Subgroups — #1952×D₇₃ #33089526

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#428×D₇₃	C₂	1	2	yes	maximal
3	C₂×#107×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#22610717	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610716	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610715	C₂	1	2	yes	maximal, complemented
8	#22610714	C₂	1	1	yes	maximal, characteristic, complemented
9	#22610713	C₂	1	2	yes	maximal, complemented
10	#343×D₇₃	C₂	1	2	yes	maximal
11	C₇₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	#117×D₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
17	C₂×#14556527	C₂²	1	1	yes	characteristic
18	C₂×#14556526	C₂²	1	2	yes	—
19	#108×D₇₃	C₄	1	8	yes	complemented
20	#17988630	C₂²	1	2	yes	—
21	#17988629	C₂²	1	2	yes	—
22	#17988628	—	2	2	no	—
23	#17988627	C₂²	1	2	yes	—
24	#17988626	—	2	2	no	—
25	C₂×#14556525	C₂²	1	1	yes	characteristic
26	C₂×#14556524	C₂²	1	2	yes	—
27	#107×D₇₃	—	2	1	no	—
28	#107×D₇₃	—	2	1	no	—
29	#107×D₇₃	—	2	1	no	—
30	#107×D₇₃	—	2	1	no	—
31	#107×D₇₃	—	2	2	no	—
32	#106×D₇₃	—	2	2	no	—
33	#17988545	C₂²	1	1	yes	characteristic
34	#17988544	—	2	1	no	—
35	#17988543	C₂²	1	1	yes	characteristic
36	#17988542	C₂²	1	1	yes	characteristic
37	#17988541	—	2	1	no	—
38	#97×D₇₃	—	2	1	no	—
39	C₄×C₈×D₇₃	—	2	1	no	—
40	#17988356	C₂²	1	2	yes	—
41	#17988355	C₂²	1	2	yes	—
42	#17988355	C₂²	1	2	yes	—
43	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
44	#428×C₇₃	C₂²	1	2	yes	—
45	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₂²	1	1	yes	characteristic
47	#343×C₇₃	C₂²	1	2	yes	—
48	C₂²×C₄×D₇₃	—	2	2	no	—
49	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
50	C₂×#11924012	C₂³	1	2	yes	—
51	C₂×#11924012	C₂³	1	1	yes	characteristic
52	C₂×#11924011	—	2	2	no	—
53	C₂×#11924011	—	2	1	no	—
54	M₁₆×D₇₃	—	2	4	no	—
55	M₁₆×D₇₃	—	2	2	no	—
56	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
57	M₁₆×D₇₃	Q₈	1	4	yes	—
58	C₂²×#10596831	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₇₃	—	2	2	no	—
60	C₂×C₈×D₇₃	—	2	1	no	—
61	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
62	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₇₃	Q₈	1	4	yes	—
67	#14556550	C₂³	1	1	yes	characteristic
68	#14556549	D₄	1	1	yes	characteristic
69	#14556549	D₄	1	1	yes	characteristic
70	#14556548	—	2	1	no	—
71	#14556547	—	2	1	no	—
72	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
73	C₂×#11924007	—	2	2	no	—
74	C₄⋊C₄×D₇₃	—	2	2	no	—
75	C₄⋊C₄×D₇₃	—	2	2	no	—
76	C₄⋊C₄×D₇₃	—	2	2	no	—
77	C₄⋊C₄×D₇₃	—	2	2	no	—
78	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
79	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
80	C₂²⋊C₄×D₇₃	—	2	1	no	—
81	C₄²×D₇₃	—	2	1	no	—
82	#14556527	C₂×C₄	1	4	yes	complemented
83	#14556526	C₂×C₄	1	8	yes	complemented
84	#14556525	—	2	2	no	—
85	#14556525	—	2	1	no	—
86	#14556525	—	2	1	no	—
87	#14556524	—	2	2	no	—
88	#14556524	—	2	2	no	—
89	#14556524	—	2	2	no	—
90	#14556524	—	2	2	no	—
91	#14556523	—	2	2	no	—
92	#14556522	—	2	2	no	—
93	#14556522	—	2	2	no	—
94	#14556502	—	2	1	no	—
95	#14556501	—	2	1	no	—
96	#14556501	—	2	1	no	—
