Subgroups — C₇₃×#18630 #32928034

Order 18688.

1282 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3498	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1641	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1639	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₇₃	—	2	1	no	—
11	C₂×#137×C₇₃	—	2	1	no	—
12	#550×C₇₃	—	2	1	no	—
13	#550×C₇₃	C₂²	1	2	yes	—
14	D₄²×C₇₃	—	2	2	no	—
15	D₄²×C₇₃	—	2	2	no	—
16	D₄²×C₇₃	—	2	1	no	—
17	D₄²×C₇₃	C₂²	1	2	yes	—
18	#535×C₇₃	—	2	2	no	—
19	#535×C₇₃	—	2	1	no	—
20	#532×C₇₃	—	2	1	no	—
21	#532×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₇₃	—	2	1	no	—
24	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
25	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
26	#500×C₇₃	—	2	1	no	—
27	#486×C₇₃	—	2	1	no	—
28	#486×C₇₃	—	2	2	no	—
29	#486×C₇₃	C₂²	1	4	yes	complemented
30	#480×C₇₃	—	2	2	no	—
31	#474×C₇₃	C₂²	1	4	yes	complemented
32	#462×C₇₃	—	2	1	no	—
33	#462×C₇₃	C₂²	1	2	yes	complemented
34	#461×C₇₃	—	2	1	no	—
35	#461×C₇₃	C₂²	1	2	yes	complemented
36	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#419×C₇₃	—	2	1	no	—
39	C₂×#102×C₇₃	—	2	2	no	—
40	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	#331×C₇₃	C₂²	1	4	yes	complemented
42	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
43	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
44	D₄⋊C₈×C₇₃	C₂²	1	4	yes	complemented
45	H(5,𝔽₂)×C₇₃	—	4	4	no	—
46	H(5,𝔽₂)×C₇₃	—	4	4	no	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	—	2	2	no	—
49	C₂×#41×C₇₃	—	2	1	no	—
50	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₇₃	—	2	1	no	—
52	C₂²×D₄×C₇₃	—	2	2	no	—
53	C₂²×D₄×C₇₃	—	2	4	no	—
54	C₂²×D₄×C₇₃	—	2	2	no	—
55	C₂²×D₄×C₇₃	—	2	2	no	—
56	C₂²×D₄×C₇₃	—	2	2	no	—
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	2	1	no	—
59	C₂²×D₄×C₇₃	D₄	1	2	yes	—
60	#137×C₇₃	—	4	4	no	—
61	C₂×Q₁₆×C₇₃	—	2	2	no	—
62	C₂×SD₁₆×C₇₃	—	2	2	no	—
63	C₂×M₁₆×C₇₃	—	2	1	no	—
64	C₂²×C₈×C₇₃	—	2	1	no	—
65	C₄⋊Q₈×C₇₃	—	2	1	no	—
66	C₄⋊Q₈×C₇₃	—	2	1	no	—
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
70	#127×C₇₃	—	2	2	no	—
71	#127×C₇₃	—	2	2	no	—
72	#127×C₇₃	—	2	2	no	—
73	#127×C₇₃	—	2	1	no	—
74	#127×C₇₃	—	2	1	no	—
75	#127×C₇₃	D₄	1	1	yes	characteristic
76	#127×C₇₃	D₄	1	2	yes	—
77	#127×C₇₃	C₂³	1	2	yes	—
78	#124×C₇₃	—	2	2	no	—
79	#124×C₇₃	—	2	1	no	—
80	#121×C₇₃	—	2	2	no	—
81	#121×C₇₃	—	2	4	no	—
82	#121×C₇₃	—	2	4	no	—
83	#121×C₇₃	—	2	1	no	—
84	#121×C₇₃	—	2	2	no	—
85	#121×C₇₃	—	2	2	no	—
86	#121×C₇₃	—	2	2	no	—
87	#121×C₇₃	D₄	1	2	yes	—
88	#120×C₇₃	—	2	4	no	—
89	#120×C₇₃	—	2	4	no	—
90	#120×C₇₃	—	2	4	no	—
91	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₇₃	—	2	2	no	—
94	C₄×D₄×C₇₃	—	2	1	no	—
95	C₄×D₄×C₇₃	—	2	1	no	—
96	C₄×D₄×C₇₃	—	2	2	no	—
97	C₄×D₄×C₇₃	—	2	1	no	—
98	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₇₃	C₂³	1	2	yes	—
101	#117×C₇₃	—	2	1	no	—
102	#117×C₇₃	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
104	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
