Subgroups — C₇₃×#25638 #32935042

Order 18688.

1134 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#497×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#463×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	2	yes	maximal
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1880	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1878	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
16	#556×C₇₃	—	2	4	no	—
17	#556×C₇₃	—	2	4	no	—
18	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#126×C₇₃	—	2	2	no	—
20	C₂×#124×C₇₃	C₂²	1	2	yes	—
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
23	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₇₃	—	2	1	no	—
27	#497×C₇₃	—	2	4	no	—
28	#463×C₇₃	—	2	4	no	—
29	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	#397×C₇₃	—	2	1	no	—
37	#393×C₇₃	—	2	1	no	—
38	#391×C₇₃	C₂²	1	2	yes	—
39	#390×C₇₃	C₂²	1	2	yes	—
40	#388×C₇₃	—	2	2	no	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#336×C₇₃	C₂²	1	2	yes	—
44	#336×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	—	2	1	no	—
51	C₂×Q₁₆×C₇₃	—	2	4	no	—
52	C₂×Q₁₆×C₇₃	—	2	4	no	—
53	C₂×Q₁₆×C₇₃	—	4	2	no	—
54	C₂×SD₁₆×C₇₃	—	2	4	no	—
55	C₂×SD₁₆×C₇₃	—	2	2	no	—
56	C₂×SD₁₆×C₇₃	—	2	4	no	—
57	C₂×SD₁₆×C₇₃	—	4	2	no	—
58	C₂×SD₁₆×C₇₃	—	4	2	no	—
59	C₂×D₈×C₇₃	—	2	2	no	—
60	C₂×D₈×C₇₃	—	4	2	no	—
61	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₇₃	—	2	2	no	—
65	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
66	#126×C₇₃	—	2	16	no	—
67	#124×C₇₃	—	2	4	no	—
68	#124×C₇₃	—	2	4	no	—
69	#124×C₇₃	—	2	2	no	—
70	#124×C₇₃	—	2	2	no	—
71	C₂²⋊Q₈×C₇₃	—	2	8	no	—
72	C₄×Q₈×C₇₃	—	2	4	no	—
73	C₄×Q₈×C₇₃	—	2	4	no	—
74	C₄×Q₈×C₇₃	—	2	2	no	—
75	C₄×Q₈×C₇₃	—	2	2	no	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	C₄×D₄×C₇₃	D₄	1	4	yes	—
78	#117×C₇₃	—	2	8	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₄²×C₇₃	—	2	2	no	—
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	2	no	—
99	#103×C₇₃	—	4	2	no	—
100	#103×C₇₃	—	4	2	no	—
101	#102×C₇₃	—	2	4	no	—
102	#102×C₇₃	—	2	2	no	—
103	#97×C₇₃	—	2	2	no	—
104	#95×C₇₃	—	2	1	no	—
105	#95×C₇₃	—	2	2	no	—
106	#95×C₇₃	—	2	2	no	—
107	C₂⁴×C₇₃	—	2	1	no	—
108	C₂⁴×C₇₃	—	2	1	no	—
109	C₂×Q₈×C₇₃	—	2	2	no	—
110	C₂×Q₈×C₇₃	—	2	2	no	—
111	C₂×Q₈×C₇₃	—	2	1	no	—
112	C₂×Q₈×C₇₃	—	2	1	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	2	no	—
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	4	2	no	—
120	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₇₃	—	2	1	no	—
122	C₂×D₄×C₇₃	—	2	1	no	—
123	C₂×D₄×C₇₃	—	2	1	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	2	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	—	2	1	no	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	4	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	4	4	no	—
135	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₇₃	—	4	8	no	—
141	SD₁₆×C₇₃	—	4	8	no	—
142	SD₁₆×C₇₃	—	4	4	no	—
143	D₈×C₇₃	—	4	4	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	1	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	#41	1	4	yes	—
151	C₄⋊C₄×C₇₃	—	2	8	no	—
152	C₄⋊C₄×C₇₃	—	2	4	no	—
153	C₄⋊C₄×C₇₃	—	2	4	no	—
154	C₄⋊C₄×C₇₃	—	2	2	no	—
155	C₄⋊C₄×C₇₃	—	2	4	no	—
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	2	2	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₇₃	—	2	8	no	—
161	C₂²⋊C₄×C₇₃	—	2	8	no	—
162	C₂²⋊C₄×C₇₃	—	2	4	no	—
163	C₂²⋊C₄×C₇₃	—	4	4	no	—
164	C₂²⋊C₄×C₇₃	—	4	2	no	—
165	C₂²⋊C₄×C₇₃	—	4	2	no	—
166	C₂²⋊C₄×C₇₃	—	8	2	no	—
167	C₄²×C₇₃	—	2	8	no	—
168	C₄²×C₇₃	—	2	2	no	—
169	C₄²×C₇₃	—	2	2	no	—
170	C₄²×C₇₃	—	8	1	no	—
171	C₄²×C₇₃	C₂×D₄	1	2	yes	—
172	C₄²×C₇₃	C₂×D₄	1	2	yes	—