97	C₄×#10596831	—	2	1	no	—
98	C₈×Dic₇₃	—	2	1	no	—
99	C₈×Dic₇₃	—	2	1	no	—
100	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
101	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	#117×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
105	#108×C₇₃	C₂×C₄	1	4	yes	complemented
106	#107×C₇₃	—	2	1	no	—
107	#107×C₇₃	—	2	1	no	—
108	#107×C₇₃	—	2	2	no	—
109	#106×C₇₃	—	2	2	no	—
110	#97×C₇₃	—	2	1	no	—
111	C₄×C₈×C₇₃	—	2	1	no	—
112	C₂³×D₇₃	#41	1	1	yes	characteristic
113	C₂²×Dic₇₃	—	2	2	no	—
114	C₂²×Dic₇₃	#41	1	1	yes	characteristic
115	C₂×C₄×D₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	4	2	no	—
118	C₂×C₄×D₇₃	—	4	2	no	—
119	C₂×C₄×D₇₃	—	8	4	no	—
120	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
121	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
126	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
127	C₂×C₄×D₇₃	#41	1	2	yes	—
128	#11924012	—	2	2	no	—
129	#11924012	—	2	1	no	—
130	#11924012	C₂²×C₄	1	4	yes	—
131	#11924012	C₂×Q₈	1	2	yes	—
132	#11924011	—	2	8	no	—
133	#11924011	—	2	4	no	—
134	C₂×#10596831	—	2	1	no	—
135	C₂×#10596831	—	2	2	no	—
136	C₂×#10596831	C₂²×C₄	1	2	yes	—
137	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
138	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
139	C₂×#10596831	C₂×Q₈	1	2	yes	—
140	C₈×D₇₃	—	2	8	no	—
141	C₈×D₇₃	—	2	4	no	—
142	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
143	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
144	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
145	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
146	C₄⋊Dic₇₃	—	2	2	no	—
147	C₄⋊Dic₇₃	—	2	2	no	—
148	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
150	#11924007	—	2	1	no	—
151	#11924007	—	2	1	no	—
152	#11924007	—	4	2	no	—
153	#11924007	—	4	2	no	—
154	C₂²⋊Dic₇₃	—	2	1	no	—
155	#11924005	—	2	1	no	—
156	#11924005	—	2	1	no	—
157	C₄×Dic₇₃	—	2	1	no	—
158	C₄×Dic₇₃	—	2	1	no	—
159	C₄×Dic₇₃	—	2	1	no	—
160	C₂²×C₄×C₇₃	—	2	2	no	—
161	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₇₃	—	2	2	no	—
163	M₁₆×C₇₃	—	2	1	no	—
164	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
165	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
166	C₂×C₈×C₇₃	—	2	1	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
172	C₄⋊C₄×C₇₃	—	2	2	no	—
173	C₄⋊C₄×C₇₃	—	2	2	no	—
174	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂²⋊C₄×C₇₃	—	2	1	no	—
177	C₄²×C₇₃	—	2	1	no	—
178	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
179	C₂²×D₇₃	—	2	2	no	—
180	C₂²×D₇₃	—	2	2	no	—
181	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
182	C₂²×D₇₃	#121	1	1	yes	characteristic
183	C₂²×D₇₃	#121	1	1	yes	characteristic
184	C₂²×D₇₃	#125	1	2	yes	—
185	C₂×C₄×C₇₃	—	2	1	no	—
186	C₂×C₄×C₇₃	—	2	1	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	8	2	no	—
189	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
195	C₂×Dic₇₃	—	2	1	no	—
196	C₂×Dic₇₃	—	2	1	no	—
197	C₂×Dic₇₃	—	4	2	no	—
198	C₂×Dic₇₃	—	8	2	no	—
199	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
200	C₂×Dic₇₃	#121	1	1	yes	characteristic
201	C₂×Dic₇₃	#121	1	1	yes	characteristic