105	C₂×C₄²×C₇₃	—	2	1	no	—
106	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
107	#107×C₇₃	—	2	4	no	—
108	C₄⋊C₈×C₇₃	—	2	1	no	—
109	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
110	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
111	#103×C₇₃	—	2	2	no	—
112	#103×C₇₃	—	2	2	no	—
113	#102×C₇₃	—	2	8	no	—
114	#102×C₇₃	—	2	4	no	—
115	C₂²⋊C₈×C₇₃	—	2	1	no	—
116	C₄×C₈×C₇₃	—	2	1	no	—
117	C₄×C₈×C₇₃	—	2	1	no	—
118	C₄×C₈×C₇₃	C₂³	1	2	yes	—
119	C₂⁴×C₇₃	—	2	4	no	—
120	C₂⁴×C₇₃	—	2	2	no	—
121	#41×C₇₃	—	2	2	no	—
122	#41×C₇₃	—	4	8	no	—
123	#41×C₇₃	—	4	4	no	—
124	#41×C₇₃	—	4	4	no	—
125	#41×C₇₃	—	4	2	no	—
126	#41×C₇₃	—	4	2	no	—
127	#41×C₇₃	D₈	1	4	yes	—
128	C₂×Q₈×C₇₃	—	2	1	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	—	4	1	no	—
131	C₂×Q₈×C₇₃	—	4	2	no	—
132	C₂×Q₈×C₇₃	—	4	2	no	—
133	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₇₃	—	2	1	no	—
135	C₂×D₄×C₇₃	—	2	4	no	—
136	C₂×D₄×C₇₃	—	2	4	no	—
137	C₂×D₄×C₇₃	—	2	2	no	—
138	C₂×D₄×C₇₃	—	2	4	no	—
139	C₂×D₄×C₇₃	—	2	4	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	2	1	no	—
142	C₂×D₄×C₇₃	—	2	2	no	—
143	C₂×D₄×C₇₃	—	2	1	no	—
144	C₂×D₄×C₇₃	—	2	2	no	—
145	C₂×D₄×C₇₃	—	2	2	no	—
146	C₂×D₄×C₇₃	—	2	2	no	—
147	C₂×D₄×C₇₃	—	4	8	no	—
148	C₂×D₄×C₇₃	—	4	4	no	—
149	C₂×D₄×C₇₃	—	4	16	no	—
150	C₂×D₄×C₇₃	—	4	4	no	—
151	C₂×D₄×C₇₃	—	4	4	no	—
152	C₂×D₄×C₇₃	—	4	2	no	—
153	C₂×D₄×C₇₃	—	4	2	no	—
154	C₂×D₄×C₇₃	—	8	2	no	—
155	C₂×D₄×C₇₃	—	8	4	no	—
156	C₂×D₄×C₇₃	—	8	4	no	—
157	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₇₃	—	2	1	no	—
161	C₂²×C₄×C₇₃	—	2	4	no	—
162	C₂²×C₄×C₇₃	—	2	1	no	—
163	C₂²×C₄×C₇₃	—	2	1	no	—
164	C₂²×C₄×C₇₃	—	2	2	no	—
165	C₂²×C₄×C₇₃	—	4	1	no	—
166	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
169	Q₁₆×C₇₃	—	4	4	no	—
170	SD₁₆×C₇₃	—	4	4	no	—
171	M₁₆×C₇₃	—	4	2	no	—
172	C₂×C₈×C₇₃	—	2	2	no	—
173	C₂×C₈×C₇₃	—	2	2	no	—
174	C₂×C₈×C₇₃	—	2	2	no	—
175	C₂×C₈×C₇₃	—	4	2	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	—	2	2	no	—
181	C₄⋊C₄×C₇₃	—	4	1	no	—
182	C₄⋊C₄×C₇₃	—	4	1	no	—
183	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
186	C₂²⋊C₄×C₇₃	—	2	4	no	—
187	C₂²⋊C₄×C₇₃	—	2	4	no	—
188	C₂²⋊C₄×C₇₃	—	2	1	no	—
189	C₂²⋊C₄×C₇₃	—	2	1	no	—
190	C₂²⋊C₄×C₇₃	—	2	2	no	—
191	C₂²⋊C₄×C₇₃	—	2	1	no	—
192	C₂²⋊C₄×C₇₃	—	2	2	no	—
193	C₄²×C₇₃	—	2	1	no	—
194	C₄²×C₇₃	—	2	1	no	—
195	C₄²×C₇₃	—	2	1	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	1	yes	characteristic
199	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
200	C₂³×C₇₃	—	2	1	no	—
201	C₂³×C₇₃	—	2	2	no	—
202	C₂³×C₇₃	—	2	4	no	—
203	C₂³×C₇₃	—	4	8	no	—
204	C₂³×C₇₃	—	4	4	no	—
205	C₂³×C₇₃	—	8	2	no	—
206	C₂³×C₇₃	—	8	2	no	—
207	C₂³×C₇₃	—	8	4	no	—
208	C₂³×C₇₃	—	8	4	no	—
209	C₂³×C₇₃	#120	1	1	yes	characteristic
210	Q₈×C₇₃	—	2	1	no	—
211	Q₈×C₇₃	—	4	2	no	—
212	Q₈×C₇₃	—	4	2	no	—
213	Q₈×C₇₃	—	4	2	no	—
214	Q₈×C₇₃	—	8	2	no	—
215	Q₈×C₇₃	C₂×D₈	1	2	yes	—
216	D₄×C₇₃	—	2	4	no	—
217	D₄×C₇₃	—	2	1	no	—
218	D₄×C₇₃	—	2	4	no	—
219	D₄×C₇₃	—	4	4	no	—
220	D₄×C₇₃	—	4	8	no	—
221	D₄×C₇₃	—	4	8	no	—
