Subgroups — C₇₃×#33541 #32942945

Order 18688.

1104 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#509×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#472×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2193	C₂	1	4	yes	maximal, complemented
6	C₇₃×#2192	C₂	1	4	yes	maximal, complemented
7	C₇₃×#2148	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2143	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	#585×C₇₃	—	2	1	no	—
11	#578×C₇₃	—	2	1	no	—
12	#578×C₇₃	C₂²	1	2	yes	complemented
13	#577×C₇₃	—	2	2	no	—
14	#577×C₇₃	—	2	2	no	—
15	#576×C₇₃	—	2	1	no	—
16	#576×C₇₃	C₂²	1	2	yes	complemented
17	#575×C₇₃	—	2	2	no	—
18	#575×C₇₃	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₇₃	—	2	1	no	—
20	C₂×#135×C₇₃	—	2	2	no	—
21	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
25	#509×C₇₃	—	2	2	no	—
26	#509×C₇₃	—	2	2	no	—
27	#509×C₇₃	—	2	2	no	—
28	#509×C₇₃	C₂²	1	4	yes	complemented
29	C₂×SD₃₂×C₇₃	—	2	1	no	—
30	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	complemented
31	C₂×D₁₆×C₇₃	—	2	1	no	—
32	C₂×D₁₆×C₇₃	C₂²	1	2	yes	complemented
33	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×M₃₂×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#472×C₇₃	—	2	2	no	—
36	#472×C₇₃	C₂²	1	4	yes	complemented
37	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#100×C₇₃	—	2	1	no	—
39	#362×C₇₃	C₂²	1	2	yes	complemented
40	#361×C₇₃	C₂²	1	2	yes	complemented
41	#359×C₇₃	C₂²	1	4	yes	complemented
42	#350×C₇₃	C₂²	1	4	yes	complemented
43	2₋¹⁺⁴×C₇₃	—	2	2	no	—
44	2₋¹⁺⁴×C₇₃	—	2	2	no	—
45	2₋¹⁺⁴×C₇₃	—	4	1	no	—
46	H(5,𝔽₂)×C₇₃	—	2	2	no	—
47	H(5,𝔽₂)×C₇₃	—	2	2	no	—
48	H(5,𝔽₂)×C₇₃	—	4	2	no	—
49	H(5,𝔽₂)×C₇₃	—	4	1	no	—
50	C₂×#41×C₇₃	—	2	4	no	—
51	C₂×#41×C₇₃	—	2	1	no	—
52	C₂×#41×C₇₃	—	2	1	no	—
53	C₂×#41×C₇₃	—	4	2	no	—
54	C₂×#41×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₇₃	—	2	1	no	—
57	#137×C₇₃	—	2	2	no	—
58	#137×C₇₃	—	2	4	no	—
59	#137×C₇₃	—	2	4	no	—
60	#137×C₇₃	—	2	2	no	—
61	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
62	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
63	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
64	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
65	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
66	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
67	#135×C₇₃	—	2	4	no	—
68	#135×C₇₃	—	2	4	no	—
69	#135×C₇₃	—	2	2	no	—
70	#135×C₇₃	—	2	2	no	—
71	#135×C₇₃	—	2	1	no	—
72	#135×C₇₃	—	2	1	no	—
