Subgroups — #22624513

Order 9344.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989332	C₂	1	2	yes	maximal, complemented
2	#17989326	C₂	1	2	yes	maximal, complemented
3	#17989319	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989307	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989282	C₂	1	2	yes	maximal, complemented
6	#17989263	C₂	1	2	yes	maximal, complemented
7	#17989255	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989247	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989244	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989242	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989231	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989197	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989190	C₂	1	2	yes	maximal, complemented
14	#17989188	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989180	C₂	1	2	yes	maximal, complemented
16	#17989175	C₂	1	2	yes	maximal, complemented
17	#17989172	C₂	1	2	yes	maximal, complemented
18	#17989157	C₂	1	1	yes	maximal, characteristic, complemented
19	#17989154	C₂	1	1	yes	maximal, characteristic, complemented
20	#17989133	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989118	C₂	1	1	yes	maximal, characteristic, complemented
22	#17989117	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11924028	C₂²	1	1	yes	characteristic
25	C₂×#11924028	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11924027	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
28	#14556591	C₂²	1	1	yes	characteristic, complemented
29	#14556589	C₂²	1	1	yes	characteristic, complemented
30	#14556587	C₂²	1	1	yes	characteristic
31	#14556587	C₂²	1	1	yes	characteristic
32	#14556587	C₂²	1	2	yes	complemented
33	#14556586	C₂²	1	1	yes	characteristic, complemented
34	#14556584	C₂²	1	2	yes	—
35	#14556584	C₂²	1	2	yes	—
36	#14556584	C₂²	1	1	yes	characteristic
37	#14556584	C₂²	1	2	yes	complemented
38	#14556584	C₂²	1	2	yes	complemented
39	#14556584	C₂²	1	2	yes	complemented
40	#14556582	C₂²	1	2	yes	complemented
41	#14556582	C₂²	1	1	yes	characteristic, complemented
42	#14556581	C₂²	1	1	yes	characteristic, complemented
43	#14556581	C₂²	1	2	yes	complemented
44	#14556580	C₂²	1	1	yes	characteristic, complemented
45	#14556578	C₂²	1	1	yes	characteristic
46	#14556578	C₂²	1	1	yes	characteristic
47	#14556578	C₂²	1	1	yes	characteristic
48	#14556578	C₂²	1	2	yes	complemented
49	#14556577	C₂²	1	2	yes	—
50	#14556577	C₂²	1	1	yes	characteristic
51	#14556577	C₂²	1	2	yes	complemented
52	#14556575	C₂²	1	1	yes	characteristic, complemented
53	#14556575	C₂²	1	2	yes	complemented
54	#14556574	C₂²	1	2	yes	complemented
55	#14556573	C₂²	1	2	yes	—
56	#14556573	C₂²	1	2	yes	complemented
57	#14556573	C₂²	1	2	yes	complemented
58	#14556573	C₂²	1	2	yes	complemented
