	#685	—	2	2	no	—
139	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
140	#683	—	2	2	no	—
141	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₅	#41	1	1	yes	characteristic
144	#681	—	4	4	no	—
145	C₂×#168	—	2	2	no	—
146	C₂×#168	—	2	1	no	—
147	C₂×#168	C₂²×C₄	1	1	yes	characteristic
148	C₂×#168	C₂²×C₄	1	1	yes	characteristic
149	C₂×#168	C₂×D₄	1	1	yes	characteristic
150	C₂×#168	C₂×D₄	1	1	yes	characteristic
151	D₄₀	M₁₆	1	4	yes	complemented
152	#676	—	2	2	no	—
153	#676	—	4	4	no	—
154	#676	D₈	1	4	yes	complemented
155	C₈×D₅	—	2	2	no	—
156	C₈×D₅	—	4	1	no	—
157	C₈×D₅	—	4	4	no	—
158	C₈×D₅	—	4	4	no	—
159	C₂²×D₈	—	5	1	no	—
160	C₂²×M₁₆	—	10	2	no	—
161	C₂×C₄×D₄	—	5	2	no	—
162	C₄×D₈	—	5	1	no	—
163	C₄×D₈	—	5	2	no	—
164	C₄×D₈	—	5	1	no	—
165	C₄×D₈	—	5	2	no	—
166	C₄×D₈	—	5	1	no	—
167	C₄×D₈	C₂×D₅	1	1	yes	characteristic
168	#436	—	5	2	no	—
169	#436	C₂×D₅	1	2	yes	complemented
170	#435	—	10	2	no	—
171	#435	—	10	2	no	—
172	C₈×D₄	—	5	2	no	—
173	C₈×D₄	—	5	2	no	—
174	#431	—	5	1	no	—
175	C₂×#107	—	5	1	no	—
176	#423	—	5	2	no	—
177	C₂×#102	—	5	2	no	—
178	#407	—	10	2	no	—
179	C₄×M₁₆	—	5	1	no	—
180	C₂×C₄×C₈	—	5	1	no	—
181	#335	—	5	2	no	—
182	#335	—	5	1	no	—
183	#335	C₂×D₅	1	1	yes	characteristic, complemented
184	D₄⋊C₈	—	5	2	no	—
185	D₄⋊C₈	—	5	2	no	—
186	D₄⋊C₈	—	5	2	no	—
187	D₄⋊C₈	C₂×D₅	1	2	yes	complemented
188	#322	—	5	1	no	—
189	#322	—	5	1	no	—
190	C₈²	—	5	1	no	—
191	C₈²	C₂×D₅	1	1	yes	characteristic, complemented
192	C₂³×C₅	—	2	2	no	—
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	—	4	4	no	—
195	C₂²×D₅	—	4	4	no	—
196	C₂²×D₅	—	8	2	no	—
197	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₂²⋊D₅	—	4	4	no	—
207	C₂×Dic₅	—	2	2	no	—
208	C₂×Dic₅	—	4	4	no	—
209	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
210	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
211	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
212	D₂₀	—	2	2	no	—
213	D₂₀	C₂×M₁₆	1	4	yes	complemented
214	C₄×D₅	—	2	1	no	—
215	C₄×D₅	—	2	1	no	—
216	C₄×D₅	—	4	1	no	—
217	C₄×D₅	—	4	4	no	—
218	C₄×D₅	—	4	2	no	—
219	C₄×D₅	—	4	2	no	—
220	C₄×D₅	—	4	4	no	—
221	C₄×D₅	C₂×D₈	1	2	yes	—
222	C₄×D₅	#135	1	2	yes	—
223	C₅×C₈	—	2	1	no	—
224	C₅×C₈	—	2	1	no	—
225	C₅×C₈	—	4	1	no	—
226	C₅×C₈	—	4	2	no	—
227	C₅×C₈	C₂×M₁₆	1	2	yes	complemented
228	C₅×C₈	C₂×D₈	1	2	yes	complemented
229	#168	—	2	1	no	—
230	#168	—	2	1	no	—
231	#168	—	2	1	no	—
232	#168	—	4	1	no	—
233	#168	—	4	2	no	—
234	#168	C₂×D₈	1	2	yes	complemented
235	C₂²×D₄	—	5	2	no	—
236	C₂³×C₄	—	10	2	no	—
237	C₂×D₈	—	5	2	no	—
238	C₂×D₈	—	5	1	no	—
239	C₂×D₈	—	10	4	no	—
240	C₂×D₈	C₄×D₅	1	1	yes	characteristic
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	5	1	no	—
243	C₂×M₁₆	—	5	1	no	—
244	C₂×M₁₆	—	10	2	no	—
245	C₂×M₁₆	—	10	2	no	—
246	C₂×M₁₆	—	20	8	no	—
247	C₂²×C₈	—	5	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	10	2	no	—
