Subgroups — C₇₃×#25594 #32934998

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 484 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×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3040	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2005	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2003	C₂	1	2	yes	maximal
7	C₇₃×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1888	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1886	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	1	yes	characteristic
14	#557×C₇₃	—	2	2	no	—
15	#556×C₇₃	—	2	2	no	—
16	#552×C₇₃	—	2	4	no	—
17	#541×C₇₃	—	2	2	no	—
18	#536×C₇₃	C₂²	1	2	yes	—
19	#533×C₇₃	—	2	2	no	—
20	#533×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#124×C₇₃	C₂²	1	2	yes	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	#519×C₇₃	C₂²	1	2	yes	—
26	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
27	#489×C₇₃	—	2	2	no	—
28	#488×C₇₃	—	2	2	no	—
29	#464×C₇₃	—	2	2	no	—
30	#463×C₇₃	—	2	2	no	—
31	#423×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#104×C₇₃	C₂²	1	2	yes	—
33	#419×C₇₃	C₂²	1	2	yes	—
34	#419×C₇₃	C₂²	1	1	yes	characteristic
35	#418×C₇₃	C₂²	1	2	yes	—
36	#418×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#101×C₇₃	C₂²	1	2	yes	—
38	C₂×#101×C₇₃	C₂²	1	2	yes	—
39	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
40	#399×C₇₃	—	2	4	no	—
41	#376×C₇₃	C₂²	1	1	yes	characteristic
42	#339×C₇₃	C₂²	1	2	yes	—
43	#339×C₇₃	C₂²	1	2	yes	—
44	#339×C₇₃	C₂²	1	2	yes	—
45	C₂×#41×C₇₃	C₂³	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	#137×C₇₃	—	4	2	no	—
50	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
51	C₂×Q₁₆×C₇₃	—	2	1	no	—
52	C₂×SD₁₆×C₇₃	—	2	1	no	—
53	C₂×SD₁₆×C₇₃	—	2	1	no	—
54	C₂×D₈×C₇₃	—	2	1	no	—
55	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
56	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	—	2	1	no	—
60	C₄⋊Q₈×C₇₃	—	2	1	no	—
61	C₄⋊Q₈×C₇₃	—	2	2	no	—
62	C₄⋊Q₈×C₇₃	—	2	4	no	—
63	C₄⋊Q₈×C₇₃	—	4	2	no	—
64	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
65	#126×C₇₃	—	2	8	no	—
66	#125×C₇₃	—	2	4	no	—
67	#125×C₇₃	—	2	8	no	—
68	#125×C₇₃	D₄	1	2	yes	—
69	#124×C₇₃	—	2	2	no	—
70	#124×C₇₃	—	2	2	no	—
71	#124×C₇₃	—	2	1	no	—
72	#124×C₇₃	—	2	1	no	—
73	#124×C₇₃	—	2	4	no	—
74	#124×C₇₃	—	4	2	no	—
75	#123×C₇₃	—	2	4	no	—
76	C₂²⋊Q₈×C₇₃	—	2	4	no	—
77	C₂²⋊Q₈×C₇₃	—	2	2	no	—
78	C₂²⋊Q₈×C₇₃	—	2	4	no	—
79	C₄×Q₈×C₇₃	—	2	4	no	—
80	C₄×Q₈×C₇₃	—	2	4	no	—
81	C₄×Q₈×C₇₃	—	2	4	no	—
82	C₄×Q₈×C₇₃	—	2	2	no	—
83	C₄×Q₈×C₇₃	D₄	1	2	yes	—
84	C₄×D₄×C₇₃	—	2	2	no	—
85	C₄×D₄×C₇₃	D₄	1	2	yes	—
86	#117×C₇₃	—	2	4	no	—
87	#117×C₇₃	—	2	4	no	—
88	#117×C₇₃	—	2	1	no	—
89	#117×C₇₃	C₂³	1	1	yes	characteristic
90	#117×C₇₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
92	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	—	2	2	no	—
99	#104×C₇₃	—	2	4	no	—
100	#103×C₇₃	—	2	2	no	—
101	#103×C₇₃	—	2	4	no	—
102	#102×C₇₃	—	2	2	no	—
103	#102×C₇₃	—	2	4	no	—
104	#101×C₇₃	—	4	2	no	—
105	#101×C₇₃	—	4	2	no	—
106	#97×C₇₃	—	2	1	no	—
107	C₄×C₈×C₇₃	—	2	1	no	—
108	#95×C₇₃	—	2	2	no	—
109	C₂⁴×C₇₃	—	2	1	no	—
110	#41×C₇₃	—	2	2	no	—
111	#41×C₇₃	—	2	2	no	—
112	C₂×Q₈×C₇₃	—	2	2	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	—	2	1	no	—
120	C₂×Q₈×C₇₃	—	2	1	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₇₃	—	2	1	no	—
125	C₂×D₄×C₇₃	—	2	1	no	—
126	C₂×D₄×C₇₃	—	2	1	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₇₃	—	4	2	no	—
138	SD₁₆×C₇₃	—	4	2	no	—
139	SD₁₆×C₇₃	—	4	2	no	—
140	D₈×C₇₃	—	4	2	no	—
141	M₁₆×C₇₃	—	2	2	no	—
142	M₁₆×C₇₃	—	2	2	no	—
143	M₁₆×C₇₃	—	2	2	no	—
144	M₁₆×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	C₄⋊C₄×C₇₃	—	2	8	no	—