59	#14556573	C₂²	1	2	yes	complemented
60	#14556573	C₂²	1	2	yes	complemented
61	#14556572	C₂²	1	1	yes	characteristic
62	#14556572	C₂²	1	2	yes	—
63	#14556572	C₂²	1	2	yes	complemented
64	#14556570	C₂²	1	1	yes	characteristic
65	#14556570	C₂²	1	2	yes	complemented
66	#14556570	C₂²	1	2	yes	complemented
67	#14556570	C₂²	1	1	yes	characteristic, complemented
68	#14556569	C₂²	1	2	yes	complemented
69	#14556568	C₂²	1	2	yes	complemented
70	#14556568	C₂²	1	2	yes	complemented
71	#14556568	C₂²	1	1	yes	characteristic, complemented
72	#14556566	C₂²	1	1	yes	characteristic, complemented
73	#14556565	C₂²	1	2	yes	complemented
74	#14556564	C₂²	1	2	yes	—
75	#14556564	C₂²	1	2	yes	complemented
76	#14556564	C₂²	1	2	yes	complemented
77	#14556563	C₂²	1	2	yes	—
78	#14556563	C₂²	1	1	yes	characteristic
79	#14556563	C₂²	1	2	yes	complemented
80	#14556563	C₂²	1	2	yes	complemented
81	#14556563	C₂²	1	2	yes	complemented
82	#14556562	C₂²	1	2	yes	—
83	#14556562	C₂²	1	2	yes	—
84	#14556562	C₂²	1	2	yes	—
85	#14556562	C₂²	1	1	yes	characteristic
86	#14556562	C₂²	1	2	yes	complemented
87	#14556560	C₂²	1	2	yes	—
88	#14556560	C₂²	1	2	yes	—
89	#14556560	C₂²	1	2	yes	—
90	Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
92	#14556556	C₂²	1	1	yes	characteristic, complemented
93	#14556556	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
96	D₄×Dic₇₃	C₂²	1	2	yes	complemented
97	#14556553	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
103	#14556551	C₂²	1	2	yes	complemented
104	#14556551	C₂²	1	2	yes	complemented
105	#14556550	C₂²	1	1	yes	characteristic
106	#14556550	C₂²	1	2	yes	complemented
107	#14556548	C₂²	1	1	yes	characteristic, complemented
108	#14556547	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₇₃	C₂²	1	2	yes	complemented
110	C₂×C₂²⋊Dic₇₃	C₂²	1	2	yes	—
111	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
114	#124×C₇₃	C₂²	1	1	yes	characteristic
115	#123×C₇₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
117	#121×C₇₃	C₂²	1	2	yes	—
118	#121×C₇₃	C₂²	1	1	yes	characteristic
119	#120×C₇₃	C₂²	1	2	yes	—
120	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
123	#11924028	—	4	2	no	—
124	#11924028	—	4	2	no	—
125	#11924027	—	4	2	no	—
126	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₄₆	C₂³	1	2	yes	—
130	Q₈×D₇₃	—	4	2	no	—
131	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
132	C₂×D₂₉₂	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
143	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
144	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
145	C₂²×Dic₇₃	C₂³	1	2	yes	—
146	C₂²×Dic₇₃	C₂³	1	2	yes	—
147	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₇₃	C₂³	1	2	yes	—
149	C₂×C₄×D₇₃	C₂³	1	2	yes	—
150	C₂×C₄×D₇₃	C₂³	1	2	yes	—
151	C₂×C₄×D₇₃	C₂³	1	2	yes	—
152	C₄⋊Dic₇₃	C₂³	1	2	yes	—
