Subgroups — C₇₃×#24001 #32933405

Order 18688.

1122 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3020	C₂	1	1	yes	maximal, characteristic
3	C₂×#456×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2884	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2031	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2009	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1912	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1906	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1905	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1830	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	1	yes	characteristic
13	#575×C₇₃	C₂²	1	2	yes	—
14	C₂×#137×C₇₃	C₂²	1	2	yes	—
15	#557×C₇₃	—	2	2	no	—
16	#556×C₇₃	—	2	2	no	—
17	#552×C₇₃	—	2	4	no	—
18	#541×C₇₃	—	2	2	no	—
19	#536×C₇₃	C₂²	1	1	yes	characteristic
20	#536×C₇₃	C₂²	1	1	yes	characteristic
21	#533×C₇₃	—	2	2	no	—
22	#533×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	#519×C₇₃	C₂²	1	1	yes	characteristic
25	#519×C₇₃	C₂²	1	1	yes	characteristic
26	#519×C₇₃	C₂²	1	1	yes	characteristic
27	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
28	#456×C₇₃	—	2	2	no	—
29	#456×C₇₃	—	2	2	no	—
30	#456×C₇₃	—	2	2	no	—
31	#454×C₇₃	—	2	2	no	—
32	#421×C₇₃	C₂²	1	2	yes	—
33	#421×C₇₃	C₂²	1	2	yes	—
34	C₂×#104×C₇₃	C₂²	1	2	yes	—
35	#419×C₇₃	C₂²	1	2	yes	—
36	C₂×#101×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#101×C₇₃	C₂²	1	1	yes	characteristic
38	#410×C₇₃	—	2	4	no	—
39	#410×C₇₃	C₂²	1	2	yes	—
40	#410×C₇₃	C₂²	1	2	yes	—
41	#344×C₇₃	C₂²	1	2	yes	—
42	#344×C₇₃	C₂²	1	2	yes	—
43	#339×C₇₃	C₂²	1	2	yes	—
44	H(3,ℤ/4)×C₇₃	C₂²	1	2	yes	—
45	2₋¹⁺⁴×C₇₃	—	2	2	no	—
46	2₋¹⁺⁴×C₇₃	—	2	2	no	—
47	2₋¹⁺⁴×C₇₃	—	4	2	no	—
48	C₂×#41×C₇₃	—	2	2	no	—
49	C₂×#41×C₇₃	—	2	2	no	—
50	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
51	C₂×#41×C₇₃	C₂³	1	2	yes	—
52	C₂²×Q₈×C₇₃	—	2	2	no	—
53	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
55	#137×C₇₃	—	2	4	no	—
56	#137×C₇₃	—	2	2	no	—
57	#137×C₇₃	—	2	2	no	—
58	#137×C₇₃	—	4	2	no	—
59	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
60	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
61	#135×C₇₃	—	4	2	no	—
62	C₂×Q₁₆×C₇₃	—	2	2	no	—
63	C₂×SD₁₆×C₇₃	—	2	2	no	—
64	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
65	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₇₃	—	2	2	no	—
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	—	2	1	no	—
69	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
70	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
71	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
72	#126×C₇₃	—	2	4	no	—
73	#126×C₇₃	—	2	4	no	—
74	#125×C₇₃	—	2	4	no	—
75	#125×C₇₃	—	2	4	no	—
76	#125×C₇₃	—	2	4	no	—
77	#125×C₇₃	—	2	1	no	—