149	C₄⋊C₄×C₇₃	—	2	8	no	—
150	C₄⋊C₄×C₇₃	—	2	4	no	—
151	C₄⋊C₄×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	—	2	4	no	—
155	C₄⋊C₄×C₇₃	—	4	8	no	—
156	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
158	C₂²⋊C₄×C₇₃	—	2	8	no	—
159	C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₂²⋊C₄×C₇₃	—	2	2	no	—
162	C₂²⋊C₄×C₇₃	—	4	8	no	—
163	C₂²⋊C₄×C₇₃	—	4	2	no	—
164	C₂²⋊C₄×C₇₃	—	4	2	no	—
165	C₄²×C₇₃	—	2	8	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	1	no	—
168	C₄²×C₇₃	—	2	2	no	—
169	C₄²×C₇₃	—	2	2	no	—
170	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇₃	C₂×D₄	1	2	yes	—
173	C₄²×C₇₃	#41	1	4	yes	—
174	C₂³×C₇₃	—	2	1	no	—
175	C₂³×C₇₃	—	4	4	no	—
176	C₂³×C₇₃	—	4	1	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₇₃	—	2	1	no	—
180	Q₈×C₇₃	—	2	1	no	—
181	Q₈×C₇₃	—	4	4	no	—
182	Q₈×C₇₃	—	4	2	no	—
183	Q₈×C₇₃	—	4	2	no	—
184	Q₈×C₇₃	—	4	2	no	—
185	Q₈×C₇₃	—	4	2	no	—
186	Q₈×C₇₃	—	4	1	no	—
187	Q₈×C₇₃	—	4	1	no	—
188	Q₈×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	2	1	no	—
190	D₄×C₇₃	—	2	1	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	4	1	no	—
193	D₄×C₇₃	—	4	1	no	—
194	D₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	4	no	—
197	C₂×C₄×C₇₃	—	2	4	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	4	no	—
200	C₂×C₄×C₇₃	—	2	4	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	4	no	—
204	C₂×C₄×C₇₃	—	4	4	no	—
205	C₂×C₄×C₇₃	—	4	2	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	#120	1	2	yes	—
209	C₂×C₄×C₇₃	#120	1	2	yes	—
210	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₇₃	—	4	1	no	—
215	C₈×C₇₃	—	4	1	no	—
216	C₈×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	2	2	no	—
218	C₂²×C₇₃	—	4	1	no	—
219	C₂²×C₇₃	—	4	2	no	—
220	C₂²×C₇₃	—	8	4	no	—
221	C₂²×C₇₃	—	8	1	no	—
222	C₂²×C₇₃	—	8	2	no	—
223	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
224	C₂²×C₇₃	#546	1	2	yes	—
225	C₄×C₇₃	—	2	2	no	—
226	C₄×C₇₃	—	2	2	no	—
227	C₄×C₇₃	—	4	4	no	—
228	C₄×C₇₃	—	4	4	no	—
229	C₄×C₇₃	—	4	1	no	—
230	C₄×C₇₃	—	4	2	no	—
231	C₄×C₇₃	—	4	4	no	—
232	C₄×C₇₃	—	8	1	no	—
233	C₄×C₇₃	#532	1	1	yes	characteristic
234	C₄×C₇₃	#535	1	1	yes	characteristic
235	C₄×C₇₃	#550	1	2	yes	—
236	#25594	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂×C₇₃	—	2	2	no	—
238	C₂×C₇₃	—	8	1	no	—
239	C₂×C₇₃	—	16	1	no	—
240	C₂×C₇₃	#2431	1	1	yes	characteristic
241	C₂×C₇₃	#3020	1	2	yes	—
242	#3509	C₂×C₇₃	1	1	yes	characteristic, complemented
243	#3140	C₂×C₇₃	1	1	yes	characteristic, complemented
244	#3040	C₂×C₇₃	1	1	yes	characteristic
245	#2658	C₂×C₇₃	1	1	yes	characteristic, complemented
246	#2005	C₂×C₇₃	1	2	yes	complemented
247	#2003	C₂×C₇₃	1	2	yes	—
248	#1995	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#1966	C₂×C₇₃	1	1	yes	characteristic, complemented
250	#1888	C₂×C₇₃	1	2	yes	complemented
251	#1886	C₂×C₇₃	1	2	yes	complemented
252	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
253	C₇₃	#25594	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
255	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	1	yes	characteristic
256	#557	—	2	2	no	—
257	#556	—	2	2	no	—
258	#552	—	2	4	no	—
259	#541	—	2	2	no	—
260	#536	C₂²×C₇₃	1	2	yes	—
261	#533	—	2	2	no	—
262	#533	C₂²×C₇₃	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
264	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
265	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₇₃	1	2	yes	—
267	#519	C₂²×C₇₃	1	2	yes	—
268	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
269	#489	—	2	2	no	—
270	#488	—	2	2	no	—
271	#464	—	2	2	no	—
272	#463	—	2	2	no	—
273	#423	C₂²×C₇₃	1	1	yes	characteristic
274	C₂×#104	C₂²×C₇₃	1	2	yes	—
