Subgroups — #13043530

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65791	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#3998	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614647	C₂	1	1	yes	maximal, characteristic
4	#10605007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊#674	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604414	C₂	1	2	yes	maximal, complemented
7	#10604413	C₂	1	2	yes	maximal, complemented
8	#10604413	C₂	1	2	yes	maximal, complemented
9	D₄×#674	C₂	1	2	yes	maximal, complemented
10	#10604367	C₂	1	1	yes	maximal, characteristic, complemented
11	#10604366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#525	C₄	1	1	yes	characteristic
13	C₂×#4094	C₂²	1	1	yes	characteristic
14	C₂³×#168	C₂²	1	1	yes	characteristic
15	#65791	—	2	4	no	—
16	C₂×#3998	—	2	4	no	—
17	C₂×#3998	C₂²	1	1	yes	characteristic
18	C₂×#3998	C₂²	1	2	yes	—
19	C₂×#3998	C₂²	1	1	yes	characteristic
20	C₂×#3998	C₂²	1	2	yes	complemented
21	C₂²×#674	C₂²	1	1	yes	characteristic
22	C₂²×#674	C₂²	1	1	yes	characteristic
23	C₂²×#674	C₂²	1	2	yes	—
24	C₂²×#674	C₂²	1	2	yes	complemented
25	#65523	C₄	1	1	yes	characteristic
26	#65496	C₄	1	1	yes	characteristic
27	#65300	C₄	1	2	yes	—
28	#65300	C₄	1	2	yes	—
29	D₄×#168	C₂²	1	2	yes	—
30	D₄×#168	C₂²	1	2	yes	—
31	#65288	C₄	1	1	yes	characteristic
32	#65286	C₂²	1	1	yes	characteristic
33	C₂²⋊#674	C₂²	1	1	yes	characteristic
34	C₂²⋊#674	C₂²	1	1	yes	characteristic
35	C₂²⋊#674	C₂²	1	1	yes	characteristic
36	C₂²⋊#674	C₂²	1	1	yes	characteristic
37	C₂²⋊#674	C₂²	1	2	yes	complemented
38	C₂²⋊#674	C₂²	1	2	yes	complemented
39	#64859	C₂²	1	2	yes	complemented
40	C₄⋊#674	C₂²	1	2	yes	complemented
41	C₄⋊#674	C₂²	1	2	yes	complemented
42	C₄×#674	C₂²	1	2	yes	complemented
43	#33436	—	5	1	no	maximal, Sylow
44	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₅×#123	C₈	1	2	yes	—
47	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
48	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
49	C₅×#121	C₈	1	1	yes	characteristic
50	C₅×#121	C₈	1	1	yes	characteristic
51	C₅×#120	C₈	1	2	yes	—
52	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
53	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
54	C₅×#117	C₂×C₄	1	1	yes	characteristic
55	#4094	—	2	2	no	—
56	#4094	—	2	2	no	—
57	C₂×#681	C₂×C₄	1	1	yes	characteristic
58	C₂×#681	C₂×C₄	1	1	yes	characteristic
59	C₂×#681	C₂×C₄	1	2	yes	—
60	C₂²×#168	—	2	2	no	—
61	C₂²×#168	—	2	2	no	—
62	C₂²×#168	C₂×C₄	1	1	yes	characteristic
63	C₂²×#168	C₂×C₄	1	1	yes	characteristic
64	C₂²×#168	C₂×C₄	1	1	yes	characteristic
65	C₂²×#168	C₂³	1	1	yes	characteristic
66	C₂²×#168	C₂³	1	1	yes	characteristic
67	C₂²×#168	C₂³	1	2	yes	—
68	C₂²×#168	C₂³	1	1	yes	characteristic
69	#3998	—	2	2	no	—
70	#3998	—	2	4	no	—
71	#3998	—	2	4	no	—
72	#3998	D₄	1	4	yes	complemented
73	C₂×#674	—	2	2	no	—
74	C₂×#674	—	2	2	no	—
75	C₂×#674	—	2	4	no	—
76	C₂×#674	—	2	4	no	—
77	C₂×#674	C₂³	1	1	yes	characteristic
78	C₂×#674	C₂³	1	1	yes	characteristic
79	C₂×#674	C₂³	1	1	yes	characteristic