78	#124×C₇₃	—	2	1	no	—
79	#124×C₇₃	D₄	1	2	yes	—
80	#123×C₇₃	—	2	2	no	—
81	#123×C₇₃	—	2	2	no	—
82	C₂²⋊Q₈×C₇₃	—	2	4	no	—
83	C₂²⋊Q₈×C₇₃	—	2	2	no	—
84	C₂²⋊Q₈×C₇₃	—	2	2	no	—
85	C₂²⋊Q₈×C₇₃	—	2	2	no	—
86	C₄×Q₈×C₇₃	—	2	4	no	—
87	C₄×Q₈×C₇₃	—	2	1	no	—
88	C₄×Q₈×C₇₃	—	2	2	no	—
89	C₄×Q₈×C₇₃	—	2	2	no	—
90	C₄×Q₈×C₇₃	—	2	2	no	—
91	C₄×Q₈×C₇₃	—	2	2	no	—
92	C₄×Q₈×C₇₃	—	2	2	no	—
93	C₄×Q₈×C₇₃	—	4	2	no	—
94	C₄×D₄×C₇₃	—	2	1	no	—
95	C₄×D₄×C₇₃	—	2	2	no	—
96	#117×C₇₃	—	2	4	no	—
97	#117×C₇₃	—	2	2	no	—
98	#117×C₇₃	—	2	1	no	—
99	#117×C₇₃	—	2	2	no	—
100	#117×C₇₃	D₄	1	4	yes	—
101	#117×C₇₃	C₂³	1	2	yes	—
102	#117×C₇₃	C₂³	1	1	yes	characteristic
103	#117×C₇₃	C₂³	1	1	yes	characteristic
104	#117×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
106	C₂×C₄²×C₇₃	—	2	1	no	—
107	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
108	#104×C₇₃	—	2	2	no	—
109	#104×C₇₃	—	2	2	no	—
110	#104×C₇₃	—	2	4	no	—
111	#104×C₇₃	—	4	2	no	—
112	#103×C₇₃	—	4	2	no	—
113	#101×C₇₃	—	2	2	no	—
114	#101×C₇₃	—	2	2	no	—
115	#99×C₇₃	—	2	4	no	—
116	#99×C₇₃	—	2	4	no	—
117	#41×C₇₃	—	2	2	no	—
118	#41×C₇₃	—	2	2	no	—
119	#41×C₇₃	—	2	2	no	—
120	#41×C₇₃	—	2	2	no	—
121	#41×C₇₃	—	2	2	no	—
122	#41×C₇₃	—	2	2	no	—
123	#41×C₇₃	—	4	4	no	—
124	#41×C₇₃	—	4	4	no	—
125	#41×C₇₃	—	4	4	no	—
126	#41×C₇₃	—	4	4	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂×Q₈×C₇₃	—	2	1	no	—
130	C₂×Q₈×C₇₃	—	2	2	no	—
131	C₂×Q₈×C₇₃	—	2	2	no	—
132	C₂×Q₈×C₇₃	—	2	2	no	—
133	C₂×Q₈×C₇₃	—	2	2	no	—
134	C₂×Q₈×C₇₃	—	4	4	no	—
135	C₂×Q₈×C₇₃	—	4	4	no	—
136	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
140	C₂×Q₈×C₇₃	#41	1	2	yes	—
141	C₂×D₄×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	2	2	no	—
143	C₂×D₄×C₇₃	—	2	1	no	—
144	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂×D₄×C₇₃	#41	1	2	yes	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	4	no	—
148	C₂²×C₄×C₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	—	2	1	no	—
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	—	2	2	no	—
152	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₇₃	—	4	4	no	—
155	Q₁₆×C₇₃	—	4	2	no	—
156	SD₁₆×C₇₃	—	4	4	no	—
157	SD₁₆×C₇₃	—	4	2	no	—
158	SD₁₆×C₇₃	—	4	2	no	—
159	D₈×C₇₃	—	4	2	no	—
160	M₁₆×C₇₃	—	2	2	no	—
161	M₁₆×C₇₃	—	2	2	no	—
162	M₁₆×C₇₃	—	2	2	no	—
163	M₁₆×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	—	2	2	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	—	2	2	no	—
167	C₄⋊C₄×C₇₃	—	2	2	no	—
168	C₄⋊C₄×C₇₃	—	2	4	no	—
169	C₄⋊C₄×C₇₃	—	2	4	no	—
170	C₄⋊C₄×C₇₃	—	2	2	no	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	—	2	4	no	—
173	C₄⋊C₄×C₇₃	—	2	4	no	—
174	C₄⋊C₄×C₇₃	—	2	4	no	—
175	C₄⋊C₄×C₇₃	—	2	4	no	—
176	C₄⋊C₄×C₇₃	—	2	1	no	—
177	C₄⋊C₄×C₇₃	—	2	1	no	—
178	C₄⋊C₄×C₇₃	—	2	1	no	—
179	C₄⋊C₄×C₇₃	—	2	2	no	—
