Subgroups — C₇₃×#24647 #32934051

Order 18688.

932 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#459×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#440×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2054	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
18	#459×C₇₃	—	2	4	no	—
19	#440×C₇₃	—	2	4	no	—
20	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×#102×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₇₃	C₂²	1	2	yes	—
29	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
30	#394×C₇₃	—	2	1	no	—
31	#394×C₇₃	—	2	1	no	—
32	#390×C₇₃	—	2	2	no	—
33	#390×C₇₃	C₂²	1	2	yes	—
34	#390×C₇₃	C₂²	1	2	yes	—
35	#388×C₇₃	—	2	2	no	—
36	#382×C₇₃	C₂²	1	1	yes	characteristic
37	#381×C₇₃	—	2	1	no	—
38	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₇₃	—	2	1	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	—	2	1	no	—
49	C₂×SD₁₆×C₇₃	—	2	2	no	—
50	C₂×SD₁₆×C₇₃	—	2	2	no	—
51	C₂×SD₁₆×C₇₃	—	2	2	no	—
52	C₂×D₈×C₇₃	—	2	4	no	—
53	C₂×D₈×C₇₃	—	4	2	no	—
54	C₂×D₈×C₇₃	—	4	2	no	—
55	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
58	#127×C₇₃	—	2	2	no	—
59	#127×C₇₃	—	2	2	no	—
60	#124×C₇₃	—	2	4	no	—
61	#124×C₇₃	—	4	2	no	—
62	C₄×Q₈×C₇₃	—	2	2	no	—
63	C₄×Q₈×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	—	2	2	no	—
65	C₄×D₄×C₇₃	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₄²×C₇₃	—	2	1	no	—
79	C₂×C₄²×C₇₃	—	2	2	no	—
80	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
82	#107×C₇₃	—	2	2	no	—
83	C₄⋊C₈×C₇₃	—	2	2	no	—
84	C₄⋊C₈×C₇₃	—	4	2	no	—
85	#103×C₇₃	—	2	2	no	—
86	#103×C₇₃	—	4	2	no	—
87	#102×C₇₃	—	2	2	no	—
88	#102×C₇₃	—	2	4	no	—
89	#102×C₇₃	—	2	4	no	—
90	#102×C₇₃	—	4	2	no	—
91	#97×C₇₃	—	2	2	no	—
92	#95×C₇₃	—	2	1	no	—
93	#95×C₇₃	—	2	2	no	—
94	#95×C₇₃	—	2	1	no	—
95	#95×C₇₃	D₄	1	1	yes	characteristic
96	#95×C₇₃	D₄	1	1	yes	characteristic
97	C₂⁴×C₇₃	—	2	1	no	—
98	C₂⁴×C₇₃	—	2	2	no	—
99	C₂×Q₈×C₇₃	—	2	1	no	—
100	C₂×Q₈×C₇₃	—	2	1	no	—
101	C₂×Q₈×C₇₃	—	2	1	no	—
102	C₂×Q₈×C₇₃	—	2	1	no	—
103	C₂×Q₈×C₇₃	—	2	1	no	—
104	C₂×Q₈×C₇₃	#41	1	2	yes	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	1	no	—
107	C₂×D₄×C₇₃	—	2	1	no	—
108	C₂×D₄×C₇₃	—	2	1	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	1	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	4	4	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	8	2	no	—
120	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	4	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	8	2	no	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
132	SD₁₆×C₇₃	—	2	8	no	—
133	D₈×C₇₃	—	4	8	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	—	2	1	no	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	1	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	#41	1	2	yes	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₄⋊C₄×C₇₃	—	4	2	no	—
150	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₇₃	—	2	4	no	—
152	C₂²⋊C₄×C₇₃	—	4	4	no	—
153	C₂²⋊C₄×C₇₃	—	4	4	no	—
154	C₂²⋊C₄×C₇₃	—	4	4	no	—
155	C₂²⋊C₄×C₇₃	—	8	2	no	—
156	C₂²⋊C₄×C₇₃	—	8	2	no	—
157	C₂²⋊C₄×C₇₃	—	8	2	no	—
158	C₄²×C₇₃	—	2	2	no	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	4	2	no	—
161	C₄²×C₇₃	—	8	2	no	—
162	C₄²×C₇₃	C₂×D₄	1	2	yes	—
163	C₄²×C₇₃	#41	1	2	yes	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	4	1	no	—
166	C₂³×C₇₃	—	4	1	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	2	no	—
171	C₂³×C₇₃	—	4	2	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₇₃	—	2	2	no	—
178	Q₈×C₇₃	—	2	2	no	—
179	Q₈×C₇₃	—	4	1	no	—