250	C₂²×C₈	—	10	2	no	—
251	C₄×D₄	—	5	2	no	—
252	C₄×D₄	—	5	2	no	—
253	C₄×D₄	—	5	2	no	—
254	C₄×D₄	—	10	2	no	—
255	C₄×D₄	—	10	2	no	—
256	C₄×D₄	C₂²×D₅	1	2	yes	—
257	C₂×C₄⋊C₄	—	5	2	no	—
258	C₂×C₂²⋊C₄	—	10	2	no	—
259	C₂×C₄²	—	5	1	no	—
260	#107	—	5	1	no	—
261	#107	—	5	2	no	—
262	#107	C₄×D₅	1	1	yes	characteristic
263	C₄⋊C₈	—	5	2	no	—
264	C₄⋊C₈	—	10	2	no	—
265	C₄⋊C₈	—	10	1	no	—
266	C₄⋊C₈	C₂²×D₅	1	2	yes	—
267	#102	—	5	2	no	—
268	#102	—	5	2	no	—
269	#102	—	5	2	no	—
270	#102	C₄×D₅	1	2	yes	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	10	2	no	—
273	C₂²⋊C₈	—	10	1	no	—
274	C₂²⋊C₈	—	10	2	no	—
275	C₂²⋊C₈	—	10	2	no	—
276	#97	—	5	1	no	—
277	#97	—	5	1	no	—
278	C₄×C₈	—	5	1	no	—
279	C₄×C₈	—	5	1	no	—
280	C₄×C₈	—	5	1	no	—
281	C₄×C₈	—	5	1	no	—
282	C₄×C₈	—	5	1	no	—
283	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	—	4	2	no	—
289	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂×D₅	—	2	1	no	—
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	2	4	no	—
293	C₂×D₅	—	4	2	no	—
294	C₂×D₅	—	4	2	no	—
295	C₂×D₅	—	8	8	no	—
296	C₂×D₅	C₄×D₈	1	2	yes	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
300	C₄×C₅	#568	1	1	yes	characteristic
301	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
302	C₄×C₅	C₂×#135	1	1	yes	characteristic
303	Dic₅	—	2	1	no	—
304	Dic₅	—	2	1	no	—
305	Dic₅	—	4	2	no	—
306	Dic₅	C₄×D₈	1	2	yes	—
307	C₂⁴	—	10	2	no	—
308	C₂×D₄	—	5	2	no	—
309	C₂×D₄	—	10	2	no	—
310	C₂×D₄	—	10	4	no	—
311	C₂×D₄	—	20	2	no	—
312	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	10	2	no	—
318	C₂²×C₄	—	10	2	no	—
319	C₂²×C₄	—	10	2	no	—
320	C₂²×C₄	—	10	2	no	—
321	C₂²×C₄	—	20	4	no	—
322	C₂²×C₄	—	20	4	no	—
323	D₈	—	2	2	no	—
324	D₈	—	5	4	no	—
325	D₈	—	10	4	no	—
326	M₁₆	—	4	4	no	—
327	M₁₆	—	5	4	no	—
328	M₁₆	—	10	2	no	—
329	M₁₆	—	20	4	no	—
330	M₁₆	—	20	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	5	1	no	—
334	C₂×C₈	—	5	1	no	—
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	10	2	no	—
338	C₂×C₈	—	10	2	no	—
339	C₂×C₈	—	10	1	no	—
340	C₂×C₈	—	20	1	no	—
341	C₂×C₈	—	20	4	no	—
342	C₂×C₈	—	20	4	no	—
343	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂×C₈	D₄×D₅	1	1	yes	characteristic
346	C₂×C₈	D₄×D₅	1	1	yes	characteristic
347	C₄⋊C₄	—	5	2	no	—
348	C₄⋊C₄	—	10	2	no	—
349	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	10	2	no	—
352	C₂²⋊C₄	—	10	2	no	—
353	C₂²⋊C₄	—	10	2	no	—
354	C₄²	—	5	1	no	—
355	C₄²	—	5	1	no	—
356	C₄²	—	5	1	no	—
357	C₄²	C₂³×D₅	1	1	yes	characteristic
358	C₂×C₅	—	8	2	no	—
359	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
360	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
361	C₂×C₅	#2957	1	1	yes	characteristic
362	D₅	—	2	2	no	—
363	D₅	—	4	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	5	1	no	—
366	C₂³	—	10	2	no	—
367	C₂³	—	20	4	no	—
368	C₂³	—	20	4	no	—
