Subgroups — #72303538

Order 2048.

At least 8357 conjugacy classes of subgroups; only the 1206 normal subgroups are shown.

The subgroup lattice has 523 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72303389	C₂	1	1	yes	maximal, characteristic, complemented
2	#72303355	C₂	1	1	yes	maximal, characteristic, complemented
3	#72303321	C₂	1	4	yes	maximal, complemented
4	#72303246	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303213	C₂	1	1	yes	maximal, characteristic, complemented
6	#72302949	C₂	1	1	yes	maximal, characteristic, complemented
7	#72280972	C₂	1	1	yes	maximal, characteristic
8	#72280610	C₂	1	4	yes	maximal, complemented
9	#72262950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#63103	C₂²	1	1	yes	characteristic
11	C₂²×#3025	C₂²	1	2	yes	—
12	#10574081	C₂²	1	1	yes	characteristic
13	C₂×#60070	C₂²	1	1	yes	characteristic
14	#7629120	C₂²	1	1	yes	characteristic
15	C₂²×#2120	C₂²	1	2	yes	complemented
16	#6628897	C₄	1	4	yes	complemented
17	#6628896	C₄	1	4	yes	complemented
18	#6374112	C₂²	1	2	yes	complemented
19	C₂×#20620	C₂²	1	4	yes	—
20	C₂×#20612	C₂²	1	4	yes	—
21	#6370734	C₂²	1	2	yes	—
22	#6370703	C₂²	1	1	yes	characteristic
23	#6370703	C₂²	1	1	yes	characteristic
24	#6370692	C₂²	1	1	yes	characteristic
25	C₂×#12589	C₂²	1	4	yes	complemented
26	C₂×#12577	C₂²	1	4	yes	complemented
27	#492886	C₂²	1	2	yes	complemented
28	#355933	C₂²	1	2	yes	complemented
29	C₂×2₋¹⁺⁶	D₄	1	2	yes	—
30	C₂×H(7,𝔽₂)	C₂×C₄	1	4	yes	—
31	C₂×H(7,𝔽₂)	D₄	1	2	yes	—
32	C₂²×#585	D₄	1	4	yes	—
33	C₂²×#585	C₂³	1	2	yes	—
34	C₂²×#585	C₂³	1	1	yes	characteristic
35	C₂²×#568	D₄	1	1	yes	characteristic, complemented
36	C₂²×#568	D₄	1	1	yes	characteristic, complemented
37	C₂²×#525	D₄	1	1	yes	characteristic
38	C₂²×#525	D₄	1	1	yes	characteristic
39	C₂²×#525	C₂³	1	1	yes	characteristic
40	C₂²×#458	C₂×C₄	1	4	yes	complemented
41	C₂²×B(4,𝔽₂)	C₂×C₄	1	4	yes	complemented
42	C₂²×#413	D₄	1	2	yes	complemented
43	C₂²×#413	D₄	1	2	yes	complemented
44	C₂²×#413	C₂³	1	2	yes	—
45	C₂²×#410	D₄	1	4	yes	complemented
46	C₂²×#410	C₂³	1	2	yes	—
47	C₂²×#410	C₂³	1	2	yes	—
48	C₂×#2879	D₄	1	2	yes	complemented
49	C₂×#2879	C₂³	1	2	yes	—
50	C₂×#2879	C₂³	1	2	yes	—
51	#35446	C₂×C₄	1	2	yes	—
52	#35446	D₄	1	2	yes	—
53	#35346	C₂×C₄	1	2	yes	—
54	#35346	D₄	1	2	yes	—
55	#34044	D₄	1	1	yes	characteristic
56	#34044	D₄	1	1	yes	characteristic
57	#34044	C₂³	1	1	yes	characteristic