80	C₂×#674	C₂³	1	2	yes	—
81	C₂×#674	C₂³	1	1	yes	characteristic
82	C₂×#674	C₂³	1	2	yes	—
83	C₂²⋊#168	C₂×C₄	1	2	yes	—
84	C₂²⋊#168	C₂×C₄	1	2	yes	—
85	C₂²⋊#168	C₂×C₄	1	2	yes	—
86	C₂²⋊#168	C₂×C₄	1	2	yes	—
87	C₄⋊#168	C₂×C₄	1	2	yes	—
88	C₄⋊#168	C₂×C₄	1	2	yes	—
89	#3935	C₂×C₄	1	2	yes	—
90	C₄×#168	C₂³	1	2	yes	—
91	C₂×#504	—	5	1	no	—
92	C₂²×M₃₂	—	5	1	no	—
93	#2929	—	5	1	no	—
94	#2169	—	5	2	no	—
95	#2168	—	5	2	no	—
96	#2168	—	5	2	no	—
97	D₄×C₁₆	—	5	2	no	—
98	#2151	—	5	1	no	—
99	#2113	—	5	1	no	—
100	C₂×C₂²⋊C₁₆	—	5	1	no	—
101	#2108	—	5	1	no	—
102	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
103	C₅×#41	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
106	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
107	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
108	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
109	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
120	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
121	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
122	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
123	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
124	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
125	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
126	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
127	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
128	C₄²×C₅	C₂²×C₄	1	2	yes	—
129	#681	—	2	2	no	—
130	#681	—	2	2	no	—
131	#681	—	2	4	no	—
132	C₂×#168	—	2	2	no	—
133	C₂×#168	—	2	2	no	—
134	C₂×#168	—	2	2	no	—
135	C₂×#168	—	2	1	no	—
136	C₂×#168	—	2	2	no	—
137	C₂×#168	—	2	1	no	—
138	C₂×#168	—	2	1	no	—
139	C₂×#168	—	2	1	no	—
140	C₂×#168	—	2	2	no	—
141	C₂×#168	C₂²×C₄	1	2	yes	—
142	C₂×#168	C₂²×C₄	1	1	yes	characteristic
143	C₂×#168	C₂²×C₄	1	1	yes	characteristic
144	C₂×#168	C₂²×C₄	1	2	yes	—
145	C₂×#168	C₂²×C₄	1	1	yes	characteristic
146	C₂×#168	C₂×D₄	1	2	yes	—
147	C₂×#168	#41	1	2	yes	—
148	C₂×#168	C₂⁴	1	1	yes	characteristic
149	#674	—	2	1	no	—
150	#674	—	2	1	no	—
151	#674	—	2	2	no	—
152	#674	—	2	1	no	—
153	#674	—	2	1	no	—
154	#674	C₂×D₄	1	4	yes	—
155	C₂×#131	—	5	1	no	—
156	C₂³×C₈	—	5	1	no	—
157	#525	AGL(1,𝔽₅)	1	1	yes	characteristic
158	#504	—	10	4	no	—
159	C₂×M₃₂	—	5	1	no	—
160	C₂×M₃₂	—	5	1	no	—
161	C₂×M₃₂	—	5	2	no	—
162	C₂×M₃₂	—	5	2	no	—
163	C₂×M₃₂	—	10	4	no	—
164	C₂²×C₁₆	—	5	1	no	—
165	C₂²×C₁₆	—	5	1	no	—
166	C₂²×C₁₆	—	5	2	no	—
167	C₂²×C₁₆	—	5	2	no	—
168	#435	—	5	2	no	—
169	#435	—	5	2	no	—
170	C₈×D₄	—	5	2	no	—
171	C₈×D₄	—	5	2	no	—
172	#424	—	5	1	no	—
173	#408	—	5	1	no	—
174	#407	—	5	1	no	—
175	#405	—	5	1	no	—
176	C₄⋊C₁₆	—	5	2	no	—
177	C₄⋊C₁₆	—	5	2	no	—
178	C₂²⋊C₁₆	—	5	1	no	—
179	C₂²⋊C₁₆	—	5	1	no	—
180	C₂²⋊C₁₆	—	5	1	no	—
181	C₂²⋊C₁₆	—	5	1	no	—
182	C₂²⋊C₁₆	—	5	2	no	—
183	C₂²⋊C₁₆	—	5	2	no	—
184	#346	—	5	2	no	—
185	C₄×C₁₆	—	5	2	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
190	C₂³×C₅	C₂²×C₈	1	2	yes	—
191	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
192	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