73	#135×C₇₃	—	2	1	no	—
74	#135×C₇₃	—	2	1	no	—
75	#135×C₇₃	D₄	1	2	yes	—
76	#135×C₇₃	D₄	1	2	yes	—
77	#135×C₇₃	D₄	1	2	yes	—
78	#135×C₇₃	C₂³	1	2	yes	—
79	C₂×Q₁₆×C₇₃	—	2	2	no	—
80	C₂×Q₁₆×C₇₃	D₄	1	1	yes	characteristic
81	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×SD₁₆×C₇₃	—	2	4	no	—
83	C₂×SD₁₆×C₇₃	—	2	1	no	—
84	C₂×SD₁₆×C₇₃	—	2	1	no	—
85	C₂×SD₁₆×C₇₃	—	4	1	no	—
86	C₂×D₈×C₇₃	—	2	2	no	—
87	C₂×D₈×C₇₃	—	2	1	no	—
88	C₂×D₈×C₇₃	—	2	1	no	—
89	C₂×D₈×C₇₃	—	2	1	no	—
90	C₂×D₈×C₇₃	—	2	1	no	—
91	C₂×D₈×C₇₃	—	2	1	no	—
92	C₂×D₈×C₇₃	—	4	1	no	—
93	C₂×D₈×C₇₃	D₄	1	1	yes	characteristic
94	C₂×D₈×C₇₃	C₂³	1	2	yes	—
95	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
96	#131×C₇₃	—	2	1	no	—
97	#131×C₇₃	—	2	1	no	—
98	#131×C₇₃	D₄	1	2	yes	—
99	#131×C₇₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₇₃	—	2	1	no	—
101	C₂×M₁₆×C₇₃	—	2	1	no	—
102	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
103	C₂²×C₈×C₇₃	—	2	1	no	—
104	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
105	SD₃₂×C₇₃	—	2	4	no	—
106	SD₃₂×C₇₃	—	2	4	no	—
107	D₁₆×C₇₃	—	2	4	no	—
108	D₁₆×C₇₃	—	2	4	no	—
109	M₃₂×C₇₃	—	2	1	no	—
110	M₃₂×C₇₃	—	2	1	no	—
111	M₃₂×C₇₃	—	2	1	no	—
112	M₃₂×C₇₃	C₂³	1	2	yes	—
113	C₂×C₁₆×C₇₃	—	2	1	no	—
114	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
115	#108×C₇₃	—	2	1	no	—
116	#108×C₇₃	C₂³	1	2	yes	—
117	#100×C₇₃	—	2	4	no	—
118	C₂⁴×C₇₃	—	4	1	no	—
119	#41×C₇₃	—	2	1	no	—
120	#41×C₇₃	—	2	1	no	—
121	#41×C₇₃	—	2	4	no	—
122	#41×C₇₃	—	2	4	no	—
123	#41×C₇₃	—	2	2	no	—
124	#41×C₇₃	—	2	2	no	—
125	#41×C₇₃	—	2	2	no	—
126	#41×C₇₃	—	2	2	no	—
127	#41×C₇₃	—	4	4	no	—
128	#41×C₇₃	—	4	4	no	—
129	#41×C₇₃	—	4	4	no	—
130	#41×C₇₃	—	4	4	no	—
131	#41×C₇₃	—	4	2	no	—
132	#41×C₇₃	—	4	2	no	—
133	#41×C₇₃	—	4	2	no	—
134	#41×C₇₃	—	4	2	no	—
135	#41×C₇₃	—	4	1	no	—
136	#41×C₇₃	—	4	1	no	—
137	#41×C₇₃	—	4	1	no	—
138	#41×C₇₃	—	4	1	no	—
139	#41×C₇₃	D₈	1	2	yes	—
140	#41×C₇₃	C₂×D₄	1	2	yes	—
141	C₂×Q₈×C₇₃	—	2	4	no	—
142	C₂×Q₈×C₇₃	—	2	1	no	—
143	C₂×Q₈×C₇₃	—	2	1	no	—
144	C₂×Q₈×C₇₃	—	4	2	no	—
145	C₂×Q₈×C₇₃	—	4	2	no	—
146	C₂×Q₈×C₇₃	D₈	1	1	yes	characteristic
147	C₂×D₄×C₇₃	—	2	1	no	—
148	C₂×D₄×C₇₃	—	2	4	no	—
149	C₂×D₄×C₇₃	—	2	1	no	—
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	—	4	4	no	—
153	C₂×D₄×C₇₃	—	4	4	no	—
154	C₂×D₄×C₇₃	—	4	2	no	—
155	C₂×D₄×C₇₃	—	4	4	no	—
156	C₂×D₄×C₇₃	—	4	1	no	—
157	C₂×D₄×C₇₃	—	4	1	no	—
158	C₂×D₄×C₇₃	—	4	2	no	—
159	C₂×D₄×C₇₃	—	4	1	no	—
160	C₂×D₄×C₇₃	—	4	1	no	—
161	C₂×D₄×C₇₃	—	4	1	no	—
