Subgroups — C₂×#11748095 #14429463

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
3	C₂×#91322	C₂	1	2	yes	maximal
4	C₂×C₃×#3951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90963	C₂	1	2	yes	maximal, complemented
6	#11748095	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65432	—	3	1	no	maximal, Hall
8	C₂²×Dic₃₀	C₂²	1	2	yes	—
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×Dic₆₀	—	2	1	no	—
12	C₂×Dic₆₀	—	2	1	no	—
13	C₂×Dic₆₀	—	2	2	no	—
14	C₂×Dic₆₀	C₂²	1	4	yes	complemented
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#901	—	2	2	no	—
17	C₅×#901	C₂²	1	4	yes	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
19	C₂×C₅×D₃×C₈	—	2	1	no	—
20	C₂×C₃×#681	C₂²	1	2	yes	—
21	#91322	—	2	4	no	—
22	#91322	C₂²	1	8	yes	—
23	C₂×#6663	—	2	2	no	—
24	C₂×#6659	—	2	2	no	—
25	C₃×#3951	C₂²	1	4	yes	complemented
26	#90963	C₂²	1	8	yes	complemented
27	C₂×#4896	—	5	1	no	maximal, Hall
28	C₂×C₅×#131	—	3	1	no	—
29	C₂×#4097	—	3	2	no	—
30	C₂²×Dic₂₀	—	3	1	no	—
31	#65432	—	3	8	no	—
32	C₂×#3956	—	3	2	no	—
33	C₂×#3951	D₃	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₅	—	2	2	no	—
36	C₂×Dic₃₀	—	2	2	no	—
37	C₂×Dic₃₀	—	2	2	no	—
38	C₂×Dic₃₀	—	2	2	no	—
39	C₂×Dic₃₀	—	2	2	no	—
40	C₂×Dic₃₀	—	2	2	no	—
41	C₂×Dic₃₀	C₂³	1	4	yes	—
42	C₂×C₅×#67	—	2	1	no	—
43	C₅×#235	—	2	1	no	—
44	C₅×#235	—	2	1	no	—
45	C₅×#235	D₄	1	2	yes	—
46	C₅×#235	C₂³	1	2	yes	—
47	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	Dic₆₀	—	2	4	no	—
55	Dic₆₀	—	2	4	no	—
56	C₅×#208	—	2	1	no	—
57	C₅×#208	C₂³	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
60	C₅×D₃×C₈	—	2	4	no	—
61	C₃×#681	—	2	2	no	—
62	C₃×#681	C₂³	1	4	yes	—
63	C₂×C₃×#168	—	2	2	no	—
64	#6663	—	2	8	no	—
65	#6659	—	2	8	no	—
66	C₂×#909	—	5	2	no	—
67	C₂²×Dic₁₂	—	5	1	no	—
68	C₂×#901	D₅	1	1	yes	characteristic
69	C₂×C₃×#108	—	5	1	no	—
70	C₂×#824	—	5	2	no	—
71	#4896	—	5	8	no	—
72	C₂×C₅×#41	—	3	1	no	—
73	C₂²×Dic₁₀	—	3	2	no	—
74	C₅×#131	—	3	4	no	—
75	C₅×#131	—	6	2	no	—
76	C₂×C₅×M₁₆	—	3	1	no	—
77	C₂×C₅×M₁₆	—	6	1	no	—
78	C₂²×C₅×C₈	—	6	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	#4097	—	3	8	no	—
81	#4097	—	6	4	no	—
82	C₂×#689	—	6	2	no	—
83	C₂×#687	—	6	2	no	—
84	C₂×#681	C₂×D₃	1	2	yes	—
85	C₂×Dic₂₀	—	3	4	no	—
86	C₂×Dic₂₀	—	6	1	no	—
87	C₂×Dic₂₀	—	6	1	no	—
88	C₂×Dic₂₀	—	6	2	no	—
89	#3956	—	3	8	no	—
90	#3951	C₂×D₃	1	4	yes	complemented
91	C₂×#473	—	15	1	no	Sylow
92	C₂³×C₃×C₅	#41	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×Dic₁₅	—	2	4	no	—
101	C₂×Dic₁₅	—	4	2	no	—
102	C₂×Dic₁₅	—	4	2	no	—
103	Dic₃₀	—	2	4	no	—
104	Dic₃₀	—	2	4	no	—
105	Dic₃₀	—	4	2	no	—
106	Dic₃₀	—	4	2	no	—
107	C₅×#67	—	2	2	no	—
108	C₅×#67	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₅×D₁₂	—	2	1	no	—
111	C₅×D₁₂	C₂×D₄	1	2	yes	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₅×Dic₆	—	2	1	no	—
115	C₅×Dic₆	C₂×D₄	1	2	yes	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
118	C₃×#168	—	2	4	no	—
119	C₅×C₃⋊C₈	—	2	2	no	—