193	C₅×Q₈	—	2	2	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
209	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
210	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
213	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₅	#131	1	2	yes	—
215	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
216	#168	—	2	1	no	—
217	#168	—	2	1	no	—
218	#168	—	2	2	no	—
219	#168	—	2	2	no	—
220	#168	C₄×D₄	1	2	yes	—
221	#168	C₂²×D₄	1	1	yes	characteristic
222	#168	C₂×#41	1	1	yes	characteristic
223	C₂×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
224	C₂³×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
225	#131	—	10	2	no	—
226	#131	—	10	2	no	—
227	C₂×M₁₆	—	5	1	no	—
228	C₂×M₁₆	—	5	2	no	—
229	C₂×M₁₆	—	5	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	5	1	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	5	1	no	—
236	C₂²×C₈	—	5	2	no	—
237	C₂²×C₈	—	10	2	no	—
238	C₂²×C₈	—	10	2	no	—
239	#123	#170	1	2	yes	—
240	C₂²⋊Q₈	#170	1	1	yes	characteristic
241	C₂²⋊Q₈	#170	1	1	yes	characteristic
242	#121	#170	1	1	yes	characteristic
243	#121	#170	1	1	yes	characteristic
244	#120	#170	1	2	yes	—
245	C₄×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
246	C₄×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
247	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
248	M₃₂	—	5	4	no	—
249	M₃₂	—	10	4	no	—
250	M₃₂	—	10	4	no	—
251	M₃₂	—	10	2	no	—
252	C₂×C₁₆	—	5	2	no	—
253	C₂×C₁₆	—	5	1	no	—
254	C₂×C₁₆	—	5	1	no	—
255	C₂×C₁₆	—	5	1	no	—
256	C₂×C₁₆	—	5	1	no	—
257	C₂×C₁₆	—	5	2	no	—
258	C₂×C₁₆	—	10	4	no	—
259	C₂×C₁₆	—	10	4	no	—
260	C₂×C₁₆	—	10	2	no	—
261	C₂×C₁₆	—	10	2	no	—
262	C₄⋊C₈	—	5	2	no	—
263	C₄⋊C₈	—	5	2	no	—
264	C₂²⋊C₈	—	5	2	no	—
265	C₂²⋊C₈	—	5	2	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	5	2	no	—
268	#97	—	5	2	no	—
269	C₄×C₈	—	5	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	4	4	no	—
281	C₂²×C₅	C₈×D₄	1	2	yes	—
282	C₂²×C₅	#504	1	2	yes	complemented
283	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	C₈×D₄	1	2	yes	—
290	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₅	C₂×#131	1	1	yes	characteristic
292	C₂⁴	C₂×#170	1	1	yes	characteristic
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	C₂×Q₈	C₂×#170	1	1	yes	characteristic
296	C₂×D₄	C₂×#170	1	2	yes	—
297	C₂×D₄	C₂×#170	1	2	yes	—
298	C₂×D₄	C₂×#170	1	1	yes	characteristic
299	C₂×D₄	C₂×#170	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×#170	1	1	yes	characteristic
303	C₂²×C₄	C₂×#170	1	1	yes	characteristic
304	C₂²×C₄	C₂×#170	1	1	yes	characteristic
305	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
306	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
308	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
309	M₁₆	—	10	4	no	—
310	M₁₆	—	10	2	no	—
311	M₁₆	—	10	2	no	—
312	C₂×C₈	—	5	2	no	—
313	C₂×C₈	—	5	2	no	—
314	C₂×C₈	—	5	1	no	—
315	C₂×C₈	—	5	1	no	—
316	C₂×C₈	—	5	2	no	—
317	C₂×C₈	—	5	1	no	—
318	C₂×C₈	—	5	1	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	—	10	1	no	—
321	C₂×C₈	—	10	2	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	10	1	no	—