162	C₂×D₄×C₇₃	—	4	1	no	—
163	C₂×D₄×C₇₃	—	4	1	no	—
164	C₂×D₄×C₇₃	D₈	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	—	2	1	no	—
166	C₂²×C₄×C₇₃	—	4	4	no	—
167	C₂²×C₄×C₇₃	—	4	1	no	—
168	C₂²×C₄×C₇₃	—	4	1	no	—
169	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
170	Q₁₆×C₇₃	—	2	4	no	—
171	Q₁₆×C₇₃	—	2	1	no	—
172	Q₁₆×C₇₃	—	2	1	no	—
173	Q₁₆×C₇₃	C₂×D₄	1	2	yes	—
174	Q₁₆×C₇₃	C₂×D₄	1	2	yes	—
175	SD₁₆×C₇₃	—	2	4	no	—
176	SD₁₆×C₇₃	—	2	4	no	—
177	SD₁₆×C₇₃	—	2	2	no	—
178	SD₁₆×C₇₃	—	2	2	no	—
179	SD₁₆×C₇₃	—	2	2	no	—
180	SD₁₆×C₇₃	—	2	2	no	—
181	SD₁₆×C₇₃	—	4	4	no	—
182	D₈×C₇₃	—	2	4	no	—
183	D₈×C₇₃	—	2	1	no	—
184	D₈×C₇₃	—	2	1	no	—
185	D₈×C₇₃	—	2	2	no	—
186	D₈×C₇₃	—	2	2	no	—
187	D₈×C₇₃	—	4	4	no	—
188	D₈×C₇₃	—	4	1	no	—
189	D₈×C₇₃	—	4	1	no	—
190	D₈×C₇₃	C₂×D₄	1	2	yes	—
191	D₈×C₇₃	C₂×D₄	1	2	yes	—
192	M₁₆×C₇₃	—	2	1	no	—
193	M₁₆×C₇₃	—	2	2	no	—
194	M₁₆×C₇₃	—	2	2	no	—
195	M₁₆×C₇₃	—	2	2	no	—
196	M₁₆×C₇₃	—	4	1	no	—
197	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₇₃	—	2	1	no	—
199	C₂×C₈×C₇₃	—	2	2	no	—
200	C₂×C₈×C₇₃	—	2	2	no	—
201	C₂×C₈×C₇₃	—	4	1	no	—
202	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
206	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
208	C₁₆×C₇₃	—	2	2	no	—
209	C₁₆×C₇₃	—	2	2	no	—
210	C₂³×C₇₃	—	2	1	no	—
211	C₂³×C₇₃	—	4	4	no	—
212	C₂³×C₇₃	—	4	1	no	—
213	C₂³×C₇₃	—	4	1	no	—
214	C₂³×C₇₃	—	4	2	no	—
215	C₂³×C₇₃	—	8	1	no	—
216	C₂³×C₇₃	—	8	1	no	—
217	C₂³×C₇₃	—	16	2	no	—
218	C₂³×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
219	Q₈×C₇₃	—	2	1	no	—
220	Q₈×C₇₃	—	2	2	no	—
221	Q₈×C₇₃	—	2	2	no	—
222	Q₈×C₇₃	—	4	4	no	—
223	Q₈×C₇₃	—	4	1	no	—
224	Q₈×C₇₃	—	4	1	no	—
225	Q₈×C₇₃	C₂×D₈	1	2	yes	—
226	D₄×C₇₃	—	2	2	no	—
227	D₄×C₇₃	—	2	2	no	—
228	D₄×C₇₃	—	2	2	no	—
229	D₄×C₇₃	—	2	2	no	—
230	D₄×C₇₃	—	2	1	no	—
231	D₄×C₇₃	—	4	4	no	—
232	D₄×C₇₃	—	4	4	no	—
233	D₄×C₇₃	—	4	4	no	—
234	D₄×C₇₃	—	4	2	no	—
235	D₄×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	2	no	—
237	D₄×C₇₃	—	4	2	no	—
238	D₄×C₇₃	—	4	2	no	—
239	D₄×C₇₃	—	4	1	no	—
240	D₄×C₇₃	—	4	2	no	—
241	D₄×C₇₃	—	4	1	no	—
242	D₄×C₇₃	—	8	1	no	—
243	D₄×C₇₃	—	8	1	no	—
244	D₄×C₇₃	C₂×D₈	1	2	yes	—
245	C₂×C₄×C₇₃	—	2	1	no	—
246	C₂×C₄×C₇₃	—	2	2	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	4	4	no	—
249	C₂×C₄×C₇₃	—	4	4	no	—
250	C₂×C₄×C₇₃	—	4	4	no	—
251	C₂×C₄×C₇₃	—	4	1	no	—
252	C₂×C₄×C₇₃	—	4	1	no	—
253	C₂×C₄×C₇₃	—	4	2	no	—
254	C₂×C₄×C₇₃	—	4	2	no	—
255	C₂×C₄×C₇₃	—	4	2	no	—
256	C₂×C₄×C₇₃	—	4	2	no	—