180	C₄⋊C₄×C₇₃	—	4	2	no	—
181	C₂²⋊C₄×C₇₃	—	2	2	no	—
182	C₂²⋊C₄×C₇₃	—	2	4	no	—
183	C₂²⋊C₄×C₇₃	—	2	1	no	—
184	C₂²⋊C₄×C₇₃	—	2	4	no	—
185	C₂²⋊C₄×C₇₃	—	2	2	no	—
186	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
187	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
188	C₄²×C₇₃	—	2	2	no	—
189	C₄²×C₇₃	—	2	4	no	—
190	C₄²×C₇₃	—	2	4	no	—
191	C₄²×C₇₃	—	2	1	no	—
192	C₄²×C₇₃	—	2	1	no	—
193	C₄²×C₇₃	—	2	1	no	—
194	C₄²×C₇₃	—	2	2	no	—
195	C₄²×C₇₃	—	4	2	no	—
196	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₇₃	C₂×D₄	1	2	yes	—
199	C₂³×C₇₃	—	2	1	no	—
200	C₂³×C₇₃	—	2	2	no	—
201	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₇₃	—	2	4	no	—
203	Q₈×C₇₃	—	2	4	no	—
204	Q₈×C₇₃	—	2	4	no	—
205	Q₈×C₇₃	—	2	2	no	—
206	Q₈×C₇₃	—	2	2	no	—
207	Q₈×C₇₃	—	2	2	no	—
208	Q₈×C₇₃	—	4	4	no	—
209	Q₈×C₇₃	—	4	4	no	—
210	Q₈×C₇₃	—	4	2	no	—
211	D₄×C₇₃	—	2	2	no	—
212	D₄×C₇₃	—	2	2	no	—
213	D₄×C₇₃	—	2	2	no	—
214	D₄×C₇₃	—	4	4	no	—
215	D₄×C₇₃	—	4	2	no	—
216	D₄×C₇₃	—	4	1	no	—
217	D₄×C₇₃	—	4	1	no	—
218	D₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	2	1	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	2	2	no	—
223	C₂×C₄×C₇₃	—	2	2	no	—
224	C₂×C₄×C₇₃	—	2	2	no	—
225	C₂×C₄×C₇₃	—	2	2	no	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	1	no	—
228	C₂×C₄×C₇₃	—	2	2	no	—
229	C₂×C₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	4	no	—
231	C₂×C₄×C₇₃	—	4	8	no	—
232	C₂×C₄×C₇₃	—	4	1	no	—
233	C₂×C₄×C₇₃	—	4	1	no	—
234	C₂×C₄×C₇₃	—	4	2	no	—
235	C₂×C₄×C₇₃	—	4	2	no	—
236	C₂×C₄×C₇₃	—	4	2	no	—
237	C₂×C₄×C₇₃	—	4	2	no	—
238	C₂×C₄×C₇₃	#120	1	4	yes	—
239	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
242	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
243	C₈×C₇₃	—	4	2	no	—
244	C₈×C₇₃	—	4	2	no	—
245	C₂²×C₇₃	—	4	1	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	1	no	—
249	C₂²×C₇₃	—	8	2	no	—
250	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
251	C₂²×C₇₃	#525	1	1	yes	characteristic
252	C₂²×C₇₃	#535	1	1	yes	characteristic
253	C₄×C₇₃	—	2	2	no	—
254	C₄×C₇₃	—	2	4	no	—
255	C₄×C₇₃	—	4	2	no	—
256	C₄×C₇₃	—	4	1	no	—
257	C₄×C₇₃	—	4	2	no	—
258	C₄×C₇₃	—	4	2	no	—
259	C₄×C₇₃	—	4	2	no	—
260	C₄×C₇₃	—	4	1	no	—
261	C₄×C₇₃	—	4	2	no	—
262	C₄×C₇₃	—	8	2	no	—
263	C₄×C₇₃	#546	1	2	yes	—
264	C₄×C₇₃	#546	1	2	yes	—
265	#24001	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂×C₇₃	—	2	1	no	—
267	C₂×C₇₃	—	2	1	no	—
268	C₂×C₇₃	—	2	1	no	—
269	C₂×C₇₃	—	8	1	no	—
270	C₂×C₇₃	—	8	2	no	—
271	C₂×C₇₃	#2404	1	1	yes	characteristic
272	#3509	C₂×C₇₃	1	1	yes	characteristic, complemented
273	#3020	C₂×C₇₃	1	1	yes	characteristic
274	C₂×#456	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#2884	C₂×C₇₃	1	1	yes	characteristic, complemented
276	#2031	C₂×C₇₃	1	2	yes	complemented