58	C₂×#1794	D₄	1	16	yes	complemented
59	#20609	C₂×C₄	1	8	yes	complemented
60	#20593	D₄	1	2	yes	complemented
61	#20592	D₄	1	2	yes	complemented
62	#20587	D₄	1	2	yes	—
63	#20586	D₄	1	2	yes	—
64	#20585	C₂×C₄	1	4	yes	—
65	#20584	D₄	1	4	yes	—
66	C₂×#585	C₂²⋊C₄	1	8	yes	—
67	C₂×#585	C₂×D₄	1	4	yes	—
68	C₂×#585	C₂×D₄	1	4	yes	—
69	C₂×#585	C₂×D₄	1	8	yes	—
70	C₂×#585	#41	1	8	yes	—
71	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
72	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
73	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
74	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
75	C₂²×2₋¹⁺⁴	#41	1	2	yes	—
76	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	8	yes	—
77	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
78	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
79	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
80	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
81	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
82	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
83	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
84	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
85	C₂³×#41	C₂×D₄	1	2	yes	—
86	C₂³×#41	C₂×D₄	1	1	yes	characteristic
87	C₂³×#41	C₂×D₄	1	1	yes	characteristic
88	C₂³×#41	C₂×D₄	1	2	yes	—
89	C₂³×#41	C₂×D₄	1	2	yes	—
90	C₂³×#41	C₂×D₄	1	1	yes	characteristic
91	C₂³×#41	C₂×D₄	1	1	yes	characteristic
92	C₂³×#41	C₂×D₄	1	1	yes	characteristic
93	C₂³×#41	C₂×D₄	1	1	yes	characteristic
94	C₂³×#41	#41	1	2	yes	—
95	C₂³×#41	C₂⁴	1	1	yes	characteristic
96	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂³×M₁₆	C₂×D₄	1	4	yes	—
98	C₂³×M₁₆	C₂×D₄	1	2	yes	—
99	C₂³×M₁₆	C₂×D₄	1	2	yes	—
100	C₂²×#123	C₂²⋊C₄	1	2	yes	—
101	C₂²×#123	C₂²⋊C₄	1	2	yes	—
102	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
103	C₂²×#123	C₂×D₄	1	1	yes	characteristic
104	C₂²×#120	C₂²⋊C₄	1	2	yes	—
105	C₂²×#120	C₂²⋊C₄	1	2	yes	—
106	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
107	C₂²×#120	C₂×D₄	1	1	yes	characteristic
108	C₂²×#117	C₂×D₄	1	1	yes	characteristic
109	C₂²×#117	C₂×D₄	1	1	yes	characteristic
110	C₂²×#117	C₂×D₄	1	1	yes	characteristic
111	C₂×#413	C₂×D₄	1	4	yes	—
112	C₂×#410	C₂×D₄	1	4	yes	—
113	C₂×#410	C₂×D₄	1	8	yes	—
114	C₂×#410	C₂×D₄	1	4	yes	—
115	C₂×#410	C₂×D₄	1	4	yes	—
116	C₂²×#99	C₂²×C₄	1	4	yes	—
117	C₂×#408	C₂×D₄	1	8	yes	—