180	Q₈×C₇₃	—	4	1	no	—
181	D₄×C₇₃	—	2	2	no	—
182	D₄×C₇₃	—	2	2	no	—
183	D₄×C₇₃	—	4	2	no	—
184	D₄×C₇₃	—	4	2	no	—
185	D₄×C₇₃	—	4	1	no	—
186	D₄×C₇₃	—	4	2	no	—
187	D₄×C₇₃	—	4	1	no	—
188	D₄×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	8	4	no	—
190	D₄×C₇₃	—	8	4	no	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	2	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	2	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	—	4	1	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	4	1	no	—
205	C₂×C₄×C₇₃	—	4	2	no	—
206	C₂×C₄×C₇₃	—	4	2	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	8	4	no	—
210	C₂×C₄×C₇₃	#121	1	2	yes	—
211	C₂×C₄×C₇₃	#121	1	2	yes	—
212	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₈×C₇₃	—	2	2	no	—
219	C₈×C₇₃	—	4	1	no	—
220	C₈×C₇₃	—	4	2	no	—
221	C₂²×C₇₃	—	4	2	no	—
222	C₂²×C₇₃	—	4	2	no	—
223	C₂²×C₇₃	—	4	2	no	—
224	C₂²×C₇₃	—	8	2	no	—
225	C₂²×C₇₃	—	8	2	no	—
226	C₂²×C₇₃	—	8	2	no	—
227	C₂²×C₇₃	—	8	2	no	—
228	C₂²×C₇₃	—	8	2	no	—
229	C₂²×C₇₃	—	8	2	no	—
230	C₂²×C₇₃	—	8	2	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
234	C₂²×C₇₃	#546	1	1	yes	characteristic
235	C₂²×C₇₃	#550	1	1	yes	characteristic
236	C₂²×C₇₃	#575	1	2	yes	—
237	C₂²×C₇₃	#576	1	2	yes	—
238	C₄×C₇₃	—	2	2	no	—
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	4	2	no	—
241	C₄×C₇₃	—	4	2	no	—
242	C₄×C₇₃	—	4	2	no	—
243	C₄×C₇₃	—	4	2	no	—
244	C₄×C₇₃	—	8	2	no	—
245	C₄×C₇₃	—	8	1	no	—
246	C₄×C₇₃	#525	1	1	yes	characteristic
247	C₄×C₇₃	#535	1	1	yes	characteristic
248	C₄×C₇₃	#553	1	1	yes	characteristic
249	C₄×C₇₃	#555	1	1	yes	characteristic
250	#24647	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂×C₇₃	—	8	2	no	—
252	C₂×C₇₃	—	16	2	no	—
253	C₂×C₇₃	#2414	1	1	yes	characteristic
254	C₂×C₇₃	#3040	1	1	yes	characteristic
255	C₂×C₇₃	#3041	1	1	yes	characteristic
256	C₂×C₇₃	#3309	1	2	yes	—
257	C₂×C₇₃	#3403	1	2	yes	—
258	C₂×#459	C₂×C₇₃	1	1	yes	characteristic
259	C₂×#440	C₂×C₇₃	1	1	yes	characteristic, complemented
260	#2548	C₂×C₇₃	1	1	yes	characteristic, complemented
261	#2357	C₂×C₇₃	1	1	yes	characteristic, complemented
262	#2054	C₂×C₇₃	1	2	yes	complemented
263	#2012	C₂×C₇₃	1	2	yes	complemented
264	#1983	C₂×C₇₃	1	2	yes	complemented
265	#1961	C₂×C₇₃	1	1	yes	characteristic, complemented
266	#1940	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#1925	C₂×C₇₃	1	2	yes	complemented
268	#1805	C₂×C₇₃	1	1	yes	characteristic, complemented
269	C₇₃	#24647	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
271	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
272	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×#124	C₂²×C₇₃	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
276	#459	—	2	4	no	—
277	#440	—	2	4	no	—
278	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
281	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×#103	C₂²×C₇₃	1	2	yes	—
283	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
284	C₂×#102	C₂²×C₇₃	1	2	yes	—
285	C₂×#102	C₂²×C₇₃	1	2	yes	—
286	C₂×#102	C₂²×C₇₃	1	2	yes	—
287	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
288	#394	—	2	1	no	—
289	#394	—	2	1	no	—
290	#390	—	2	2	no	—
291	#390	C₂²×C₇₃	1	2	yes	—
292	#390	C₂²×C₇₃	1	2	yes	—
293	#388	—	2	2	no	—
294	#382	C₂²×C₇₃	1	1	yes	characteristic
295	#381	—	2	1	no	—
296	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
297	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	—	2	1	no	—
299	#340	C₂²×C₇₃	1	2	yes	—
300	#336	C₂²×C₇₃	1	2	yes	—
301	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