222	D₄×C₇₃	—	4	4	no	—
223	D₄×C₇₃	—	4	2	no	—
224	D₄×C₇₃	—	4	2	no	—
225	D₄×C₇₃	—	4	4	no	—
226	D₄×C₇₃	—	4	2	no	—
227	D₄×C₇₃	—	4	4	no	—
228	D₄×C₇₃	—	4	4	no	—
229	D₄×C₇₃	—	4	2	no	—
230	D₄×C₇₃	—	8	2	no	—
231	D₄×C₇₃	—	8	4	no	—
232	D₄×C₇₃	—	8	4	no	—
233	D₄×C₇₃	C₂×D₈	1	2	yes	—
234	C₂×C₄×C₇₃	—	2	1	no	—
235	C₂×C₄×C₇₃	—	2	2	no	—
236	C₂×C₄×C₇₃	—	2	4	no	—
237	C₂×C₄×C₇₃	—	2	2	no	—
238	C₂×C₄×C₇₃	—	2	1	no	—
239	C₂×C₄×C₇₃	—	2	1	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	4	8	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	2	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	8	2	no	—
248	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
249	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
250	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
252	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
253	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₇₃	—	4	2	no	—
257	C₈×C₇₃	—	4	2	no	—
258	C₈×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	2	1	no	—
260	C₂²×C₇₃	—	2	1	no	—
261	C₂²×C₇₃	—	2	2	no	—
262	C₂²×C₇₃	—	4	1	no	—
263	C₂²×C₇₃	—	4	1	no	—
264	C₂²×C₇₃	—	4	4	no	—
265	C₂²×C₇₃	—	4	2	no	—
266	C₂²×C₇₃	—	4	2	no	—
267	C₂²×C₇₃	—	4	4	no	—
268	C₂²×C₇₃	—	4	4	no	—
269	C₂²×C₇₃	—	4	2	no	—
270	C₂²×C₇₃	—	16	4	no	—
271	C₂²×C₇₃	—	16	8	no	—
272	C₂²×C₇₃	#447	1	2	yes	—
273	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
274	C₄×C₇₃	—	2	2	no	—
275	C₄×C₇₃	—	2	1	no	—
276	C₄×C₇₃	—	2	1	no	—
277	C₄×C₇₃	—	4	2	no	—
278	C₄×C₇₃	—	4	1	no	—
279	C₄×C₇₃	—	4	1	no	—
280	C₄×C₇₃	—	8	2	no	—
281	C₄×C₇₃	#447	1	2	yes	—
282	C₄×C₇₃	#455	1	2	yes	—
283	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
284	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₇₃	#577	1	2	yes	—
286	#18630	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₇₃	—	2	2	no	—
288	C₂×C₇₃	—	4	2	no	—
289	C₂×C₇₃	—	8	2	no	—
290	C₂×C₇₃	—	8	4	no	—
291	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
292	C₂×C₇₃	#3009	1	1	yes	characteristic
293	C₂×C₇₃	C₂×#455	1	1	yes	characteristic
294	#3498	C₂×C₇₃	1	1	yes	characteristic
295	#3226	C₂×C₇₃	1	1	yes	characteristic, complemented
296	C₂×#486	C₂×C₇₃	1	1	yes	characteristic, complemented
297	#3039	C₂×C₇₃	1	1	yes	characteristic, complemented
298	#1641	C₂×C₇₃	1	4	yes	complemented
299	#1639	C₂×C₇₃	1	4	yes	complemented
300	#1545	C₂×C₇₃	1	1	yes	characteristic, complemented
301	#1492	C₂×C₇₃	1	1	yes	characteristic, complemented
302	#1476	C₂×C₇₃	1	1	yes	characteristic, complemented
303	C₇₃	#18630	1	1	yes	characteristic, direct product factor, Sylow
304	C₂×H(5,𝔽₂)	—	2	1	no	—
305	C₂×#137	—	2	1	no	—
306	#550	—	2	1	no	—
307	#550	C₂²×C₇₃	1	2	yes	—
308	D₄²	—	2	2	no	—
309	D₄²	—	2	2	no	—
310	D₄²	—	2	1	no	—
311	D₄²	C₂²×C₇₃	1	2	yes	—
312	#535	—	2	2	no	—
313	#535	—	2	1	no	—
314	#532	—	2	1	no	—
315	#532	C₂²×C₇₃	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
317	C₂×#127	—	2	1	no	—
318	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