118	#2308	C₂²⋊C₄	1	2	yes	—
119	#2308	C₂²⋊C₄	1	2	yes	—
120	#2308	C₂²⋊C₄	1	2	yes	—
121	#2308	C₂²⋊C₄	1	2	yes	—
122	#2308	C₂²×C₄	1	2	yes	—
123	#2308	C₂×D₄	1	2	yes	—
124	#1782	C₂²⋊C₄	1	8	yes	—
125	#1781	C₂²⋊C₄	1	8	yes	—
126	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	#585	#120	1	8	yes	—
128	#585	#121	1	16	yes	—
129	#585	#123	1	8	yes	—
130	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
131	C₂×H(5,𝔽₂)	C₄×D₄	1	16	yes	—
132	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂²×#41	C₄×D₄	1	2	yes	—
135	C₂²×#41	C₄×D₄	1	2	yes	—
136	C₂²×#41	C₄×D₄	1	2	yes	—
137	C₂²×#41	C₄×D₄	1	2	yes	—
138	C₂²×#41	#120	1	2	yes	—
139	C₂²×#41	#120	1	1	yes	characteristic
140	C₂²×#41	#120	1	1	yes	characteristic
141	C₂²×#41	#120	1	2	yes	—
142	C₂²×#41	#120	1	1	yes	characteristic
143	C₂²×#41	#120	1	1	yes	characteristic
144	C₂²×#41	#120	1	1	yes	characteristic
145	C₂²×#41	#120	1	1	yes	characteristic
146	C₂²×#41	#120	1	1	yes	characteristic
147	C₂²×#41	#120	1	1	yes	characteristic
148	C₂²×#41	#120	1	2	yes	—
149	C₂²×#41	#120	1	2	yes	—
150	C₂²×#41	#120	1	2	yes	—
151	C₂²×#41	#121	1	1	yes	characteristic
152	C₂²×#41	#121	1	1	yes	characteristic
153	C₂²×#41	#121	1	2	yes	—
154	C₂²×#41	#121	1	2	yes	—
155	C₂²×#41	#121	1	2	yes	—
156	C₂²×#41	#121	1	2	yes	—
157	C₂²×#41	#121	1	1	yes	characteristic
158	C₂²×#41	#121	1	1	yes	characteristic
159	C₂²×#41	#121	1	2	yes	—
160	C₂²×#41	#121	1	1	yes	characteristic
161	C₂²×#41	#121	1	1	yes	characteristic
162	C₂²×#41	#121	1	2	yes	—
163	C₂²×#41	#121	1	2	yes	—
164	C₂²×#41	#121	1	2	yes	—
165	C₂²×#41	#121	1	2	yes	—
166	C₂²×#41	#123	1	2	yes	—
167	C₂²×#41	#123	1	2	yes	—
168	C₂²×#41	#123	1	2	yes	—
169	C₂²×#41	#123	1	2	yes	—
170	C₂²×#41	#123	1	2	yes	—
171	C₂²×#41	#124	1	2	yes	—
172	C₂²×#41	#124	1	2	yes	—
173	C₂²×#41	#127	1	1	yes	characteristic
174	C₂²×#41	#127	1	1	yes	characteristic
175	C₂²×#41	#127	1	2	yes	—
176	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
177	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
178	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
179	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
180	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
181	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
182	C₂²×#41	C₂²×D₄	1	4	yes	—
183	C₂²×#41	C₂×#41	1	1	yes	characteristic
184	C₂²×#41	C₂×#41	1	1	yes	characteristic
185	C₂²×#41	C₂×#41	1	4	yes	—