275	#419	C₂²×C₇₃	1	2	yes	—
276	#419	C₂²×C₇₃	1	1	yes	characteristic
277	#418	C₂²×C₇₃	1	2	yes	—
278	#418	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×#101	C₂²×C₇₃	1	2	yes	—
280	C₂×#101	C₂²×C₇₃	1	2	yes	—
281	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
282	#399	—	2	4	no	—
283	#376	C₂²×C₇₃	1	1	yes	characteristic
284	#339	C₂²×C₇₃	1	2	yes	—
285	#339	C₂²×C₇₃	1	2	yes	—
286	#339	C₂²×C₇₃	1	2	yes	—
287	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
290	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
291	#137	—	4	2	no	—
292	AGL(1,ℤ/8)	—	4	2	no	—
293	C₂×Q₁₆	—	2	1	no	—
294	C₂×SD₁₆	—	2	1	no	—
295	C₂×SD₁₆	—	2	1	no	—
296	C₂×D₈	—	2	1	no	—
297	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
298	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
299	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	4	no	—
305	C₄⋊Q₈	—	4	2	no	—
306	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
307	#126	—	2	8	no	—
308	#125	—	2	4	no	—
309	#125	—	2	8	no	—
310	#125	D₄×C₇₃	1	2	yes	—
311	#124	—	2	2	no	—
312	#124	—	2	2	no	—
313	#124	—	2	1	no	—
314	#124	—	2	1	no	—
315	#124	—	2	4	no	—
316	#124	—	4	2	no	—
317	#123	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	4	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	D₄×C₇₃	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	D₄×C₇₃	1	2	yes	—
328	#117	—	2	4	no	—
329	#117	—	2	4	no	—
330	#117	—	2	1	no	—
331	#117	C₂³×C₇₃	1	1	yes	characteristic
332	#117	C₂³×C₇₃	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
340	C₄⋊C₈	—	2	2	no	—
341	#104	—	2	4	no	—
342	#103	—	2	2	no	—
343	#103	—	2	4	no	—
344	#102	—	2	2	no	—
345	#102	—	2	4	no	—
346	#101	—	4	2	no	—
347	#101	—	4	2	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	#95	—	2	2	no	—
351	C₂⁴	—	2	1	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
379	Q₁₆	—	4	2	no	—
380	SD₁₆	—	4	2	no	—
381	SD₁₆	—	4	2	no	—
382	D₈	—	4	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	4	8	no	—
398	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	4	8	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₇₃	1	2	yes	—
415	C₄²	#41×C₇₃	1	4	yes	—
416	C₂³	—	2	1	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	#120×C₇₃	1	2	yes	—
451	C₂×C₄	#120×C₇₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
455	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
466	C₂²	#546×C₇₃	1	2	yes	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	8	1	no	—
475	C₄	#532×C₇₃	1	1	yes	characteristic
476	C₄	#535×C₇₃	1	1	yes	characteristic
477	C₄	#550×C₇₃	1	2	yes	—
478	C₂	—	2	2	no	—
479	C₂	—	8	1	no	—
480	C₂	—	16	1	no	—
481	C₂	C₇₃×#2431	1	1	yes	characteristic
482	C₂	C₇₃×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×AGL(1,ℤ/8)×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3509	C₂	semidirect
2. C₇₃×#3140	C₂	semidirect
4. C₇₃×#2658	C₂	semidirect
5. C₇₃×#2005	C₂	semidirect
7. C₇₃×#1995	C₂	semidirect
8. C₇₃×#1966	C₂	semidirect
9. C₇₃×#1888	C₂	semidirect
10. C₇₃×#1886	C₂	semidirect
11. C₇₃×#1759	C₂	semidirect
236. #25594	C₇₃	direct (N × H)
242. #3509	C₂×C₇₃	semidirect
243. #3140	C₂×C₇₃	semidirect
245. #2658	C₂×C₇₃	semidirect
246. #2005	C₂×C₇₃	semidirect
248. #1995	C₂×C₇₃	semidirect
249. #1966	C₂×C₇₃	semidirect
250. #1888	C₂×C₇₃	semidirect
251. #1886	C₂×C₇₃	semidirect
252. #1759	C₂×C₇₃	semidirect
253. C₇₃	#25594	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×#3140	2
C₇₃×#3040	2
C₇₃×#2658	2
C₇₃×#2005	2
C₇₃×#2003	2
C₇₃×#1995	2
C₇₃×#1966	2
C₇₃×#1888	2
C₇₃×#1886	2
C₇₃×#1759	2
#25594	73

Subgroups — C73×#25594 #32934998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25594 #32934998