319	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
320	#500	—	2	1	no	—
321	#486	—	2	2	no	—
322	#486	—	2	1	no	—
323	#486	C₂²×C₇₃	1	4	yes	complemented
324	#480	—	2	2	no	—
325	#474	C₂²×C₇₃	1	4	yes	complemented
326	#462	—	2	1	no	—
327	#462	C₂²×C₇₃	1	2	yes	complemented
328	#461	—	2	1	no	—
329	#461	C₂²×C₇₃	1	2	yes	complemented
330	#431	C₂²×C₇₃	1	1	yes	characteristic, complemented
331	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
332	#419	—	2	1	no	—
333	C₂×#102	—	2	2	no	—
334	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
335	#331	C₂²×C₇₃	1	4	yes	complemented
336	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
337	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
338	D₄⋊C₈	C₂²×C₇₃	1	4	yes	complemented
339	H(5,𝔽₂)	—	4	4	no	—
340	H(5,𝔽₂)	—	4	4	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	D₄×C₇₃	1	2	yes	—
354	#137	—	4	4	no	—
355	C₂×Q₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	—	2	1	no	—
361	C₄⋊Q₈	—	2	1	no	—
362	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
363	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
364	#127	—	2	2	no	—
365	#127	—	2	2	no	—
366	#127	—	2	2	no	—
367	#127	—	2	1	no	—
368	#127	—	2	1	no	—
369	#127	D₄×C₇₃	1	1	yes	characteristic
370	#127	D₄×C₇₃	1	2	yes	—
371	#127	C₂³×C₇₃	1	2	yes	—
372	#124	—	2	2	no	—
373	#124	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	4	no	—
376	#121	—	2	4	no	—
377	#121	—	2	1	no	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	D₄×C₇₃	1	2	yes	—
382	#120	—	2	4	no	—
383	#120	—	2	4	no	—
384	#120	—	2	4	no	—
385	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
393	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₇₃	1	2	yes	—
395	#117	—	2	1	no	—
396	#117	D₄×C₇₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
401	#107	—	2	4	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
404	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
405	#103	—	2	2	no	—
406	#103	—	2	2	no	—
407	#102	—	2	8	no	—
408	#102	—	2	4	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	C₂³×C₇₃	1	2	yes	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	4	8	no	—
417	#41	—	4	4	no	—
418	#41	—	4	4	no	—
419	#41	—	4	2	no	—
420	#41	—	4	2	no	—
421	#41	D₈×C₇₃	1	4	yes	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	2	no	—
426	C₂×Q₈	—	4	2	no	—
427	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	16	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	—	8	2	no	—
449	C₂×D₄	—	8	4	no	—
450	C₂×D₄	—	8	4	no	—
451	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
452	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
453	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
463	Q₁₆	—	4	4	no	—
464	SD₁₆	—	4	4	no	—
465	M₁₆	—	4	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	4	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
491	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
493	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	8	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	8	2	no	—