186	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
187	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
188	C₂³×Q₈	#120	1	1	yes	characteristic
189	C₂³×Q₈	#120	1	1	yes	characteristic
190	C₂³×Q₈	#121	1	1	yes	characteristic
191	C₂³×Q₈	#121	1	1	yes	characteristic
192	C₂³×Q₈	#121	1	1	yes	characteristic
193	C₂³×Q₈	#121	1	2	yes	—
194	C₂³×Q₈	#121	1	2	yes	—
195	C₂³×Q₈	#123	1	2	yes	—
196	C₂³×Q₈	#124	1	2	yes	—
197	C₂³×Q₈	#127	1	1	yes	characteristic
198	C₂³×Q₈	C₂×#41	1	1	yes	characteristic
199	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂³×D₄	C₄×D₄	1	2	yes	—
204	C₂³×D₄	C₄×D₄	1	2	yes	—
205	C₂³×D₄	C₄×D₄	1	2	yes	—
206	C₂³×D₄	C₄×D₄	1	2	yes	—
207	C₂³×D₄	#120	1	1	yes	characteristic
208	C₂³×D₄	#120	1	1	yes	characteristic
209	C₂³×D₄	#120	1	2	yes	—
210	C₂³×D₄	#120	1	2	yes	—
211	C₂³×D₄	#120	1	2	yes	—
212	C₂³×D₄	#121	1	1	yes	characteristic
213	C₂³×D₄	#121	1	1	yes	characteristic
214	C₂³×D₄	#121	1	1	yes	characteristic
215	C₂³×D₄	#121	1	2	yes	—
216	C₂³×D₄	#121	1	2	yes	—
217	C₂³×D₄	#121	1	2	yes	—
218	C₂³×D₄	#121	1	2	yes	—
219	C₂³×D₄	#123	1	2	yes	—
220	C₂³×D₄	#123	1	2	yes	—
221	C₂³×D₄	#124	1	2	yes	—
222	C₂³×D₄	#127	1	1	yes	characteristic
223	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
224	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×#41	1	1	yes	characteristic
226	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂⁴×C₄	#120	1	2	yes	—
228	C₂⁴×C₄	#120	1	2	yes	—
229	C₂⁴×C₄	#121	1	2	yes	—
230	C₂⁴×C₄	#121	1	2	yes	—
231	C₂⁴×C₄	#121	1	2	yes	—
232	C₂⁴×C₄	#127	1	2	yes	—
233	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
235	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
236	C₂²×M₁₆	#120	1	4	yes	complemented
237	C₂³×C₈	#120	1	4	yes	complemented
238	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
242	#410	#120	1	8	yes	complemented
243	C₂×#99	C₂×C₂²⋊C₄	1	8	yes	—
244	C₂⁵	#379	1	2	yes	—
245	C₂⁵	#386	1	2	yes	—
246	C₂⁵	#386	1	2	yes	—
247	C₂⁵	#390	1	2	yes	—
248	C₂⁵	#392	1	2	yes	—
249	C₂⁵	#394	1	2	yes	—
250	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
251	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂⁵	C₂×#121	1	1	yes	characteristic
253	H(5,𝔽₂)	#386	1	16	yes	—
254	C₂×#41	B(4,𝔽₂)	1	4	yes	—
255	C₂×#41	B(4,𝔽₂)	1	4	yes	—
256	C₂×#41	B(4,𝔽₂)	1	4	yes	—
257	C₂×#41	B(4,𝔽₂)	1	4	yes	—
258	C₂×#41	C₂×#120	1	2	yes	—
259	C₂×#41	C₂×#120	1	2	yes	—
260	C₂×#41	C₂×#121	1	4	yes	—