120	C₂×#235	C₂×D₅	1	1	yes	characteristic
121	C₂²×Dic₆	—	5	2	no	—
122	C₂×C₃×M₁₆	—	5	2	no	—
123	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
124	C₂×#208	C₂×D₅	1	1	yes	characteristic
125	#909	—	5	8	no	—
126	#909	—	10	4	no	—
127	C₂×Dic₁₂	—	5	4	no	—
128	C₂×Dic₁₂	—	10	2	no	—
129	C₂×Dic₁₂	—	10	1	no	—
130	C₂×Dic₁₂	—	10	1	no	—
131	C₂×Dic₁₂	—	10	2	no	—
132	C₂×#204	—	10	2	no	—
133	#901	—	2	2	no	—
134	#901	C₂×D₅	1	4	yes	—
135	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
136	C₂×D₃×C₈	—	2	1	no	—
137	C₃×#108	—	5	4	no	—
138	#824	—	5	8	no	—
139	C₅×#41	—	3	2	no	—
140	C₅×#41	—	3	2	no	—
141	C₅×#41	—	6	1	no	—
142	C₅×#41	—	6	1	no	—
143	C₂×C₅×Q₈	—	3	1	no	—
144	C₂×C₅×D₄	—	3	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×Dic₅	—	6	2	no	—
149	C₂×Dic₁₀	—	3	4	no	—
150	C₂×Dic₁₀	—	6	2	no	—
151	C₂×Dic₁₀	—	6	2	no	—
152	C₂×Dic₁₀	—	6	2	no	—
153	C₂×Dic₁₀	—	6	2	no	—
154	C₂×Dic₁₀	—	6	2	no	—
155	C₅×M₁₆	—	3	2	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₅×M₁₆	—	6	4	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₂×C₅×C₈	—	6	4	no	—
160	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
161	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
162	C₂×C₅×C₈	D₁₂	1	2	yes	—
163	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
164	#689	—	6	8	no	—
165	#687	—	6	8	no	—
166	#681	—	2	2	no	—
167	#681	C₂²×D₃	1	4	yes	—
168	C₂×#168	—	2	2	no	—
169	Dic₂₀	—	6	4	no	—
170	Dic₂₀	—	6	4	no	—
171	C₂×#137	—	15	2	no	—
172	C₂²×Q₁₆	—	15	1	no	—
173	C₂×#131	—	3	1	no	—
174	#473	—	15	8	no	—
175	C₂×#108	—	5	1	no	—
176	C₂×#101	—	15	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	#121	1	1	yes	characteristic
179	C₂²×C₃×C₅	#121	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	4	2	no	—
183	C₃×C₄×C₅	#121	1	1	yes	characteristic
184	C₃×C₄×C₅	#121	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	Dic₁₅	—	4	4	no	—
188	C₅×Dic₃	—	2	2	no	—
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₂×#67	—	2	1	no	—
191	C₂²×Dic₃	—	10	2	no	—
192	#235	—	2	1	no	—
193	#235	—	2	1	no	—
194	#235	D₂₀	1	2	yes	—
195	#235	C₂²×D₅	1	2	yes	—
196	C₂×D₁₂	D₂₀	1	1	yes	characteristic
197	C₂×C₄×D₃	—	2	1	no	—
198	C₂×Dic₆	—	5	4	no	—
199	C₂×Dic₆	—	10	2	no	—
200	C₂×Dic₆	—	10	2	no	—
201	C₂×Dic₆	—	10	2	no	—
202	C₂×Dic₆	—	10	2	no	—
203	C₂×Dic₆	—	10	2	no	—
204	C₂×Dic₆	D₂₀	1	1	yes	characteristic
205	C₃×M₁₆	—	5	4	no	—
206	C₃×M₁₆	—	10	2	no	—
207	C₂×C₃×C₈	—	10	2	no	—
208	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
211	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
212	#208	—	2	1	no	—
213	#208	C₂²×D₅	1	2	yes	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	Dic₁₂	—	10	8	no	—
216	Dic₁₂	—	10	4	no	—
217	Dic₁₂	—	10	4	no	—
218	#204	—	10	8	no	—
219	ΓL(1,𝔽₂₅)	—	2	4	no	—
220	D₃×C₈	—	2	4	no	—
221	C₂³×C₅	—	6	1	no	—
222	C₂³×C₅	#239	1	1	yes	characteristic
223	C₅×Q₈	—	3	2	no	—
224	C₅×Q₈	—	6	1	no	—
225	C₅×D₄	—	3	2	no	—
226	C₅×D₄	—	6	2	no	—
227	C₅×D₄	—	6	2	no	—
228	C₅×D₄	—	6	1	no	—
229	C₂×C₄×C₅	—	6	1	no	—