277	#2009	C₂×C₇₃	1	2	yes	complemented
278	#1912	C₂×C₇₃	1	1	yes	characteristic, complemented
279	#1906	C₂×C₇₃	1	2	yes	complemented
280	#1905	C₂×C₇₃	1	2	yes	complemented
281	#1886	C₂×C₇₃	1	1	yes	characteristic, complemented
282	#1830	C₂×C₇₃	1	1	yes	characteristic, complemented
283	C₇₃	#24001	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	1	yes	characteristic
285	#575	C₂²×C₇₃	1	2	yes	—
286	C₂×#137	C₂²×C₇₃	1	2	yes	—
287	#557	—	2	2	no	—
288	#556	—	2	2	no	—
289	#552	—	2	4	no	—
290	#541	—	2	2	no	—
291	#536	C₂²×C₇₃	1	1	yes	characteristic
292	#536	C₂²×C₇₃	1	1	yes	characteristic
293	#533	—	2	2	no	—
294	#533	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
296	#519	C₂²×C₇₃	1	1	yes	characteristic
297	#519	C₂²×C₇₃	1	1	yes	characteristic
298	#519	C₂²×C₇₃	1	1	yes	characteristic
299	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
300	#456	—	2	2	no	—
301	#456	—	2	2	no	—
302	#456	—	2	2	no	—
303	#454	—	2	2	no	—
304	#421	C₂²×C₇₃	1	2	yes	—
305	#421	C₂²×C₇₃	1	2	yes	—
306	C₂×#104	C₂²×C₇₃	1	2	yes	—
307	#419	C₂²×C₇₃	1	2	yes	—
308	C₂×#101	C₂²×C₇₃	1	1	yes	characteristic
309	C₂×#101	C₂²×C₇₃	1	1	yes	characteristic
310	#410	—	2	4	no	—
311	#410	C₂²×C₇₃	1	2	yes	—
312	#410	C₂²×C₇₃	1	2	yes	—
313	#344	C₂²×C₇₃	1	2	yes	—
314	#344	C₂²×C₇₃	1	2	yes	—
315	#339	C₂²×C₇₃	1	2	yes	—
316	H(3,ℤ/4)	C₂²×C₇₃	1	2	yes	—
317	2₋¹⁺⁴	—	2	2	no	—
318	2₋¹⁺⁴	—	2	2	no	—
319	2₋¹⁺⁴	—	4	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
323	C₂×#41	C₂³×C₇₃	1	2	yes	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
327	#137	—	2	4	no	—
328	#137	—	2	2	no	—
329	#137	—	2	2	no	—
330	#137	—	4	2	no	—
331	AGL(1,ℤ/8)	—	2	2	no	—
332	AGL(1,ℤ/8)	—	2	2	no	—
333	#135	—	4	2	no	—
334	C₂×Q₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
337	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
342	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
343	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
344	#126	—	2	4	no	—
345	#126	—	2	4	no	—
346	#125	—	2	4	no	—
347	#125	—	2	4	no	—
348	#125	—	2	4	no	—
349	#125	—	2	1	no	—
350	#124	—	2	1	no	—
351	#124	D₄×C₇₃	1	2	yes	—
352	#123	—	2	2	no	—
353	#123	—	2	2	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	4	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	4	2	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	2	no	—
368	#117	—	2	4	no	—
369	#117	—	2	2	no	—
370	#117	—	2	1	no	—
371	#117	—	2	2	no	—
372	#117	D₄×C₇₃	1	4	yes	—
373	#117	C₂³×C₇₃	1	2	yes	—
374	#117	C₂³×C₇₃	1	1	yes	characteristic
375	#117	C₂³×C₇₃	1	1	yes	characteristic
376	#117	C₂³×C₇₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
380	#104	—	2	2	no	—
381	#104	—	2	2	no	—
382	#104	—	2	4	no	—
383	#104	—	4	2	no	—
384	#103	—	4	2	no	—
385	#101	—	2	2	no	—