261	C₂×#41	C₂×#123	1	2	yes	—
262	C₂×#41	#525	1	4	yes	—
263	C₂×#41	#525	1	2	yes	—
264	C₂×#41	#534	1	2	yes	—
265	C₂×#41	#534	1	2	yes	—
266	C₂×#41	#534	1	2	yes	—
267	C₂×#41	#534	1	4	yes	—
268	C₂×#41	#535	1	2	yes	—
269	C₂×#41	#538	1	4	yes	—
270	C₂×#41	D₄²	1	4	yes	—
271	C₂×#41	D₄²	1	4	yes	—
272	C₂×#41	D₄²	1	4	yes	—
273	C₂×#41	#546	1	4	yes	—
274	C₂×#41	#546	1	4	yes	—
275	C₂×#41	#546	1	4	yes	—
276	C₂×#41	#546	1	4	yes	—
277	C₂×#41	#551	1	4	yes	—
278	C₂²×Q₈	#386	1	2	yes	—
279	C₂²×Q₈	#390	1	2	yes	—
280	C₂²×Q₈	#392	1	1	yes	characteristic
281	C₂²×Q₈	#392	1	1	yes	characteristic
282	C₂²×Q₈	#392	1	2	yes	—
283	C₂²×Q₈	#392	1	1	yes	characteristic
284	C₂²×Q₈	#392	1	1	yes	characteristic
285	C₂²×Q₈	#394	1	2	yes	—
286	C₂²×Q₈	#394	1	2	yes	—
287	C₂²×Q₈	#394	1	2	yes	—
288	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
289	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
290	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
291	C₂²×Q₈	#525	1	4	yes	—
292	C₂²×Q₈	C₂×#124	1	1	yes	characteristic
293	C₂²×Q₈	#538	1	4	yes	—
294	C₂²×D₄	#379	1	2	yes	—
295	C₂²×D₄	#379	1	2	yes	—
296	C₂²×D₄	#386	1	2	yes	—
297	C₂²×D₄	#386	1	2	yes	—
298	C₂²×D₄	#386	1	2	yes	—
299	C₂²×D₄	#386	1	2	yes	—
300	C₂²×D₄	#386	1	2	yes	—
301	C₂²×D₄	#386	1	2	yes	—
302	C₂²×D₄	#386	1	2	yes	—
303	C₂²×D₄	#386	1	2	yes	—
304	C₂²×D₄	#386	1	2	yes	—
305	C₂²×D₄	#390	1	2	yes	—
306	C₂²×D₄	#390	1	2	yes	—
307	C₂²×D₄	#390	1	2	yes	—
308	C₂²×D₄	#392	1	1	yes	characteristic
309	C₂²×D₄	#392	1	1	yes	characteristic
310	C₂²×D₄	#392	1	2	yes	—
311	C₂²×D₄	#392	1	1	yes	characteristic
312	C₂²×D₄	#392	1	1	yes	characteristic
313	C₂²×D₄	#392	1	2	yes	—
314	C₂²×D₄	#392	1	2	yes	—
315	C₂²×D₄	#394	1	2	yes	—
316	C₂²×D₄	#394	1	2	yes	—
317	C₂²×D₄	#394	1	2	yes	—
318	C₂²×D₄	#394	1	2	yes	—
319	C₂²×D₄	#394	1	2	yes	—
320	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
325	C₂²×D₄	#518	1	4	yes	—
326	C₂²×D₄	C₂×#120	1	1	yes	characteristic
327	C₂²×D₄	C₂×#120	1	1	yes	characteristic
328	C₂²×D₄	C₂×#120	1	1	yes	characteristic
329	C₂²×D₄	C₂×#121	1	1	yes	characteristic
330	C₂²×D₄	C₂×#121	1	1	yes	characteristic
331	C₂²×D₄	C₂×#123	1	1	yes	characteristic
332	C₂²×D₄	C₂×#123	1	1	yes	characteristic
333	C₂²×D₄	C₂×#124	1	1	yes	characteristic
334	C₂²×D₄	D₄²	1	4	yes	—
335	C₂²×D₄	#546	1	4	yes	—
336	C₂²×D₄	#546	1	4	yes	—
337	C₂²×D₄	#551	1	4	yes	—
338	C₂³×C₄	#379	1	2	yes	—
339	C₂³×C₄	#386	1	2	yes	—