153	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₇₃	C₂³	1	2	yes	—
157	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₇₃	C₂³	1	2	yes	—
159	C₄⋊Dic₇₃	C₂³	1	2	yes	—
160	#11924007	C₂³	1	2	yes	—
161	#11924007	C₂³	1	2	yes	—
162	#11924007	C₂³	1	2	yes	—
163	#11924007	C₂³	1	1	yes	characteristic
164	#11924007	C₂³	1	1	yes	characteristic
165	#11924007	C₂³	1	1	yes	characteristic
166	#11924007	C₂³	1	1	yes	characteristic
167	#11924007	C₂³	1	1	yes	characteristic
168	#11924007	C₂³	1	2	yes	—
169	#11924007	C₂³	1	2	yes	—
170	#11924007	C₂³	1	2	yes	—
171	#11924007	C₂³	1	2	yes	—
172	#11924007	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
187	#11924005	C₂³	1	1	yes	characteristic
188	#11924005	C₂³	1	1	yes	characteristic
189	#11924005	C₂³	1	2	yes	—
190	#11924005	C₂³	1	2	yes	—
191	#11924005	C₂³	1	1	yes	characteristic
192	#11924005	C₂³	1	1	yes	characteristic
193	#11924005	C₂³	1	2	yes	—
194	#11924005	C₂³	1	2	yes	—
195	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₇₃	C₂³	1	2	yes	—
200	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₇₃	C₂³	1	2	yes	—
202	C₄×Dic₇₃	C₂³	1	2	yes	—
203	C₂⁴×C₇₃	C₂³	1	2	yes	—
204	#41×C₇₃	—	4	2	no	—
205	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₇₃	—	4	2	no	—
207	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₇₃	C₂³	1	2	yes	—
211	C₂×D₄×C₇₃	C₂³	1	2	yes	—
212	C₂×D₄×C₇₃	C₂³	1	2	yes	—
213	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
216	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
227	C₄²×C₇₃	C₂³	1	1	yes	characteristic
228	C₂³×C₇₃	—	4	2	no	—
229	C₂³×C₇₃	—	4	2	no	—
230	C₂³×C₇₃	—	4	2	no	—
231	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₇₃	C₂⁴	1	2	yes	—
233	C₂³×C₇₃	C₂⁴	1	2	yes	—
234	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₇₃	C₂⁴	1	2	yes	—
237	Q₈×C₇₃	—	2	2	no	—
238	D₄×C₇₃	—	2	2	no	—
239	D₄×C₇₃	—	2	2	no	—
240	D₄×C₇₃	—	4	2	no	—
241	D₄×C₇₃	—	4	1	no	—
242	D₄×C₇₃	—	4	2	no	—
243	D₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	2	2	no	—
245	C₂×C₄×C₇₃	—	2	2	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	4	2	no	—
248	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₇₃	—	4	1	no	—
256	C₂²⋊D₇₃	—	4	2	no	—
257	C₂²⋊D₇₃	—	4	2	no	—
258	C₂²⋊D₇₃	—	4	2	no	—
259	C₂²⋊D₇₃	—	4	2	no	—
260	C₂²⋊D₇₃	—	4	2	no	—
261	C₂²⋊D₇₃	—	4	1	no	—
262	C₂²⋊D₇₃	—	4	2	no	—
263	C₂²⋊D₇₃	—	4	2	no	—
264	C₂²⋊D₇₃	—	4	2	no	—
265	C₂×Dic₇₃	—	4	1	no	—
266	C₂×Dic₇₃	—	4	2	no	—
267	C₂×Dic₇₃	—	4	1	no	—
268	C₂×Dic₇₃	—	4	2	no	—
269	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₇₃	C₂⁴	1	2	yes	—
276	C₂×Dic₇₃	C₂⁴	1	2	yes	—
277	C₂×Dic₇₃	C₂⁴	1	2	yes	—
278	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
279	D₂₉₂	—	2	2	no	—
280	D₂₉₂	—	4	2	no	—
281	C₄×D₇₃	—	2	2	no	—
282	C₄×D₇₃	—	4	2	no	—
283	C₄×D₇₃	—	4	2	no	—
284	C₄×D₇₃	—	4	2	no	—
285	C₄×D₇₃	—	4	2	no	—