324	C₂×C₈	—	10	1	no	—
325	C₂×C₈	—	10	2	no	—
326	C₂×C₈	—	10	2	no	—
327	C₂×C₈	—	10	2	no	—
328	C₂×C₈	—	10	2	no	—
329	C₄⋊C₄	C₂×#170	1	1	yes	characteristic
330	C₄⋊C₄	C₂×#170	1	1	yes	characteristic
331	C₄⋊C₄	C₂×#170	1	2	yes	—
332	C₄⋊C₄	C₂×#170	1	2	yes	—
333	C₂²⋊C₄	C₂×#170	1	2	yes	—
334	C₂²⋊C₄	C₂×#170	1	2	yes	—
335	C₂²⋊C₄	C₂×#170	1	2	yes	—
336	C₂²⋊C₄	C₂×#170	1	2	yes	—
337	C₂²⋊C₄	C₂×#170	1	2	yes	—
338	C₄²	C₂²×AGL(1,𝔽₅)	1	2	yes	—
339	C₁₆	—	5	4	no	—
340	C₁₆	—	10	1	no	—
341	C₁₆	—	10	2	no	—
342	C₁₆	—	10	1	no	—
343	C₁₆	—	10	1	no	—
344	C₁₆	—	10	1	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	4	2	no	—
348	C₂×C₅	—	4	1	no	—
349	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
350	C₂×C₅	C₂×#504	1	1	yes	characteristic
351	C₂×C₅	#3407	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	C₂²×#170	1	1	yes	characteristic
356	C₂³	C₂²×#170	1	2	yes	—
357	C₂³	C₂²×#170	1	1	yes	characteristic
358	C₂³	C₂²×#170	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	D₄	—	2	4	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	#4131	1	2	yes	—
374	C₂×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
375	C₂×C₄	C₂²×#170	1	2	yes	—
376	C₂×C₄	C₂²×#170	1	2	yes	—
377	C₂×C₄	C₂²×#170	1	1	yes	characteristic
378	C₂×C₄	C₂²×#170	1	1	yes	characteristic
379	C₂×C₄	C₂²×#170	1	2	yes	—
380	C₂×C₄	C₂²×#170	1	1	yes	characteristic
381	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₈	—	5	1	no	—
383	C₈	—	5	1	no	—
384	C₈	—	5	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	1	no	—
387	C₈	—	10	1	no	—
388	C₈	—	10	2	no	—
389	C₅	#33436	1	1	yes	characteristic, complemented, Sylow
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	D₄×#170	1	2	yes	—
402	C₂²	#65791	1	2	yes	complemented
403	C₂²	C₂³×#170	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	D₄×#170	1	2	yes	—
410	C₄	C₂×#4131	1	1	yes	characteristic
411	C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×D₄×#170	1	1	yes	characteristic
417	C₂	C₂×#65791	1	1	yes	characteristic
418	C₂	#10617530	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting, prime radical	C₅×#525	C₄
cosocle	C₂×#168	C₂⁴
hypercenter	#525	AGL(1,𝔽₅)
hypocenter	C₅	#33436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#65791	C₂	semidirect
2. C₂²×#3998	C₂	semidirect
4. #10605007	C₂	semidirect
5. C₂×C₂²⋊#674	C₂	semidirect
6. #10604414	C₂	semidirect
7. #10604413	C₂	semidirect
8. #10604413	C₂	semidirect
9. D₄×#674	C₂	semidirect
10. #10604367	C₂	semidirect
11. #10604366	C₂	semidirect
20. C₂×#3998	C₂²	semidirect
24. C₂²×#674	C₂²	semidirect
37. C₂²⋊#674	C₂²	semidirect
38. C₂²⋊#674	C₂²	semidirect
39. #64859	C₂²	semidirect
40. C₄⋊#674	C₂²	semidirect
41. C₄⋊#674	C₂²	semidirect
42. C₄×#674	C₂²	semidirect
72. #3998	D₄	semidirect
282. C₂²×C₅	#504	semidirect
389. C₅	#33436	semidirect
402. C₂²	#65791	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65791	2
C₂²×#3998	2
#10614647	2
#10605007	2
C₂×C₂²⋊#674	2
#10604414	2
#10604413	2
D₄×#674	2
#10604367	2
#10604366	2
#33436	5