202	C₂×Dic₇₃	#125	1	2	yes	—
203	C₄×D₇₃	—	4	2	no	—
204	C₄×D₇₃	—	4	2	no	—
205	C₄×D₇₃	—	8	4	no	—
206	C₄×D₇₃	—	8	4	no	—
207	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
208	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
209	C₄×D₇₃	C₄×D₄	1	2	yes	—
210	C₄×D₇₃	C₄×D₄	1	2	yes	—
211	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
212	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
213	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
214	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
215	C₈×C₇₃	—	2	4	no	—
216	C₈×C₇₃	—	2	2	no	—
217	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
218	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
219	#10596831	—	2	4	no	—
220	#10596831	—	2	2	no	—
221	#10596831	C₂×C₄⋊C₄	1	2	yes	—
222	#10596831	C₂×C₄⋊C₄	1	2	yes	—
223	C₂²×C₇₃	—	2	1	no	—
224	C₂²×C₇₃	—	2	1	no	—
225	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
227	C₂²×C₇₃	C₂×#125	1	1	yes	characteristic
228	C₂×D₇₃	—	2	1	no	—
229	C₂×D₇₃	—	2	1	no	—
230	C₂×D₇₃	—	2	4	no	—
231	C₂×D₇₃	—	2	4	no	—
232	C₂×D₇₃	#389	1	2	yes	—
233	C₂×D₇₃	#389	1	2	yes	—
234	C₂×D₇₃	#472	1	2	yes	—
235	C₂×D₇₃	#473	1	2	yes	—
236	C₄×C₇₃	—	4	1	no	—
237	C₄×C₇₃	—	4	1	no	—
238	C₄×C₇₃	—	8	2	no	—
239	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	Dic₇₃	—	4	1	no	—
244	Dic₇₃	—	4	1	no	—
245	Dic₇₃	—	8	2	no	—
246	Dic₇₃	#389	1	2	yes	—
247	Dic₇₃	#389	1	2	yes	—
248	C₂×#1952	—	73	1	no	maximal, Sylow
249	C₂×C₇₃	—	2	1	no	—
250	C₂×C₇₃	—	2	1	no	—
251	C₂×C₇₃	C₂×#389	1	1	yes	characteristic
252	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
253	C₂×C₇₃	C₂×#473	1	1	yes	characteristic
254	D₇₃	—	2	2	no	—
255	D₇₃	#1952	1	4	yes	direct product factor
256	C₂²×#108	—	73	1	no	—
257	C₂×#428	—	73	2	no	—
258	C₂²×#107	—	73	1	no	—
259	C₂×#405	—	73	1	no	—
260	#1952	—	73	1	no	—
261	#1952	—	73	2	no	—
262	#1952	—	73	1	no	—
263	#1952	—	73	1	no	—
264	#1952	—	73	2	no	—
265	#1952	D₇₃	1	1	yes	characteristic, direct product factor
266	C₂×#343	—	73	2	no	—
267	C₇₃	C₂×#1952	1	1	yes	characteristic, complemented, Sylow
268	C₂²×M₁₆	—	73	1	no	—
269	C₂²×M₁₆	—	73	2	no	—
270	C₂³×C₈	—	73	1	no	—
271	C₂×#117	—	73	1	no	—
272	C₂²×C₄⋊C₄	—	73	2	no	—
273	C₂×#108	—	73	2	no	—
274	C₂×#108	—	73	1	no	—
275	C₂×#108	—	73	8	no	—
276	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
277	#428	—	73	2	no	—
278	#428	—	73	2	no	—
279	#428	—	73	2	no	—
280	#428	—	146	2	no	—
281	#428	—	146	2	no	—
282	#428	C₂×D₇₃	1	2	yes	—
283	C₂×#107	—	73	1	no	—
284	C₂×#107	—	73	2	no	—
285	C₂×#107	—	146	2	no	—
286	C₂×#107	—	146	1	no	—
287	C₂×#107	—	146	1	no	—
288	C₂×#107	—	146	1	no	—
289	C₂×#107	—	146	1	no	—
290	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
291	C₂×#106	—	146	2	no	—
292	#405	—	73	1	no	—
293	#405	—	73	1	no	—
294	#405	—	73	1	no	—
295	#405	—	146	1	no	—
296	#405	—	146	1	no	—
297	#405	C₂×D₇₃	1	1	yes	characteristic
298	C₂×#97	—	146	1	no	—
299	C₂×C₄×C₈	—	146	1	no	—
300	#343	—	73	2	no	—
301	#343	—	73	2	no	—
302	#343	—	73	2	no	—
303	#343	C₂×D₇₃	1	2	yes	—
304	C₂³×C₄	—	73	1	no	—
305	C₂³×C₄	—	146	2	no	—
306	C₂×M₁₆	—	73	1	no	—
307	C₂×M₁₆	—	73	2	no	—