257	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
258	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
260	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
261	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₇₃	—	2	2	no	—
264	C₈×C₇₃	—	4	2	no	—
265	C₈×C₇₃	#120	1	1	yes	characteristic
266	C₈×C₇₃	#120	1	1	yes	characteristic
267	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
269	C₂²×C₇₃	—	2	2	no	—
270	C₂²×C₇₃	—	4	1	no	—
271	C₂²×C₇₃	—	4	2	no	—
272	C₂²×C₇₃	—	4	2	no	—
273	C₂²×C₇₃	—	8	1	no	—
274	C₂²×C₇₃	—	8	2	no	—
275	C₂²×C₇₃	—	16	1	no	—
276	C₂²×C₇₃	—	16	1	no	—
277	C₂²×C₇₃	—	16	2	no	—
278	C₂²×C₇₃	—	16	2	no	—
279	C₂²×C₇₃	—	16	2	no	—
280	C₂²×C₇₃	—	16	4	no	—
281	C₂²×C₇₃	#447	1	1	yes	characteristic
282	C₂²×C₇₃	#447	1	1	yes	characteristic
283	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₄×C₇₃	—	2	2	no	—
285	C₄×C₇₃	—	4	2	no	—
286	C₄×C₇₃	—	4	2	no	—
287	C₄×C₇₃	#447	1	1	yes	characteristic
288	C₄×C₇₃	#447	1	1	yes	characteristic
289	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
290	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
291	#33541	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂×C₇₃	—	2	1	no	—
293	C₂×C₇₃	—	2	1	no	—
294	C₂×C₇₃	—	2	1	no	—
295	C₂×C₇₃	—	4	2	no	—
296	C₂×C₇₃	—	8	2	no	—
297	C₂×C₇₃	—	8	2	no	—
298	C₂×C₇₃	—	16	2	no	—
299	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
300	#3584	C₂×C₇₃	1	1	yes	characteristic, complemented
301	C₂×#509	C₂×C₇₃	1	1	yes	characteristic, complemented
302	C₂×#509	C₂×C₇₃	1	1	yes	characteristic, complemented
303	C₂×#472	C₂×C₇₃	1	1	yes	characteristic, complemented
304	#2193	C₂×C₇₃	1	4	yes	complemented
305	#2192	C₂×C₇₃	1	4	yes	complemented
306	#2148	C₂×C₇₃	1	1	yes	characteristic, complemented
307	#2143	C₂×C₇₃	1	1	yes	characteristic, complemented
308	#2117	C₂×C₇₃	1	1	yes	characteristic, complemented
309	C₇₃	#33541	1	1	yes	characteristic, direct product factor, Sylow
310	#585	—	2	1	no	—
311	#578	—	2	1	no	—
312	#578	C₂²×C₇₃	1	2	yes	complemented
313	#577	—	2	2	no	—
314	#577	—	2	2	no	—
315	#576	—	2	1	no	—
316	#576	C₂²×C₇₃	1	2	yes	complemented
317	#575	—	2	2	no	—
318	#575	—	2	1	no	—
319	C₂×AGL(1,ℤ/8)	—	2	1	no	—
320	C₂×#135	—	2	2	no	—
321	C₂×#135	C₂²×C₇₃	1	1	yes	characteristic
322	C₂×#135	C₂²×C₇₃	1	1	yes	characteristic
323	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
324	C₂×#131	C₂²×C₇₃	1	1	yes	characteristic
325	#509	—	2	2	no	—
326	#509	—	2	2	no	—
327	#509	—	2	2	no	—