286	Dic₁₄₆	—	2	2	no	—
287	Dic₁₄₆	—	2	2	no	—
288	Dic₁₄₆	—	4	2	no	—
289	Dic₁₄₆	—	4	1	no	—
290	C₂²×C₇₃	—	2	2	no	—
291	C₂²×C₇₃	—	2	1	no	—
292	C₂²×C₇₃	—	2	1	no	—
293	C₂²×C₇₃	—	2	2	no	—
294	C₂²×C₇₃	—	2	1	no	—
295	C₂²×C₇₃	—	2	2	no	—
296	C₂²×C₇₃	—	2	1	no	—
297	C₂²×C₇₃	—	2	2	no	—
298	C₂²×C₇₃	—	2	2	no	—
299	C₂²×C₇₃	—	2	2	no	—
300	C₂²×C₇₃	—	2	1	no	—
301	C₂²×C₇₃	—	2	1	no	—
302	C₂²×C₇₃	—	8	4	no	—
303	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
304	C₂×D₇₃	—	2	1	no	—
305	C₂×D₇₃	—	2	2	no	—
306	C₂×D₇₃	—	2	2	no	—
307	C₂×D₇₃	—	2	1	no	—
308	C₂×D₇₃	—	2	2	no	—
309	C₂×D₇₃	—	2	1	no	—
310	C₄×C₇₃	—	2	2	no	—
311	C₄×C₇₃	—	2	1	no	—
312	C₄×C₇₃	—	2	1	no	—
313	C₄×C₇₃	—	2	1	no	—
314	C₄×C₇₃	—	2	1	no	—
315	C₄×C₇₃	—	2	2	no	—
316	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
317	Dic₇₃	—	2	2	no	—
318	Dic₇₃	—	2	2	no	—
319	Dic₇₃	—	2	1	no	—
320	Dic₇₃	—	2	1	no	—
321	Dic₇₃	—	2	1	no	—
322	Dic₇₃	—	2	2	no	—
323	Dic₇₃	—	2	1	no	—
324	Dic₇₃	—	2	1	no	—
325	Dic₇₃	—	2	1	no	—
326	Dic₇₃	—	2	1	no	—
327	C₂×C₇₃	—	4	1	no	—
328	C₂×C₇₃	—	4	2	no	—
329	C₂×C₇₃	—	4	2	no	—
330	C₂×C₇₃	—	4	1	no	—
331	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₇₃	#585	1	1	yes	characteristic
333	C₂×C₇₃	#585	1	1	yes	characteristic
334	D₇₃	—	4	1	no	—
335	D₇₃	—	4	2	no	—
336	#3562	—	73	1	no	maximal, Sylow
337	C₇₃	#3562	1	1	yes	characteristic, complemented, Sylow
338	#562	—	73	2	no	—
339	#560	—	73	2	no	—
340	#559	—	73	1	no	—
341	#556	—	73	1	no	—
342	#553	—	73	2	no	—
343	#551	—	73	2	no	—
344	#550	—	73	1	no	—
345	#548	—	73	1	no	—
346	#548	—	73	1	no	—
347	#547	—	73	1	no	—
348	#546	—	73	1	no	—
349	#546	D₇₃	1	1	yes	characteristic, complemented
350	#541	—	73	1	no	—
351	#540	—	73	2	no	—
352	#540	—	73	1	no	—
353	#539	—	73	2	no	—
354	#538	—	73	2	no	—
355	#538	—	73	2	no	—
356	#536	—	73	1	no	—
357	#535	—	73	1	no	—
358	#532	—	73	1	no	—
359	#529	—	73	1	no	—
360	#529	—	73	1	no	—
361	C₂×#41	—	73	1	no	—
362	C₂×#41	—	73	1	no	—
363	C₂×#41	—	73	1	no	—
364	C₂×#41	C₂×D₇₃	1	1	yes	characteristic
365	C₂²×Q₈	—	73	1	no	—
366	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
367	C₄⋊Q₈	—	73	1	no	—
368	C₄⋊Q₈	—	73	1	no	—
369	#127	—	73	1	no	—
370	#127	—	73	1	no	—
371	#127	—	73	2	no	—
372	#126	—	73	1	no	—
373	#126	—	73	2	no	—
374	#126	—	73	1	no	—
375	#126	—	73	2	no	—
376	#126	—	73	2	no	—
377	#126	—	73	2	no	—
378	#126	—	73	2	no	—
379	#125	—	73	1	no	—
380	#125	—	73	1	no	—
381	#125	—	73	2	no	—
382	#125	—	73	2	no	—
383	#124	—	73	1	no	—
384	#124	—	73	1	no	—
385	#124	—	73	1	no	—
386	#124	—	73	1	no	—
387	#124	—	73	2	no	—
388	#124	—	73	1	no	—
389	#124	—	73	2	no	—
390	#124	—	73	2	no	—
391	#124	C₂×D₇₃	1	1	yes	characteristic
392	#123	—	73	1	no	—
393	#123	—	73	2	no	—
394	#123	—	73	2	no	—
395	#123	—	73	2	no	—
396	#123	—	73	1	no	—
397	#123	—	73	2	no	—
398	#123	—	73	2	no	—