369	C₂³	—	40	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	5	4	no	—
373	D₄	—	10	2	no	—
374	D₄	—	20	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	10	1	no	—
384	C₂×C₄	—	10	1	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	20	1	no	—
387	C₂×C₄	—	20	4	no	—
388	C₂×C₄	—	20	4	no	—
389	C₂×C₄	—	20	4	no	—
390	C₂×C₄	—	20	2	no	—
391	C₂×C₄	—	20	2	no	—
392	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
394	C₂×C₄	D₅×#41	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	5	2	no	—
400	C₈	—	10	1	no	—
401	C₈	—	10	1	no	—
402	C₈	—	10	1	no	—
403	C₈	—	20	1	no	—
404	C₈	—	20	2	no	—
405	C₈	D₅×M₁₆	1	2	yes	complemented
406	C₈	D₅×D₈	1	2	yes	complemented
407	C₅	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	5	2	no	—
412	C₂²	—	10	1	no	—
413	C₂²	—	10	1	no	—
414	C₂²	—	10	4	no	—
415	C₂²	—	20	2	no	—
416	C₂²	—	20	2	no	—
417	C₂²	—	40	8	no	—
418	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
419	C₄	—	2	1	no	—
420	C₄	—	4	2	no	—
421	C₄	—	5	2	no	—
422	C₄	—	10	1	no	—
423	C₄	—	10	1	no	—
424	C₄	—	20	2	no	—
425	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
426	C₄	#66084	1	1	yes	characteristic
427	C₄	C₂×D₅×D₈	1	1	yes	characteristic
428	C₄	D₅×#135	1	1	yes	characteristic
429	C₂	—	8	2	no	—
430	C₂	—	10	2	no	—
431	C₂	—	20	4	no	—
432	C₂	#10611271	1	1	yes	characteristic
433	C₂	C₄×D₅×D₈	1	1	yes	characteristic
434	C₂	#10611621	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1589	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×D₅×D₈	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1589	D₅
hypocenter	C₅	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #10611271	C₂	semidirect
3. C₅×#1589	C₂	semidirect
4. #10601674	C₂	semidirect
5. #10601655	C₂	semidirect
6. #10599362	C₂	semidirect
7. #10599349	C₂	semidirect
8. #10598965	C₂	semidirect
9. #10598946	C₂	semidirect
10. C₈×D₄₀	C₂	semidirect
11. C₈×#676	C₂	semidirect
16. C₅×#436	C₂²	semidirect
20. #65301	C₂²	semidirect
24. #65123	C₂²	semidirect
31. C₈×D₂₀	C₂²	semidirect
34. C₅×#335	C₂²	semidirect
35. C₅×D₄⋊C₈	C₂²	semidirect
36. C₅×C₈²	C₂²	semidirect
37. D₄⋊#168	C₂²	semidirect
38. #64703	C₂²	semidirect
39. #64699	C₂²	semidirect
40. #64679	C₂²	semidirect
41. #64678	C₂²	semidirect
42. #64675	C₂²	semidirect
43. #64674	C₂²	semidirect
44. C₈×#168	C₂²	semidirect
100. #1589	D₅	semidirect
151. D₄₀	M₁₆	semidirect
154. #676	D₈	semidirect
169. #436	C₂×D₅	semidirect
183. #335	C₂×D₅	semidirect
187. D₄⋊C₈	C₂×D₅	semidirect
191. C₈²	C₂×D₅	semidirect
213. D₂₀	C₂×M₁₆	semidirect
227. C₅×C₈	C₂×M₁₆	semidirect
228. C₅×C₈	C₂×D₈	semidirect
234. #168	C₂×D₈	semidirect
405. C₈	D₅×M₁₆	semidirect
406. C₈	D₅×D₈	semidirect
407. C₅	M₁₆×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₅×D₈	2
#10611271	2
C₅×#1589	2
#10601674	2
#10601655	2
#10599362	2
#10599349	2
#10598965	2
#10598946	2
C₈×D₄₀	2
C₈×#676	2
M₁₆×D₈	5