340	C₂³×C₄	#386	1	2	yes	—
341	C₂³×C₄	#386	1	2	yes	—
342	C₂³×C₄	#386	1	2	yes	—
343	C₂³×C₄	#390	1	2	yes	—
344	C₂³×C₄	#390	1	2	yes	—
345	C₂³×C₄	#390	1	2	yes	—
346	C₂³×C₄	#392	1	2	yes	—
347	C₂³×C₄	#392	1	2	yes	—
348	C₂³×C₄	#392	1	2	yes	—
349	C₂³×C₄	#392	1	2	yes	—
350	C₂³×C₄	#392	1	2	yes	—
351	C₂³×C₄	#392	1	2	yes	—
352	C₂³×C₄	#392	1	2	yes	—
353	C₂³×C₄	#394	1	2	yes	—
354	C₂³×C₄	#394	1	2	yes	—
355	C₂³×C₄	#394	1	2	yes	—
356	C₂³×C₄	#394	1	2	yes	—
357	C₂³×C₄	#394	1	2	yes	—
358	C₂³×C₄	#394	1	2	yes	—
359	C₂³×C₄	#394	1	2	yes	—
360	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
361	C₂³×C₄	C₂×#120	1	2	yes	—
362	C₂³×C₄	C₂×#120	1	1	yes	characteristic
363	C₂³×C₄	C₂×#120	1	1	yes	characteristic
364	C₂³×C₄	C₂×#120	1	1	yes	characteristic
365	C₂³×C₄	C₂×#120	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	1	yes	characteristic
367	C₂³×C₄	C₂×#121	1	1	yes	characteristic
368	C₂³×C₄	C₂×#121	1	1	yes	characteristic
369	C₂³×C₄	C₂×#121	1	1	yes	characteristic
370	C₂³×C₄	C₂×#121	1	1	yes	characteristic
371	C₂³×C₄	C₂×#121	1	1	yes	characteristic
372	C₂³×C₄	C₂×#121	1	1	yes	characteristic
373	C₂³×C₄	C₂×#121	1	1	yes	characteristic
374	C₂³×C₄	C₂×#123	1	1	yes	characteristic
375	C₂³×C₄	#525	1	2	yes	—
376	C₂³×C₄	C₂×#127	1	1	yes	characteristic
377	C₂³×C₄	C₂×#127	1	1	yes	characteristic
378	C₂³×C₄	#534	1	2	yes	—
379	C₂³×C₄	#535	1	2	yes	—
380	C₂³×C₄	D₄²	1	4	yes	—
381	C₂³×C₄	D₄²	1	4	yes	—
382	C₂³×C₄	#546	1	4	yes	—
383	C₂³×C₄	#546	1	4	yes	—
384	C₂⁴	#1438	1	2	yes	—
385	C₂⁴	#1438	1	2	yes	—
386	C₂⁴	#1438	1	2	yes	—
387	C₂⁴	#1438	1	2	yes	—
388	C₂⁴	C₂×#379	1	1	yes	characteristic
389	C₂⁴	C₂×#386	1	1	yes	characteristic
390	C₂⁴	C₂×#386	1	1	yes	characteristic
391	C₂⁴	C₂×#386	1	1	yes	characteristic
392	C₂⁴	C₂×#390	1	1	yes	characteristic
393	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
394	C₂⁴	#2358	1	4	yes	—
395	C₂⁴	C₂×#392	1	1	yes	characteristic
396	C₂⁴	C₂×#394	1	1	yes	characteristic
397	C₂⁴	#2408	1	2	yes	—
398	C₂⁴	#2534	1	2	yes	—
399	C₂×Q₈	#2021	1	4	yes	—
400	C₂×Q₈	#2021	1	4	yes	—
401	C₂×Q₈	#2424	1	4	yes	—
402	C₂×Q₈	#2472	1	4	yes	—
403	C₂×Q₈	#2617	1	2	yes	—
404	C₂×Q₈	#2622	1	2	yes	—
405	C₂×Q₈	#2847	1	2	yes	—
406	C₂×Q₈	#2849	1	2	yes	—
407	C₂×D₄	#1889	1	8	yes	—
408	C₂×D₄	#1889	1	8	yes	—
409	C₂×D₄	#2021	1	4	yes	—
410	C₂×D₄	#2021	1	4	yes	—
411	C₂×D₄	C₂×#386	1	2	yes	—
412	C₂×D₄	C₄×#120	1	2	yes	—
413	C₂×D₄	#2308	1	2	yes	—
414	C₂×D₄	#2321	1	2	yes	—