399	#123	—	73	2	no	—
400	#123	—	73	2	no	—
401	#123	—	73	2	no	—
402	#123	—	73	2	no	—
403	#123	—	73	2	no	—
404	#123	C₂×D₇₃	1	2	yes	—
405	C₂²⋊Q₈	—	73	1	no	—
406	C₂²⋊Q₈	—	73	2	no	—
407	C₂²⋊Q₈	—	73	2	no	—
408	C₂²⋊Q₈	—	73	1	no	—
409	C₂²⋊Q₈	—	73	2	no	—
410	C₂²⋊Q₈	—	73	1	no	—
411	C₂²⋊Q₈	—	73	2	no	—
412	C₂²⋊Q₈	—	73	2	no	—
413	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
414	#121	—	73	1	no	—
415	#121	—	73	2	no	—
416	#121	—	73	2	no	—
417	#121	—	73	2	no	—
418	#121	—	73	2	no	—
419	#121	—	73	2	no	—
420	#121	—	73	2	no	—
421	#121	—	73	1	no	—
422	#121	—	73	2	no	—
423	#121	—	73	2	no	—
424	#121	—	73	2	no	—
425	#121	—	73	1	no	—
426	#121	—	73	2	no	—
427	#121	—	73	2	no	—
428	#121	—	73	2	no	—
429	#121	C₂×D₇₃	1	1	yes	characteristic
430	#121	C₂×D₇₃	1	2	yes	—
431	#120	—	73	2	no	—
432	#120	—	73	2	no	—
433	#120	—	73	2	no	—
434	#120	C₂×D₇₃	1	2	yes	—
435	C₄×Q₈	—	73	1	no	—
436	C₄×Q₈	—	73	1	no	—
437	C₄×Q₈	—	73	1	no	—
438	C₄×Q₈	—	73	1	no	—
439	C₄×D₄	—	73	2	no	—
440	C₄×D₄	—	73	1	no	—
441	C₄×D₄	—	73	1	no	—
442	C₄×D₄	—	73	1	no	—
443	C₄×D₄	—	73	2	no	—
444	C₄×D₄	—	73	2	no	—
445	C₄×D₄	—	73	2	no	—
446	C₄×D₄	—	73	2	no	—
447	C₄×D₄	—	73	2	no	—
448	C₄×D₄	—	73	2	no	—
449	C₄×D₄	—	73	1	no	—
450	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
451	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
452	#117	—	73	1	no	—
453	#117	—	73	2	no	—
454	#117	—	73	2	no	—
455	#117	—	73	1	no	—
456	C₂×C₄⋊C₄	—	73	2	no	—
457	C₂×C₂²⋊C₄	—	73	2	no	—
458	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
459	C₂×C₄²	—	73	1	no	—
460	C₂⁴	C₂²×D₇₃	1	2	yes	—
461	#41	—	4	2	no	—
462	#41	—	292	2	no	—
463	#41	—	292	2	no	—
464	#41	—	292	2	no	—
465	C₂×Q₈	—	292	2	no	—
466	C₂×Q₈	—	73	1	no	—
467	C₂×Q₈	—	73	2	no	—
468	C₂×Q₈	—	73	1	no	—
469	C₂×Q₈	—	73	1	no	—
470	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	73	1	no	—
473	C₂×D₄	—	73	2	no	—
474	C₂×D₄	—	73	2	no	—
475	C₂×D₄	—	73	2	no	—
476	C₂×D₄	—	73	2	no	—
477	C₂×D₄	—	73	2	no	—
478	C₂×D₄	—	73	1	no	—
479	C₂×D₄	—	73	2	no	—
480	C₂×D₄	—	73	2	no	—
481	C₂×D₄	—	73	2	no	—
482	C₂×D₄	—	73	2	no	—
483	C₂×D₄	—	73	1	no	—
484	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₇₃	1	2	yes	—
487	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₇₃	1	2	yes	—
489	C₂×D₄	C₂²×D₇₃	1	2	yes	—
490	C₂²×C₄	—	73	1	no	—
491	C₂²×C₄	—	73	1	no	—
492	C₂²×C₄	—	73	2	no	—
493	C₂²×C₄	—	73	2	no	—
494	C₂²×C₄	—	73	2	no	—
495	C₂²×C₄	—	73	2	no	—
496	C₂²×C₄	—	73	2	no	—
497	C₂²×C₄	—	73	2	no	—
498	C₂²×C₄	—	73	1	no	—
499	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
502	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
503	C₄⋊C₄	—	73	2	no	—
504	C₄⋊C₄	—	73	2	no	—
505	C₄⋊C₄	—	73	2	no	—
506	C₄⋊C₄	—	73	1	no	—
507	C₄⋊C₄	—	73	1	no	—
508	C₄⋊C₄	—	73	1	no	—
509	C₄⋊C₄	—	73	1	no	—
510	C₄⋊C₄	—	73	2	no	—
511	C₄⋊C₄	—	73	2	no	—