386	#101	—	2	2	no	—
387	#99	—	2	4	no	—
388	#99	—	2	4	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	4	4	no	—
396	#41	—	4	4	no	—
397	#41	—	4	4	no	—
398	#41	—	4	4	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
409	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
410	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
411	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
412	C₂×Q₈	#41×C₇₃	1	2	yes	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
417	C₂×D₄	#41×C₇₃	1	2	yes	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
426	Q₁₆	—	4	4	no	—
427	Q₁₆	—	4	2	no	—
428	SD₁₆	—	4	4	no	—
429	SD₁₆	—	4	2	no	—
430	SD₁₆	—	4	2	no	—
431	D₈	—	4	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
459	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	4	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	4	2	no	—
468	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₇₃	1	2	yes	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	4	4	no	—
481	Q₈	—	4	4	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	#120×C₇₃	1	4	yes	—
511	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
514	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
515	C₈	—	4	2	no	—
516	C₈	—	4	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	8	2	no	—
522	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
523	C₂²	#525×C₇₃	1	1	yes	characteristic
524	C₂²	#535×C₇₃	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	—	8	2	no	—
535	C₄	#546×C₇₃	1	2	yes	—
536	C₄	#546×C₇₃	1	2	yes	—
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	8	1	no	—
541	C₂	—	8	2	no	—
542	C₂	C₇₃×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₃	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3020	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3509	C₂	semidirect
3. C₂×#456×C₇₃	C₂	semidirect
4. C₇₃×#2884	C₂	semidirect
5. C₇₃×#2031	C₂	semidirect
6. C₇₃×#2009	C₂	semidirect
7. C₇₃×#1912	C₂	semidirect
8. C₇₃×#1906	C₂	semidirect
9. C₇₃×#1905	C₂	semidirect
10. C₇₃×#1886	C₂	semidirect
11. C₇₃×#1830	C₂	semidirect
265. #24001	C₇₃	direct (N × H)
272. #3509	C₂×C₇₃	semidirect
274. C₂×#456	C₂×C₇₃	semidirect
275. #2884	C₂×C₇₃	semidirect
276. #2031	C₂×C₇₃	semidirect
277. #2009	C₂×C₇₃	semidirect
278. #1912	C₂×C₇₃	semidirect
279. #1906	C₂×C₇₃	semidirect
280. #1905	C₂×C₇₃	semidirect
281. #1886	C₂×C₇₃	semidirect
282. #1830	C₂×C₇₃	semidirect
283. C₇₃	#24001	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3509	2
C₇₃×#3020	2
C₂×#456×C₇₃	2
C₇₃×#2884	2
C₇₃×#2031	2
C₇₃×#2009	2
C₇₃×#1912	2
C₇₃×#1906	2
C₇₃×#1905	2
C₇₃×#1886	2
C₇₃×#1830	2
#24001	73

Subgroups — C73×#24001 #32933405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24001 #32933405