328	#509	C₂²×C₇₃	1	4	yes	complemented
329	C₂×SD₃₂	—	2	1	no	—
330	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	complemented
331	C₂×D₁₆	—	2	1	no	—
332	C₂×D₁₆	C₂²×C₇₃	1	2	yes	complemented
333	C₂×M₃₂	C₂²×C₇₃	1	1	yes	characteristic, complemented
334	C₂×M₃₂	C₂²×C₇₃	1	1	yes	characteristic, complemented
335	#472	—	2	2	no	—
336	#472	C₂²×C₇₃	1	4	yes	complemented
337	C₂×#108	C₂²×C₇₃	1	1	yes	characteristic, complemented
338	C₂×#100	—	2	1	no	—
339	#362	C₂²×C₇₃	1	2	yes	complemented
340	#361	C₂²×C₇₃	1	2	yes	complemented
341	#359	C₂²×C₇₃	1	4	yes	complemented
342	#350	C₂²×C₇₃	1	4	yes	complemented
343	2₋¹⁺⁴	—	2	2	no	—
344	2₋¹⁺⁴	—	2	2	no	—
345	2₋¹⁺⁴	—	4	1	no	—
346	H(5,𝔽₂)	—	2	2	no	—
347	H(5,𝔽₂)	—	2	2	no	—
348	H(5,𝔽₂)	—	4	2	no	—
349	H(5,𝔽₂)	—	4	1	no	—
350	C₂×#41	—	2	4	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	4	2	no	—
354	C₂×#41	—	4	2	no	—
355	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
356	C₂²×D₄	—	2	1	no	—
357	#137	—	2	2	no	—
358	#137	—	2	4	no	—
359	#137	—	2	4	no	—
360	#137	—	2	2	no	—
361	AGL(1,ℤ/8)	—	2	2	no	—
362	AGL(1,ℤ/8)	—	2	4	no	—
363	AGL(1,ℤ/8)	—	2	4	no	—
364	AGL(1,ℤ/8)	—	2	4	no	—
365	AGL(1,ℤ/8)	—	2	2	no	—
366	AGL(1,ℤ/8)	—	4	2	no	—
367	#135	—	2	4	no	—
368	#135	—	2	4	no	—
369	#135	—	2	2	no	—
370	#135	—	2	2	no	—
371	#135	—	2	1	no	—
372	#135	—	2	1	no	—
373	#135	—	2	1	no	—
374	#135	—	2	1	no	—
375	#135	D₄×C₇₃	1	2	yes	—
376	#135	D₄×C₇₃	1	2	yes	—
377	#135	D₄×C₇₃	1	2	yes	—
378	#135	C₂³×C₇₃	1	2	yes	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	D₄×C₇₃	1	1	yes	characteristic
381	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
382	C₂×SD₁₆	—	2	4	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	2	1	no	—
385	C₂×SD₁₆	—	4	1	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×D₈	—	2	1	no	—
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	2	1	no	—
390	C₂×D₈	—	2	1	no	—
391	C₂×D₈	—	2	1	no	—
392	C₂×D₈	—	4	1	no	—
393	C₂×D₈	D₄×C₇₃	1	1	yes	characteristic
394	C₂×D₈	C₂³×C₇₃	1	2	yes	—
395	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
396	#131	—	2	1	no	—
397	#131	—	2	1	no	—
398	#131	D₄×C₇₃	1	2	yes	—
399	#131	C₂³×C₇₃	1	2	yes	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	D₄×C₇₃	1	1	yes	characteristic
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
405	SD₃₂	—	2	4	no	—
406	SD₃₂	—	2	4	no	—
407	D₁₆	—	2	4	no	—
408	D₁₆	—	2	4	no	—
409	M₃₂	—	2	1	no	—
410	M₃₂	—	2	1	no	—
411	M₃₂	—	2	1	no	—
412	M₃₂	C₂³×C₇₃	1	2	yes	—
413	C₂×C₁₆	—	2	1	no	—