305	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×D₈	—	2	4	no	—
311	C₂×D₈	—	4	2	no	—
312	C₂×D₈	—	4	2	no	—
313	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
314	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
316	#127	—	2	2	no	—
317	#127	—	2	2	no	—
318	#124	—	2	4	no	—
319	#124	—	4	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	D₄×C₇₃	1	4	yes	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	C₄⋊C₈	—	4	2	no	—
343	#103	—	2	2	no	—
344	#103	—	4	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	4	no	—
347	#102	—	2	4	no	—
348	#102	—	4	2	no	—
349	#97	—	2	2	no	—
350	#95	—	2	1	no	—
351	#95	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	D₄×C₇₃	1	1	yes	characteristic
354	#95	D₄×C₇₃	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂⁴	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	#41×C₇₃	1	2	yes	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	8	2	no	—
378	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
390	SD₁₆	—	2	8	no	—
391	D₈	—	4	8	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	#41×C₇₃	1	2	yes	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₂²⋊C₄	—	8	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	2	no	—
419	C₄²	—	8	2	no	—
420	C₄²	C₂×D₄×C₇₃	1	2	yes	—
421	C₄²	#41×C₇₃	1	2	yes	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	2	no	—
447	D₄	—	8	4	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	8	4	no	—
468	C₂×C₄	#121×C₇₃	1	2	yes	—
469	C₂×C₄	#121×C₇₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
474	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
475	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
476	C₈	—	2	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	1	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
492	C₂²	#546×C₇₃	1	1	yes	characteristic
493	C₂²	#550×C₇₃	1	1	yes	characteristic
494	C₂²	#575×C₇₃	1	2	yes	—
495	C₂²	#576×C₇₃	1	2	yes	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	8	1	no	—
503	C₄	—	8	2	no	—
504	C₄	#525×C₇₃	1	1	yes	characteristic
505	C₄	#535×C₇₃	1	1	yes	characteristic
506	C₄	#553×C₇₃	1	1	yes	characteristic
507	C₄	#555×C₇₃	1	1	yes	characteristic
508	C₂	—	8	2	no	—
509	C₂	—	16	2	no	—
510	C₂	C₇₃×#2414	1	1	yes	characteristic
511	C₂	C₇₃×#3040	1	1	yes	characteristic
512	C₂	C₇₃×#3041	1	1	yes	characteristic
513	C₂	C₇₃×#3309	1	2	yes	—
514	C₂	C₇₃×#3403	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#459×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₄⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#440×C₇₃	C₂	semidirect
3. C₇₃×#2548	C₂	semidirect
4. C₇₃×#2357	C₂	semidirect
5. C₇₃×#2054	C₂	semidirect
6. C₇₃×#2012	C₂	semidirect
7. C₇₃×#1983	C₂	semidirect
8. C₇₃×#1961	C₂	semidirect
9. C₇₃×#1940	C₂	semidirect
10. C₇₃×#1925	C₂	semidirect
11. C₇₃×#1805	C₂	semidirect
250. #24647	C₇₃	direct (N × H)
259. C₂×#440	C₂×C₇₃	semidirect
260. #2548	C₂×C₇₃	semidirect
261. #2357	C₂×C₇₃	semidirect
262. #2054	C₂×C₇₃	semidirect
263. #2012	C₂×C₇₃	semidirect
264. #1983	C₂×C₇₃	semidirect
265. #1961	C₂×C₇₃	semidirect
266. #1940	C₂×C₇₃	semidirect
267. #1925	C₂×C₇₃	semidirect
268. #1805	C₂×C₇₃	semidirect
269. C₇₃	#24647	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×#459×C₇₃	2
C₂×#440×C₇₃	2
C₇₃×#2548	2
C₇₃×#2357	2
C₇₃×#2054	2
C₇₃×#2012	2
C₇₃×#1983	2
C₇₃×#1961	2
C₇₃×#1940	2
C₇₃×#1925	2
C₇₃×#1805	2
#24647	73

Subgroups — C73×#24647 #32934051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24647 #32934051