512	C₄⋊C₄	—	73	1	no	—
513	C₄⋊C₄	—	73	2	no	—
514	C₄⋊C₄	—	73	2	no	—
515	C₄⋊C₄	—	73	1	no	—
516	C₄⋊C₄	—	73	2	no	—
517	C₄⋊C₄	—	73	1	no	—
518	C₄⋊C₄	—	73	1	no	—
519	C₄⋊C₄	—	73	1	no	—
520	C₄⋊C₄	—	73	2	no	—
521	C₄⋊C₄	—	73	1	no	—
522	C₄⋊C₄	—	73	2	no	—
523	C₄⋊C₄	—	73	2	no	—
524	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
527	C₂²⋊C₄	—	73	1	no	—
528	C₂²⋊C₄	—	73	2	no	—
529	C₂²⋊C₄	—	73	2	no	—
530	C₂²⋊C₄	—	73	2	no	—
531	C₂²⋊C₄	—	73	1	no	—
532	C₂²⋊C₄	—	73	1	no	—
533	C₂²⋊C₄	—	73	2	no	—
534	C₂²⋊C₄	—	73	2	no	—
535	C₂²⋊C₄	—	73	2	no	—
536	C₂²⋊C₄	—	73	2	no	—
537	C₂²⋊C₄	—	73	2	no	—
538	C₂²⋊C₄	—	73	2	no	—
539	C₂²⋊C₄	—	73	2	no	—
540	C₂²⋊C₄	—	73	1	no	—
541	C₂²⋊C₄	—	73	1	no	—
542	C₂²⋊C₄	—	73	1	no	—
543	C₂²⋊C₄	—	73	1	no	—
544	C₂²⋊C₄	—	73	1	no	—
545	C₂²⋊C₄	—	73	2	no	—
546	C₂²⋊C₄	—	73	2	no	—
547	C₂²⋊C₄	—	73	2	no	—
548	C₂²⋊C₄	—	73	2	no	—
549	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
556	C₄²	—	73	1	no	—
557	C₄²	—	73	1	no	—
558	C₄²	—	73	1	no	—
559	C₄²	—	73	1	no	—
560	C₄²	—	73	2	no	—
561	C₄²	—	73	1	no	—
562	C₄²	—	73	2	no	—
563	C₄²	—	73	2	no	—
564	C₄²	C₂²×D₇₃	1	1	yes	characteristic
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	73	1	no	—
569	C₂³	—	73	2	no	—
570	C₂³	C₂³×D₇₃	1	1	yes	characteristic
571	C₂³	C₂³×D₇₃	1	2	yes	—
572	C₂³	C₂³×D₇₃	1	2	yes	—
573	C₂³	C₂³×D₇₃	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	292	2	no	—
576	Q₈	—	292	1	no	—
577	Q₈	—	146	2	no	—
578	Q₈	—	146	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	1	no	—
585	D₄	—	292	2	no	—
586	D₄	—	292	2	no	—
587	D₄	—	292	2	no	—
588	D₄	—	292	2	no	—
589	D₄	—	292	2	no	—
590	D₄	—	292	1	no	—
591	D₄	—	292	2	no	—
592	D₄	—	292	2	no	—
593	D₄	—	292	2	no	—
594	D₄	—	292	1	no	—
595	D₄	—	292	2	no	—
596	D₄	—	146	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	292	2	no	—
602	C₂×C₄	—	292	2	no	—
603	C₂×C₄	—	292	2	no	—
604	C₂×C₄	—	292	2	no	—
605	C₂×C₄	—	292	2	no	—
606	C₂×C₄	—	292	1	no	—
607	C₂×C₄	—	292	2	no	—
608	C₂×C₄	—	292	1	no	—
609	C₂×C₄	—	73	1	no	—
610	C₂×C₄	—	73	1	no	—
611	C₂×C₄	—	73	1	no	—
612	C₂×C₄	—	73	1	no	—
613	C₂×C₄	—	73	1	no	—
614	C₂×C₄	—	73	1	no	—
615	C₂×C₄	—	73	2	no	—
616	C₂×C₄	—	73	2	no	—
617	C₂×C₄	—	73	2	no	—
618	C₂×C₄	—	73	1	no	—
619	C₂×C₄	—	146	2	no	—
620	C₂×C₄	C₂³×D₇₃	1	2	yes	—
621	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₇₃	1	2	yes	—
623	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	8	4	no	—
640	C₂²	—	146	1	no	—
641	C₂²	—	146	2	no	—
642	C₂²	—	146	1	no	—
643	C₂²	—	146	2	no	—
644	C₂²	—	146	2	no	—
645	C₂²	—	146	1	no	—
646	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	146	1	no	—
654	C₄	—	146	2	no	—
655	C₄	—	146	2	no	—
656	C₄	—	146	1	no	—
657	C₄	—	146	1	no	—
658	C₄	—	146	1	no	—
659	C₄	—	146	1	no	—
660	C₄	—	146	2	no	—
661	C₄	—	146	1	no	—
662	C₄	—	146	1	no	—