414	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
415	#108	—	2	1	no	—
416	#108	C₂³×C₇₃	1	2	yes	—
417	#100	—	2	4	no	—
418	C₂⁴	—	4	1	no	—
419	#41	—	2	1	no	—
420	#41	—	2	1	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	4	4	no	—
428	#41	—	4	4	no	—
429	#41	—	4	4	no	—
430	#41	—	4	4	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	2	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	D₈×C₇₃	1	2	yes	—
440	#41	C₂×D₄×C₇₃	1	2	yes	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	4	2	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	D₈×C₇₃	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	D₈×C₇₃	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
470	Q₁₆	—	2	4	no	—
471	Q₁₆	—	2	1	no	—
472	Q₁₆	—	2	1	no	—
473	Q₁₆	C₂×D₄×C₇₃	1	2	yes	—
474	Q₁₆	C₂×D₄×C₇₃	1	2	yes	—
475	SD₁₆	—	2	4	no	—
476	SD₁₆	—	2	4	no	—
477	SD₁₆	—	2	2	no	—
478	SD₁₆	—	2	2	no	—
479	SD₁₆	—	2	2	no	—
480	SD₁₆	—	2	2	no	—
481	SD₁₆	—	4	4	no	—
482	D₈	—	2	4	no	—
483	D₈	—	2	1	no	—
484	D₈	—	2	1	no	—
485	D₈	—	2	2	no	—
486	D₈	—	2	2	no	—
487	D₈	—	4	4	no	—
488	D₈	—	4	1	no	—
489	D₈	—	4	1	no	—
490	D₈	C₂×D₄×C₇₃	1	2	yes	—
491	D₈	C₂×D₄×C₇₃	1	2	yes	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	C₂×D₄×C₇₃	1	2	yes	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	4	1	no	—
502	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
506	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
507	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
508	C₁₆	—	2	2	no	—
509	C₁₆	—	2	2	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	8	1	no	—
516	C₂³	—	8	1	no	—
517	C₂³	—	16	2	no	—
518	C₂³	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
519	Q₈	—	2	1	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	4	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	C₂×D₈×C₇₃	1	2	yes	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	1	no	—
544	D₄	C₂×D₈×C₇₃	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
558	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
559	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
560	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
561	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
563	C₈	—	2	2	no	—
564	C₈	—	4	2	no	—
565	C₈	#120×C₇₃	1	1	yes	characteristic
566	C₈	#120×C₇₃	1	1	yes	characteristic
567	C₈	C₂²×D₄×C₇₃	1	1	yes	characteristic
568	C₈	C₂²×D₄×C₇₃	1	1	yes	characteristic
569	C₂²	—	2	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	16	1	no	—