415	C₂×D₄	D₄×C₂²⋊C₄	1	4	yes	—
416	C₂×D₄	#2358	1	4	yes	—
417	C₂×D₄	#2403	1	2	yes	—
418	C₂×D₄	#2403	1	2	yes	—
419	C₂×D₄	#2404	1	2	yes	—
420	C₂×D₄	#2405	1	2	yes	—
421	C₂×D₄	#2410	1	4	yes	—
422	C₂×D₄	#2410	1	2	yes	—
423	C₂×D₄	#2410	1	2	yes	—
424	C₂×D₄	#2411	1	2	yes	—
425	C₂×D₄	#2412	1	2	yes	—
426	C₂×D₄	#2412	1	4	yes	—
427	C₂×D₄	#2418	1	4	yes	—
428	C₂×D₄	#2472	1	4	yes	—
429	C₂²×C₄	#1438	1	2	yes	—
430	C₂²×C₄	#1438	1	2	yes	—
431	C₂²×C₄	#1438	1	2	yes	—
432	C₂²×C₄	#1438	1	2	yes	—
433	C₂²×C₄	#2021	1	4	yes	—
434	C₂²×C₄	#2021	1	4	yes	—
435	C₂²×C₄	#2021	1	4	yes	—
436	C₂²×C₄	#2021	1	4	yes	—
437	C₂²×C₄	C₂×#386	1	1	yes	characteristic
438	C₂²×C₄	C₂×#390	1	1	yes	characteristic
439	C₂²×C₄	C₄×#120	1	2	yes	—
440	C₂²×C₄	#2321	1	2	yes	—
441	C₂²×C₄	C₂×#392	1	1	yes	characteristic
442	C₂²×C₄	C₂×#392	1	1	yes	characteristic
443	C₂²×C₄	C₂×#392	1	1	yes	characteristic
444	C₂²×C₄	C₂×#394	1	1	yes	characteristic
445	C₂²×C₄	C₂×#394	1	1	yes	characteristic
446	C₂²×C₄	C₂×#394	1	1	yes	characteristic
447	C₂²×C₄	#2403	1	2	yes	—
448	C₂²×C₄	#2403	1	2	yes	—
449	C₂²×C₄	#2404	1	2	yes	—
450	C₂²×C₄	#2405	1	2	yes	—
451	C₂²×C₄	#2408	1	2	yes	—
452	C₂²×C₄	#2410	1	2	yes	—
453	C₂²×C₄	#2410	1	2	yes	—
454	C₂²×C₄	#2410	1	4	yes	—
455	C₂²×C₄	#2410	1	4	yes	—
456	C₂²×C₄	#2411	1	2	yes	—
457	C₂²×C₄	#2412	1	2	yes	—
458	C₂²×C₄	#2418	1	4	yes	—
459	C₂²×C₄	#2424	1	4	yes	—
460	C₂²×C₄	#2424	1	4	yes	—
461	C₂²×C₄	#2424	1	4	yes	—
462	C₂²×C₄	#2433	1	2	yes	—
463	C₂²×C₄	#2433	1	2	yes	—
464	C₂²×C₄	#2534	1	2	yes	—
465	C₂²×C₄	#2539	1	2	yes	—
466	C₂²×C₄	#2539	1	2	yes	—
467	C₂²×C₄	#2613	1	1	yes	characteristic
468	C₂²×C₄	#2613	1	1	yes	characteristic
469	C₂²×C₄	#2617	1	2	yes	—
470	C₂²×C₄	#2846	1	1	yes	characteristic
471	C₂²×C₄	#2847	1	2	yes	—
472	C₂²×C₄	#2849	1	1	yes	characteristic
473	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
474	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
475	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
476	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
477	C₂³	#10991	1	4	yes	—
478	C₂³	#10991	1	4	yes	—
479	C₂³	C₂×#1438	1	1	yes	characteristic
480	C₂³	#13867	1	2	yes	—
481	C₂³	#13967	1	2	yes	—
482	C₂³	#13967	1	2	yes	—
483	C₂³	#13995	1	2	yes	—
484	C₂³	#14134	1	2	yes	—
485	C₂³	#14715	1	1	yes	characteristic
486	C₂³	#14725	1	2	yes	—
487	C₂³	#14911	1	1	yes	characteristic
488	C₂³	C₂×#1889	1	2	yes	—