173	C₂³×C₇₃	—	2	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	4	1	no	—
177	C₂³×C₇₃	—	4	1	no	—
178	C₂³×C₇₃	—	4	1	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	—	4	1	no	—
182	C₂³×C₇₃	—	4	1	no	—
183	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₇₃	—	2	4	no	—
185	Q₈×C₇₃	—	2	4	no	—
186	Q₈×C₇₃	—	4	4	no	—
187	Q₈×C₇₃	—	4	2	no	—
188	Q₈×C₇₃	—	4	2	no	—
189	Q₈×C₇₃	—	4	1	no	—
190	Q₈×C₇₃	—	4	1	no	—
191	Q₈×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	2	2	no	—
193	D₄×C₇₃	—	2	2	no	—
194	D₄×C₇₃	—	4	1	no	—
195	D₄×C₇₃	—	4	1	no	—
196	D₄×C₇₃	—	4	2	no	—
197	D₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	4	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	4	8	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	2	no	—
212	C₂×C₄×C₇₃	—	4	2	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	2	no	—
215	C₂×C₄×C₇₃	—	4	2	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	#120	1	2	yes	—
219	C₂×C₄×C₇₃	#120	1	2	yes	—
220	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
224	C₈×C₇₃	—	2	4	no	—
225	C₈×C₇₃	—	4	1	no	—
226	C₈×C₇₃	—	4	1	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	4	2	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	8	2	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	—	8	2	no	—
234	C₂²×C₇₃	—	8	1	no	—
235	C₂²×C₇₃	—	8	1	no	—
236	C₂²×C₇₃	—	8	1	no	—
237	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
238	C₂²×C₇₃	#550	1	2	yes	—
239	C₂²×C₇₃	#575	1	2	yes	—
240	C₂²×C₇₃	#577	1	1	yes	characteristic
241	C₂²×C₇₃	#578	1	1	yes	characteristic
242	C₄×C₇₃	—	2	2	no	—
243	C₄×C₇₃	—	2	2	no	—
244	C₄×C₇₃	—	4	4	no	—
245	C₄×C₇₃	—	4	2	no	—
246	C₄×C₇₃	—	4	2	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	8	2	no	—
249	C₄×C₇₃	—	8	1	no	—
250	C₄×C₇₃	#532	1	1	yes	characteristic
251	C₄×C₇₃	#535	1	1	yes	characteristic
252	C₄×C₇₃	#546	1	2	yes	—
253	#25638	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	8	2	no	—
255	C₂×C₇₃	—	16	1	no	—
256	C₂×C₇₃	#2431	1	1	yes	characteristic
257	C₂×C₇₃	#3005	1	1	yes	characteristic
258	C₂×C₇₃	#3013	1	1	yes	characteristic
259	C₂×C₇₃	#3401	1	2	yes	—
260	C₂×C₇₃	#3402	1	2	yes	—
261	C₂×#556	C₂×C₇₃	1	1	yes	characteristic, complemented
262	C₂×#497	C₂×C₇₃	1	1	yes	characteristic, complemented
263	C₂×#463	C₂×C₇₃	1	1	yes	characteristic
264	#2592	C₂×C₇₃	1	1	yes	characteristic, complemented
265	#2015	C₂×C₇₃	1	2	yes	complemented
266	#2012	C₂×C₇₃	1	2	yes	—
267	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
268	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
269	#1880	C₂×C₇₃	1	2	yes	complemented
270	#1878	C₂×C₇₃	1	2	yes	complemented
271	#1762	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₇₃	#25638	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
274	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
275	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
276	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
277	#556	—	2	4	no	—
278	#556	—	2	4	no	—
279	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×#126	—	2	2	no	—
281	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₇₃	1	2	yes	—
283	C₂×C₂²⋊Q₈	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×#117	—	2	1	no	—
288	#497	—	2	4	no	—
289	#463	—	2	4	no	—
290	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×#103	C₂²×C₇₃	1	2	yes	—
293	C₂×#103	C₂²×C₇₃	1	2	yes	—
294	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₇₃	1	2	yes	—
296	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
297	#397	—	2	1	no	—
298	#393	—	2	1	no	—
299	#391	C₂²×C₇₃	1	2	yes	—
300	#390	C₂²×C₇₃	1	2	yes	—