576	C₂²	—	16	1	no	—
577	C₂²	—	16	2	no	—
578	C₂²	—	16	2	no	—
579	C₂²	—	16	2	no	—
580	C₂²	—	16	4	no	—
581	C₂²	#447×C₇₃	1	1	yes	characteristic
582	C₂²	#447×C₇₃	1	1	yes	characteristic
583	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	#447×C₇₃	1	1	yes	characteristic
588	C₄	#447×C₇₃	1	1	yes	characteristic
589	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
590	C₄	C₂²×D₈×C₇₃	1	1	yes	characteristic
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	4	2	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	2	no	—
597	C₂	—	16	2	no	—
598	C₂	C₂×#447×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₃	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#131×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3584	C₂	semidirect
2. C₂×#509×C₇₃	C₂	semidirect
3. C₂×#509×C₇₃	C₂	semidirect
4. C₂×#472×C₇₃	C₂	semidirect
5. C₇₃×#2193	C₂	semidirect
6. C₇₃×#2192	C₂	semidirect
7. C₇₃×#2148	C₂	semidirect
8. C₇₃×#2143	C₂	semidirect
9. C₇₃×#2117	C₂	semidirect
12. #578×C₇₃	C₂²	semidirect
16. #576×C₇₃	C₂²	semidirect
23. C₂²×D₈×C₇₃	C₂²	semidirect
28. #509×C₇₃	C₂²	semidirect
30. C₂×SD₃₂×C₇₃	C₂²	semidirect
32. C₂×D₁₆×C₇₃	C₂²	semidirect
33. C₂×M₃₂×C₇₃	C₂²	semidirect
34. C₂×M₃₂×C₇₃	C₂²	semidirect
36. #472×C₇₃	C₂²	semidirect
37. C₂×#108×C₇₃	C₂²	semidirect
39. #362×C₇₃	C₂²	semidirect
40. #361×C₇₃	C₂²	semidirect
41. #359×C₇₃	C₂²	semidirect
42. #350×C₇₃	C₂²	semidirect
291. #33541	C₇₃	direct (N × H)
300. #3584	C₂×C₇₃	semidirect
301. C₂×#509	C₂×C₇₃	semidirect
302. C₂×#509	C₂×C₇₃	semidirect
303. C₂×#472	C₂×C₇₃	semidirect
304. #2193	C₂×C₇₃	semidirect
305. #2192	C₂×C₇₃	semidirect
306. #2148	C₂×C₇₃	semidirect
307. #2143	C₂×C₇₃	semidirect
308. #2117	C₂×C₇₃	semidirect
309. C₇₃	#33541	direct (N × H)
312. #578	C₂²×C₇₃	semidirect
316. #576	C₂²×C₇₃	semidirect
323. C₂²×D₈	C₂²×C₇₃	semidirect
328. #509	C₂²×C₇₃	semidirect
330. C₂×SD₃₂	C₂²×C₇₃	semidirect
332. C₂×D₁₆	C₂²×C₇₃	semidirect
333. C₂×M₃₂	C₂²×C₇₃	semidirect
334. C₂×M₃₂	C₂²×C₇₃	semidirect
336. #472	C₂²×C₇₃	semidirect
337. C₂×#108	C₂²×C₇₃	semidirect
339. #362	C₂²×C₇₃	semidirect
340. #361	C₂²×C₇₃	semidirect
341. #359	C₂²×C₇₃	semidirect
342. #350	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×#3584	2
C₂×#509×C₇₃	2
C₂×#472×C₇₃	2
C₇₃×#2193	2
C₇₃×#2192	2
C₇₃×#2148	2
C₇₃×#2143	2
C₇₃×#2117	2
#33541	73

Subgroups — C73×#33541 #32942945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#33541 #32942945