489	C₂³	C₂×#1889	1	2	yes	—
490	C₂×C₄	#10991	1	4	yes	—
491	C₂×C₄	#10991	1	4	yes	—
492	C₂×C₄	#13995	1	2	yes	—
493	C₂×C₄	#14255	1	1	yes	characteristic
494	C₂×C₄	#14694	1	1	yes	characteristic
495	C₂×C₄	#14715	1	1	yes	characteristic
496	C₂×C₄	#14716	1	2	yes	—
497	C₂×C₄	#14716	1	2	yes	—
498	C₂×C₄	#14718	1	2	yes	—
499	C₂×C₄	#14718	1	2	yes	—
500	C₂×C₄	#14725	1	2	yes	—
501	C₂×C₄	#14911	1	1	yes	characteristic
502	C₂×C₄	C₂×#2021	1	1	yes	characteristic
503	C₂×C₄	C₂×#2021	1	1	yes	characteristic
504	C₂×C₄	C₂×#2021	1	1	yes	characteristic
505	C₂×C₄	C₂×#2021	1	1	yes	characteristic
506	C₂×C₄	C₂×#2021	1	2	yes	—
507	C₂×C₄	C₂×#2021	1	2	yes	—
508	C₂×C₄	#23900	1	4	yes	—
509	C₂×C₄	#23900	1	4	yes	—
510	C₂×C₄	#23984	1	4	yes	—
511	C₂×C₄	#23984	1	4	yes	—
512	C₂²	#154195	1	1	yes	characteristic
513	C₂²	C₂×#10991	1	1	yes	characteristic
514	C₂²	C₂×#10991	1	1	yes	characteristic
515	C₂²	#364410	1	4	yes	—
516	C₄	#394058	1	1	yes	characteristic
517	C₄	#394058	1	1	yes	characteristic
518	C₄	#394167	1	4	yes	—
519	C₄	#405156	1	1	yes	characteristic
520	C₄	#405156	1	1	yes	characteristic
521	C₂	#72218766	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#394058
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
socle	C₂	#72218766
prime radical	#72280972	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72303389	C₂	semidirect
2. #72303355	C₂	semidirect
3. #72303321	C₂	semidirect
4. #72303246	C₂	semidirect
5. #72303213	C₂	semidirect
6. #72302949	C₂	semidirect
8. #72280610	C₂	semidirect
9. #72262950	C₂	semidirect
15. C₂²×#2120	C₂²	semidirect
16. #6628897	C₄	semidirect
17. #6628896	C₄	semidirect
18. #6374112	C₂²	semidirect
25. C₂×#12589	C₂²	semidirect
26. C₂×#12577	C₂²	semidirect
27. #492886	C₂²	semidirect
28. #355933	C₂²	semidirect
35. C₂²×#568	D₄	semidirect
36. C₂²×#568	D₄	semidirect
40. C₂²×#458	C₂×C₄	semidirect
41. C₂²×B(4,𝔽₂)	C₂×C₄	semidirect
42. C₂²×#413	D₄	semidirect
43. C₂²×#413	D₄	semidirect
45. C₂²×#410	D₄	semidirect
48. C₂×#2879	D₄	semidirect
58. C₂×#1794	D₄	semidirect
59. #20609	C₂×C₄	semidirect
60. #20593	D₄	semidirect
61. #20592	D₄	semidirect
236. C₂²×M₁₆	#120	semidirect
237. C₂³×C₈	#120	semidirect
242. #410	#120	semidirect

Maximal subgroups

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

subgroup	index
#72303389	2
#72303355	2
#72303321	2
#72303246	2
#72303213	2
#72302949	2
#72280972	2
#72280610	2
#72262950	2