230	C₂×C₄×C₅	—	6	2	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
234	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	#239	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₂×Dic₅	—	6	4	no	—
239	C₂×Dic₅	—	12	2	no	—
240	C₂×Dic₅	—	12	2	no	—
241	Dic₁₀	—	6	4	no	—
242	Dic₁₀	—	6	4	no	—
243	Dic₁₀	—	12	2	no	—
244	Dic₁₀	—	12	2	no	—
245	C₅×C₈	—	6	2	no	—
246	C₅×C₈	C₂×D₁₂	1	2	yes	—
247	C₅×C₈	C₂×D₁₂	1	2	yes	—
248	#168	—	2	4	no	—
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	—	15	2	no	—
251	#137	—	15	8	no	—
252	#137	—	30	4	no	—
253	C₂×Q₁₆	—	15	4	no	—
254	C₂×Q₁₆	—	30	2	no	—
255	C₂×Q₁₆	—	30	1	no	—
256	C₂×Q₁₆	—	30	1	no	—
257	C₂×Q₁₆	—	30	2	no	—
258	C₂×SD₁₆	—	30	2	no	—
259	#131	—	3	4	no	—
260	#131	—	6	2	no	—
261	C₂×M₁₆	—	3	1	no	—
262	C₂×M₁₆	—	5	2	no	—
263	C₂×M₁₆	—	6	1	no	—
264	C₂²×C₈	—	6	1	no	—
265	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
266	#108	—	5	4	no	—
267	#101	—	15	8	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	#473	1	2	yes	complemented
271	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
272	C₅×D₃	—	4	2	no	—
273	C₂³×C₃	#709	1	1	yes	characteristic
274	C₂²×D₃	—	2	1	no	—
275	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
277	C₂×C₃×C₄	#709	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
281	#67	—	2	2	no	—
282	#67	—	2	2	no	—
283	C₂×Dic₃	—	2	1	no	—
284	C₂×Dic₃	—	10	4	no	—
285	C₂×Dic₃	—	20	2	no	—
286	C₂×Dic₃	—	20	2	no	—
287	D₁₂	—	2	1	no	—
288	D₁₂	C₂×D₂₀	1	2	yes	—
289	C₄×D₃	—	2	2	no	—
290	C₄×D₃	—	2	2	no	—
291	Dic₆	—	2	1	no	—
292	Dic₆	—	10	4	no	—
293	Dic₆	—	10	4	no	—
294	Dic₆	—	20	2	no	—
295	Dic₆	—	20	2	no	—
296	Dic₆	C₂×D₂₀	1	2	yes	—
297	C₃×C₈	—	10	4	no	—
298	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
299	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
300	C₃⋊C₈	—	2	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	#895	1	1	yes	characteristic
305	C₂²×C₅	#895	1	1	yes	characteristic
306	C₂²×C₅	C₂×#239	1	1	yes	characteristic
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	#895	1	1	yes	characteristic
309	C₄×C₅	#895	1	1	yes	characteristic
310	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
311	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
312	Dic₅	—	12	4	no	—
313	#41	—	3	2	no	—
314	#41	—	3	2	no	—
315	#41	—	6	1	no	—
316	#41	—	6	1	no	—
317	C₂×Q₈	—	3	1	no	—
318	C₂×Q₈	—	15	4	no	—
319	C₂×Q₈	—	30	2	no	—
320	C₂×Q₈	—	30	2	no	—
321	C₂×Q₈	—	30	2	no	—
322	C₂×Q₈	—	30	2	no	—
323	C₂×Q₈	—	30	2	no	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂²×C₄	—	6	1	no	—
327	C₂²×C₄	—	30	2	no	—
328	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
329	Q₁₆	—	30	8	no	—
330	Q₁₆	—	30	4	no	—
331	Q₁₆	—	30	4	no	—
332	SD₁₆	—	30	8	no	—
333	M₁₆	—	3	2	no	—
334	M₁₆	—	5	4	no	—
335	M₁₆	—	6	1	no	—
336	M₁₆	—	6	4	no	—
337	M₁₆	—	10	2	no	—
338	C₂×C₈	—	6	1	no	—
339	C₂×C₈	—	6	4	no	—
340	C₂×C₈	—	10	2	no	—
341	C₂×C₈	#1203	1	1	yes	characteristic
342	C₂×C₈	#1203	1	1	yes	characteristic