663	C₄	#14556636	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	1	no	—
668	C₂	—	292	1	no	—
669	C₂	—	292	2	no	—
670	C₂	C₂×#14556636	1	1	yes	characteristic
671	C₂	#17989422	1	1	yes	characteristic
672	C₂	#17989423	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#546×C₇₃	C₂
hypercenter	#546	D₇₃
hypocenter	C₇₃	#3562
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #17989332	C₂	semidirect
2. #17989326	C₂	semidirect
3. #17989319	C₂	semidirect
4. #17989307	C₂	semidirect
5. #17989282	C₂	semidirect
6. #17989263	C₂	semidirect
7. #17989255	C₂	semidirect
8. #17989247	C₂	semidirect
9. #17989244	C₂	semidirect
10. #17989242	C₂	semidirect
11. #17989231	C₂	semidirect
12. #17989197	C₂	semidirect
13. #17989190	C₂	semidirect
14. #17989188	C₂	semidirect
15. #17989180	C₂	semidirect
16. #17989175	C₂	semidirect
17. #17989172	C₂	semidirect
18. #17989157	C₂	semidirect
19. #17989154	C₂	semidirect
20. #17989133	C₂	semidirect
21. #17989118	C₂	semidirect
22. #17989117	C₂	semidirect
23. #546×C₇₃	C₂	semidirect
25. C₂×#11924028	C₂²	semidirect
27. C₂×Q₈×D₇₃	C₂²	semidirect
28. #14556591	C₂²	semidirect
29. #14556589	C₂²	semidirect
32. #14556587	C₂²	semidirect
33. #14556586	C₂²	semidirect
37. #14556584	C₂²	semidirect
38. #14556584	C₂²	semidirect
39. #14556584	C₂²	semidirect
40. #14556582	C₂²	semidirect
41. #14556582	C₂²	semidirect
42. #14556581	C₂²	semidirect
43. #14556581	C₂²	semidirect
44. #14556580	C₂²	semidirect
48. #14556578	C₂²	semidirect
51. #14556577	C₂²	semidirect
52. #14556575	C₂²	semidirect
53. #14556575	C₂²	semidirect
54. #14556574	C₂²	semidirect
56. #14556573	C₂²	semidirect
57. #14556573	C₂²	semidirect
58. #14556573	C₂²	semidirect
59. #14556573	C₂²	semidirect
60. #14556573	C₂²	semidirect
63. #14556572	C₂²	semidirect
65. #14556570	C₂²	semidirect
66. #14556570	C₂²	semidirect
67. #14556570	C₂²	semidirect
68. #14556569	C₂²	semidirect
69. #14556568	C₂²	semidirect
70. #14556568	C₂²	semidirect
71. #14556568	C₂²	semidirect
72. #14556566	C₂²	semidirect
73. #14556565	C₂²	semidirect
75. #14556564	C₂²	semidirect
76. #14556564	C₂²	semidirect
79. #14556563	C₂²	semidirect
80. #14556563	C₂²	semidirect
81. #14556563	C₂²	semidirect
86. #14556562	C₂²	semidirect
90. Q₈×Dic₇₃	C₂²	semidirect
91. C₄×Dic₁₄₆	C₂²	semidirect
92. #14556556	C₂²	semidirect
93. #14556556	C₂²	semidirect
94. C₄×D₂₉₂	C₂²	semidirect
96. D₄×Dic₇₃	C₂²	semidirect
97. #14556553	C₂²	semidirect
99. C₄×C₂²⋊D₇₃	C₂²	semidirect
100. C₄×C₂²⋊D₇₃	C₂²	semidirect
101. C₄×C₂²⋊D₇₃	C₂²	semidirect
102. C₄×C₂²⋊D₇₃	C₂²	semidirect
103. #14556551	C₂²	semidirect
104. #14556551	C₂²	semidirect
106. #14556550	C₂²	semidirect
107. #14556548	C₂²	semidirect
108. #14556547	C₂²	semidirect
109. C₄⋊C₄×D₇₃	C₂²	semidirect
111. C₂×C₄×Dic₇₃	C₂²	semidirect
337. C₇₃	#3562	semidirect
349. #546	D₇₃	semidirect