308	C₂×M₁₆	—	73	8	no	—
309	C₂×M₁₆	—	73	4	no	—
310	C₂×M₁₆	—	146	1	no	—
311	C₂×M₁₆	—	146	2	no	—
312	C₂×M₁₆	—	146	2	no	—
313	C₂×M₁₆	—	146	4	no	—
314	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
315	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
316	C₂²×C₈	—	73	1	no	—
317	C₂²×C₈	—	73	4	no	—
318	C₂²×C₈	—	73	1	no	—
319	C₂²×C₈	—	73	1	no	—
320	C₂²×C₈	—	73	1	no	—
321	C₂²×C₈	—	73	1	no	—
322	C₂²×C₈	—	73	4	no	—
323	C₂²×C₈	—	146	1	no	—
324	C₂²×C₈	—	146	2	no	—
325	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
326	#117	—	73	1	no	—
327	#117	—	73	1	no	—
328	#117	—	73	1	no	—
329	#117	—	146	1	no	—
330	#117	—	146	1	no	—
331	#117	C₂²×D₇₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	73	1	no	—
333	C₂×C₄⋊C₄	—	73	1	no	—
334	C₂×C₄⋊C₄	—	73	2	no	—
335	C₂×C₄⋊C₄	—	146	2	no	—
336	C₂×C₄⋊C₄	—	146	2	no	—
337	C₂×C₄⋊C₄	—	146	2	no	—
338	C₂×C₄⋊C₄	—	146	2	no	—
339	C₂×C₄⋊C₄	—	146	2	no	—
340	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
341	C₂×C₂²⋊C₄	—	146	1	no	—
342	C₂×C₄²	—	146	1	no	—
343	#108	—	73	8	no	—
344	#108	—	73	4	no	—
345	#108	C₄×D₇₃	1	4	yes	complemented
346	#107	—	2	1	no	—
347	#107	—	2	1	no	—
348	#107	—	2	2	no	—
349	#107	—	146	2	no	—
350	#107	—	146	2	no	—
351	#107	—	146	2	no	—
352	#107	—	146	2	no	—
353	#107	—	146	1	no	—
354	#107	—	146	1	no	—
355	#107	—	146	2	no	—
356	#106	—	2	2	no	—
357	#106	—	146	2	no	—
358	#106	—	146	2	no	—
359	#106	—	146	2	no	—
360	#97	—	2	1	no	—
361	#97	—	146	1	no	—
362	#97	—	146	1	no	—
363	#97	—	146	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	146	1	no	—
366	C₄×C₈	—	146	1	no	—
367	C₄×C₈	—	146	1	no	—
368	C₂⁴	—	73	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	292	2	no	—
371	C₂²×C₄	—	292	2	no	—
372	C₂²×C₄	—	584	4	no	—
373	C₂²×C₄	—	73	1	no	—
374	C₂²×C₄	—	73	2	no	—
375	C₂²×C₄	—	73	1	no	—
376	C₂²×C₄	—	73	1	no	—
377	C₂²×C₄	—	73	1	no	—
378	C₂²×C₄	—	73	1	no	—
379	C₂²×C₄	—	73	2	no	—
380	C₂²×C₄	—	73	2	no	—
381	C₂²×C₄	—	73	2	no	—
382	C₂²×C₄	—	146	1	no	—
383	C₂²×C₄	—	146	1	no	—
384	C₂²×C₄	—	146	2	no	—
385	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	73	4	no	—
389	M₁₆	—	73	2	no	—
390	M₁₆	—	146	8	no	—
391	M₁₆	—	146	4	no	—
392	M₁₆	—	146	2	no	—
393	M₁₆	—	146	1	no	—
394	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
395	M₁₆	Q₈×D₇₃	1	2	yes	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	73	2	no	—
399	C₂×C₈	—	73	1	no	—
400	C₂×C₈	—	73	1	no	—
401	C₂×C₈	—	73	2	no	—
402	C₂×C₈	—	73	4	no	—
403	C₂×C₈	—	73	4	no	—
404	C₂×C₈	—	73	4	no	—
405	C₂×C₈	—	73	4	no	—
406	C₂×C₈	—	146	8	no	—
407	C₂×C₈	—	146	4	no	—
408	C₂×C₈	—	146	1	no	—
409	C₂×C₈	—	146	2	no	—
410	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
411	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
412	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
413	C₂×C₈	Q₈×D₇₃	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	292	2	no	—
417	C₄⋊C₄	—	292	2	no	—
418	C₄⋊C₄	—	73	1	no	—
419	C₄⋊C₄	—	73	1	no	—
420	C₄⋊C₄	—	146	1	no	—
421	C₄⋊C₄	—	146	1	no	—
422	C₄⋊C₄	—	146	2	no	—
423	C₄⋊C₄	—	146	2	no	—
424	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