501	C₂³	—	8	4	no	—
502	C₂³	—	8	4	no	—
503	C₂³	#120×C₇₃	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	8	2	no	—
509	Q₈	C₂×D₈×C₇₃	1	2	yes	—
510	D₄	—	2	4	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	8	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	4	no	—
524	D₄	—	8	2	no	—
525	D₄	—	8	4	no	—
526	D₄	—	8	4	no	—
527	D₄	C₂×D₈×C₇₃	1	2	yes	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
543	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
544	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
545	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
546	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₈	—	4	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	16	4	no	—
565	C₂²	—	16	8	no	—
566	C₂²	#447×C₇₃	1	2	yes	—
567	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	2	no	—
575	C₄	#447×C₇₃	1	2	yes	—
576	C₄	#455×C₇₃	1	2	yes	—
577	C₄	C₂²×D₈×C₇₃	1	1	yes	characteristic
578	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
579	C₄	#577×C₇₃	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	4	2	no	—
582	C₂	—	8	2	no	—
583	C₂	—	8	4	no	—
584	C₂	C₂×#447×C₇₃	1	1	yes	characteristic
585	C₂	C₇₃×#3009	1	1	yes	characteristic
586	C₂	C₂×#455×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	C₇₃×#3498	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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
2. C₇₃×#3226	C₂	semidirect
3. C₂×#486×C₇₃	C₂	semidirect
4. C₇₃×#3039	C₂	semidirect
5. C₇₃×#1641	C₂	semidirect
6. C₇₃×#1639	C₂	semidirect
7. C₇₃×#1545	C₂	semidirect
8. C₇₃×#1492	C₂	semidirect
9. C₇₃×#1476	C₂	semidirect
22. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
29. #486×C₇₃	C₂²	semidirect
31. #474×C₇₃	C₂²	semidirect
33. #462×C₇₃	C₂²	semidirect
35. #461×C₇₃	C₂²	semidirect
36. #431×C₇₃	C₂²	semidirect
37. #423×C₇₃	C₂²	semidirect
40. C₂×C₄×C₈×C₇₃	C₂²	semidirect
41. #331×C₇₃	C₂²	semidirect
42. Q₈⋊C₈×C₇₃	C₂²	semidirect
43. D₄⋊C₈×C₇₃	C₂²	semidirect
44. D₄⋊C₈×C₇₃	C₂²	semidirect
286. #18630	C₇₃	direct (N × H)
295. #3226	C₂×C₇₃	semidirect
296. C₂×#486	C₂×C₇₃	semidirect
297. #3039	C₂×C₇₃	semidirect
298. #1641	C₂×C₇₃	semidirect
299. #1639	C₂×C₇₃	semidirect
300. #1545	C₂×C₇₃	semidirect
301. #1492	C₂×C₇₃	semidirect
302. #1476	C₂×C₇₃	semidirect
303. C₇₃	#18630	direct (N × H)
316. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
323. #486	C₂²×C₇₃	semidirect
325. #474	C₂²×C₇₃	semidirect
327. #462	C₂²×C₇₃	semidirect
329. #461	C₂²×C₇₃	semidirect
330. #431	C₂²×C₇₃	semidirect
331. #423	C₂²×C₇₃	semidirect
334. C₂×C₄×C₈	C₂²×C₇₃	semidirect
335. #331	C₂²×C₇₃	semidirect
336. Q₈⋊C₈	C₂²×C₇₃	semidirect
337. D₄⋊C₈	C₂²×C₇₃	semidirect
338. D₄⋊C₈	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3498	2
C₇₃×#3226	2
C₂×#486×C₇₃	2
C₇₃×#3039	2
C₇₃×#1641	2
C₇₃×#1639	2
C₇₃×#1545	2
C₇₃×#1492	2
C₇₃×#1476	2
#18630	73

Subgroups — C73×#18630 #32928034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18630 #32928034