301	#388	—	2	2	no	—
302	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
303	#340	C₂²×C₇₃	1	2	yes	—
304	#336	C₂²×C₇₃	1	2	yes	—
305	#336	C₂²×C₇₃	1	2	yes	—
306	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
308	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
309	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
311	C₂³×C₄	—	2	1	no	—
312	C₂×Q₁₆	—	2	4	no	—
313	C₂×Q₁₆	—	2	4	no	—
314	C₂×Q₁₆	—	4	2	no	—
315	C₂×SD₁₆	—	2	4	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	4	no	—
318	C₂×SD₁₆	—	4	2	no	—
319	C₂×SD₁₆	—	4	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	4	2	no	—
322	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
327	#126	—	2	16	no	—
328	#124	—	2	4	no	—
329	#124	—	2	4	no	—
330	#124	—	2	2	no	—
331	#124	—	2	2	no	—
332	C₂²⋊Q₈	—	2	8	no	—
333	C₄×Q₈	—	2	4	no	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	D₄×C₇₃	1	4	yes	—
339	#117	—	2	8	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
357	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
358	C₄⋊C₈	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	4	2	no	—
361	#103	—	4	2	no	—
362	#102	—	2	4	no	—
363	#102	—	2	2	no	—
364	#97	—	2	2	no	—
365	#95	—	2	1	no	—
366	#95	—	2	2	no	—
367	#95	—	2	2	no	—
368	C₂⁴	—	2	1	no	—
369	C₂⁴	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
401	Q₁₆	—	4	8	no	—
402	SD₁₆	—	4	8	no	—
403	SD₁₆	—	4	4	no	—
404	D₈	—	4	4	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	#41×C₇₃	1	4	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	8	2	no	—
428	C₄²	—	2	8	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	8	1	no	—
432	C₄²	C₂×D₄×C₇₃	1	2	yes	—
433	C₄²	C₂×D₄×C₇₃	1	2	yes	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
445	Q₈	—	2	4	no	—
446	Q₈	—	2	4	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	1	no	—
451	Q₈	—	4	1	no	—
452	Q₈	—	4	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	#120×C₇₃	1	2	yes	—
480	C₂×C₄	#120×C₇₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
484	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
485	C₈	—	2	4	no	—
486	C₈	—	4	1	no	—
487	C₈	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
499	C₂²	#550×C₇₃	1	2	yes	—
500	C₂²	#575×C₇₃	1	2	yes	—
501	C₂²	#577×C₇₃	1	1	yes	characteristic
502	C₂²	#578×C₇₃	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	8	2	no	—
510	C₄	—	8	1	no	—
511	C₄	#532×C₇₃	1	1	yes	characteristic
512	C₄	#535×C₇₃	1	1	yes	characteristic
513	C₄	#546×C₇₃	1	2	yes	—
514	C₂	—	8	2	no	—
515	C₂	—	16	1	no	—
516	C₂	C₇₃×#2431	1	1	yes	characteristic
517	C₂	C₇₃×#3005	1	1	yes	characteristic
518	C₂	C₇₃×#3013	1	1	yes	characteristic
519	C₂	C₇₃×#3401	1	2	yes	—
520	C₂	C₇₃×#3402	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₇₃	C₂	semidirect
2. C₂×#497×C₇₃	C₂	semidirect
4. C₇₃×#2592	C₂	semidirect
5. C₇₃×#2015	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
8. C₇₃×#1981	C₂	semidirect
9. C₇₃×#1880	C₂	semidirect
10. C₇₃×#1878	C₂	semidirect
11. C₇₃×#1762	C₂	semidirect
253. #25638	C₇₃	direct (N × H)
261. C₂×#556	C₂×C₇₃	semidirect
262. C₂×#497	C₂×C₇₃	semidirect
264. #2592	C₂×C₇₃	semidirect
265. #2015	C₂×C₇₃	semidirect
267. #1985	C₂×C₇₃	semidirect
268. #1981	C₂×C₇₃	semidirect
269. #1880	C₂×C₇₃	semidirect
270. #1878	C₂×C₇₃	semidirect
271. #1762	C₂×C₇₃	semidirect
272. C₇₃	#25638	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×#556×C₇₃	2
C₂×#497×C₇₃	2
C₂×#463×C₇₃	2
C₇₃×#2592	2
C₇₃×#2015	2
C₇₃×#2012	2
C₇₃×#1985	2
C₇₃×#1981	2
C₇₃×#1880	2
C₇₃×#1878	2
C₇₃×#1762	2
#25638	73

Subgroups — C73×#25638 #32935042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25638 #32935042