343	C₂×C₈	#1203	1	2	yes	—
344	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	#4076	1	1	yes	characteristic
348	C₂²×C₃	#4076	1	1	yes	characteristic
349	C₂²×C₃	C₂×#709	1	1	yes	characteristic
350	C₂×D₃	—	2	2	no	—
351	C₂×D₃	—	4	2	no	—
352	C₃×C₄	#4076	1	1	yes	characteristic
353	C₃×C₄	#4076	1	1	yes	characteristic
354	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
355	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
356	Dic₃	—	2	2	no	—
357	Dic₃	—	20	4	no	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	12	2	no	—
361	C₂×C₅	#4896	1	2	yes	complemented
362	C₂×C₅	C₂×#895	1	1	yes	characteristic
363	C₂³	—	6	1	no	—
364	C₂³	#6769	1	1	yes	characteristic
365	Q₈	—	3	2	no	—
366	Q₈	—	6	1	no	—
367	Q₈	—	30	4	no	—
368	Q₈	—	30	4	no	—
369	Q₈	—	60	2	no	—
370	Q₈	—	60	2	no	—
371	D₄	—	3	2	no	—
372	D₄	—	6	2	no	—
373	D₄	—	6	2	no	—
374	D₄	—	6	1	no	—
375	C₂×C₄	—	6	1	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	30	4	no	—
379	C₂×C₄	—	60	2	no	—
380	C₂×C₄	—	60	2	no	—
381	C₂×C₄	#6769	1	1	yes	characteristic
382	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
383	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
384	C₂×C₄	C₂×#1203	1	1	yes	characteristic
385	C₂×C₄	C₂×#1203	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
387	C₈	—	6	2	no	—
388	C₈	—	10	4	no	—
389	C₈	C₂×#1203	1	2	yes	—
390	C₈	C₂×#1203	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	#65432	1	2	yes	complemented
394	C₂×C₃	C₂×#4076	1	1	yes	characteristic
395	D₃	—	4	2	no	—
396	C₅	C₂×#4896	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	6	2	no	—
399	C₂²	—	12	2	no	—
400	C₂²	#91460	1	1	yes	characteristic
401	C₂²	#91460	1	1	yes	characteristic
402	C₂²	C₂×#6769	1	1	yes	characteristic
403	C₄	—	6	2	no	—
404	C₄	—	60	4	no	—
405	C₄	#91460	1	1	yes	characteristic
406	C₄	#91460	1	1	yes	characteristic
407	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
408	C₄	C₂²×#1203	1	1	yes	characteristic
409	C₃	C₂×#65432	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	12	2	no	—
413	C₂	#11748095	1	2	yes	direct product factor
414	C₂	C₂×#91460	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#91460
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#473
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₆₀	C₂	semidirect
4. C₂×C₃×#3951	C₂	semidirect
5. C₂×#90963	C₂	semidirect
6. #11748095	C₂	direct (N × H)
14. C₂×Dic₆₀	C₂²	semidirect
25. C₃×#3951	C₂²	semidirect
26. #90963	C₂²	semidirect
33. C₂×#3951	D₃	semidirect
90. #3951	C₂×D₃	semidirect
270. C₂×C₃×C₅	#473	semidirect
345. C₃×C₅	C₂×#473	semidirect
361. C₂×C₅	#4896	semidirect
393. C₂×C₃	#65432	semidirect
396. C₅	C₂×#4896	semidirect
409. C₃	C₂×#65432	semidirect
413. C₂	#11748095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₆₀	2
C₂×C₅×#901	2
C₂×#91322	2
C₂×C₃×#3951	2
C₂×#90963	2
#11748095	2
C₂×#65432	3
C₂×#4896	5

Subgroups — C2×#11748095 #14429463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748095 #14429463