425	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	146	1	no	—
428	C₂²⋊C₄	—	146	1	no	—
429	C₂²⋊C₄	—	146	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	146	1	no	—
432	C₄²	—	146	1	no	—
433	C₄²	—	146	1	no	—
434	C₂³	—	73	1	no	—
435	C₂³	—	73	2	no	—
436	C₂³	—	73	1	no	—
437	C₂³	—	73	2	no	—
438	C₂³	—	146	2	no	—
439	C₂³	—	146	2	no	—
440	C₂³	#41×D₇₃	1	1	yes	characteristic
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	292	2	no	—
446	C₂×C₄	—	292	2	no	—
447	C₂×C₄	—	292	2	no	—
448	C₂×C₄	—	584	4	no	—
449	C₂×C₄	—	584	4	no	—
450	C₂×C₄	—	584	2	no	—
451	C₂×C₄	—	73	2	no	—
452	C₂×C₄	—	73	1	no	—
453	C₂×C₄	—	73	1	no	—
454	C₂×C₄	—	73	2	no	—
455	C₂×C₄	—	73	2	no	—
456	C₂×C₄	—	73	2	no	—
457	C₂×C₄	—	73	2	no	—
458	C₂×C₄	—	73	2	no	—
459	C₂×C₄	—	73	2	no	—
460	C₂×C₄	—	73	2	no	—
461	C₂×C₄	—	73	2	no	—
462	C₂×C₄	—	73	2	no	—
463	C₂×C₄	—	146	1	no	—
464	C₂×C₄	—	146	1	no	—
465	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
468	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
469	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
470	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
471	C₈	—	2	4	no	—
472	C₈	—	2	2	no	—
473	C₈	—	73	2	no	—
474	C₈	—	73	2	no	—
475	C₈	—	146	4	no	—
476	C₈	—	146	2	no	—
477	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
478	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	73	2	no	—
482	C₂²	—	73	2	no	—
483	C₂²	—	73	2	no	—
484	C₂²	—	73	2	no	—
485	C₂²	—	146	4	no	—
486	C₂²	—	146	4	no	—
487	C₂²	—	146	1	no	—
488	C₂²	—	146	1	no	—
489	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
490	C₂²	#121×D₇₃	1	1	yes	characteristic
491	C₂²	#125×D₇₃	1	1	yes	characteristic
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	8	2	no	—
495	C₄	—	292	1	no	—
496	C₄	—	292	1	no	—
497	C₄	—	584	2	no	—
498	C₄	—	73	2	no	—
499	C₄	—	73	2	no	—
500	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
501	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
502	C₄	C₂²⋊Q₈×D₇₃	1	1	yes	characteristic
503	C₄	C₄⋊Q₈×D₇₃	1	1	yes	characteristic
504	C₂	—	2	1	no	—
505	C₂	—	2	1	no	—
506	C₂	—	73	4	no	—
507	C₂	—	146	2	no	—
508	C₂	#389×D₇₃	1	1	yes	characteristic
509	C₂	#472×D₇₃	1	1	yes	characteristic
510	C₂	#473×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1952	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1952	D₇₃
hypocenter	C₇₃	C₂×#1952
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
5. #22610717	C₂	semidirect
6. #22610716	C₂	semidirect
7. #22610715	C₂	semidirect
8. #22610714	C₂	semidirect
9. #22610713	C₂	semidirect
11. C₇₃×#1952	C₂	semidirect
19. #108×D₇₃	C₄	semidirect
82. #14556527	C₂×C₄	semidirect
83. #14556526	C₂×C₄	semidirect
105. #108×C₇₃	C₂×C₄	semidirect
255. D₇₃	#1952	direct (N × H)
265. #1952	D₇₃	direct (N × H)
267. C₇₃	C₂×#1952	semidirect
345. #108	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₇₃	2
#428×D₇₃	2
C₂×#107×D₇₃	2
#405×D₇₃	2
#22610717	2
#22610716	2
#22610715	2
#22610714	2
#22610713	2
#343×D₇₃	2
C₇₃×#1952	2
C₂×#1952	73

Subgroups — #1952×D73 #33089526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1952×D₇₃ #33089526