Subgroups — C₁₇×#62146 #16919890

Order 4352.

1700 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3482	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3383	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3353	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3352	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3328	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3327	C₂	1	4	yes	maximal, complemented
9	C₁₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3252	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3233	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#3104	C₂	1	2	yes	maximal, complemented
15	C₁₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#3078	C₂	1	2	yes	maximal, complemented
17	C₁₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₇×#557	—	2	1	no	—
19	C₁₇×#557	C₂²	1	1	yes	characteristic
20	C₁₇×#557	C₂²	1	2	yes	—
21	C₁₇×#556	—	2	1	no	—
22	C₁₇×#556	—	2	1	no	—
23	C₁₇×#556	C₂²	1	1	yes	characteristic
24	C₁₇×#556	C₂²	1	2	yes	—
25	C₁₇×#552	—	2	2	no	—
26	C₁₇×#552	—	2	2	no	—
27	C₁₇×#552	C₂²	1	2	yes	—
28	C₁₇×#552	C₂²	1	4	yes	—
29	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#548	C₂²	1	2	yes	—
31	C₁₇×#547	—	2	1	no	—
32	C₁₇×#547	C₂²	1	1	yes	characteristic
33	C₁₇×#541	—	2	2	no	—
34	C₁₇×#536	—	2	1	no	—
35	C₁₇×#533	—	2	1	no	—
36	C₁₇×#533	C₂²	1	2	yes	—
37	C₁₇×#533	C₂²	1	1	yes	characteristic
38	C₁₇×#533	C₂²	1	2	yes	—
39	C₁₇×#533	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₇×#529	—	2	2	no	—
42	C₁₇×#529	C₂²	1	2	yes	—
43	C₁₇×#519	—	2	1	no	—
44	C₄×#41×C₁₇	—	2	1	no	—
45	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
46	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
48	C₁₇×#500	C₂²	1	2	yes	—
49	C₁₇×#499	C₂²	1	4	yes	—
50	C₁₇×#488	C₂²	1	4	yes	—
51	C₁₇×#487	C₂²	1	2	yes	—
52	C₁₇×#485	C₂²	1	4	yes	—
53	C₁₇×#485	C₂²	1	2	yes	—
54	C₁₇×#484	C₂²	1	4	yes	—
55	C₁₇×#484	C₂²	1	4	yes	—
56	C₁₇×#482	C₂²	1	4	yes	—
57	C₁₇×#479	C₂²	1	4	yes	—
58	C₁₇×#479	C₂²	1	4	yes	—
59	C₁₇×#479	C₂²	1	4	yes	—
60	C₁₇×#477	C₂²	1	2	yes	—
61	C₁₇×#477	C₂²	1	2	yes	—
62	C₁₇×#477	C₂²	1	2	yes	—
63	C₁₇×#476	C₂²	1	2	yes	—
64	C₁₇×#475	C₂²	1	2	yes	—
65	C₁₇×#475	C₂²	1	2	yes	—
66	C₁₇×#475	C₂²	1	2	yes	—
67	C₁₇×#475	C₂²	1	1	yes	characteristic
68	C₁₇×#474	C₂²	1	1	yes	characteristic
69	C₁₇×#474	C₂²	1	2	yes	—
70	C₁₇×#470	C₂²	1	4	yes	—
71	C₁₇×#470	C₂²	1	4	yes	—
72	C₁₇×#468	C₂²	1	4	yes	—
73	C₁₇×#464	C₂²	1	4	yes	—
74	C₁₇×#462	C₂²	1	2	yes	—
75	C₁₇×#462	C₂²	1	2	yes	—
76	C₁₇×#462	C₂²	1	1	yes	characteristic
77	C₁₇×#461	C₂²	1	1	yes	characteristic
78	C₁₇×#452	C₂²	1	2	yes	—
79	C₁₇×#451	C₂²	1	4	yes	—
80	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
82	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
85	C₁₇×#436	C₂²	1	4	yes	—
86	C₁₇×#436	C₂²	1	2	yes	—
87	C₁₇×#431	C₂²	1	1	yes	characteristic
88	C₁₇×#431	C₂²	1	2	yes	—
89	C₁₇×#428	C₂²	1	4	yes	—
90	C₁₇×#428	C₂²	1	2	yes	—
91	C₁₇×#423	C₂²	1	2	yes	—
92	C₁₇×#423	C₂²	1	1	yes	characteristic
93	C₁₇×#419	C₂²	1	4	yes	—
94	C₁₇×#417	C₂²	1	2	yes	—
95	C₂×#41×C₁₇	—	2	1	no	—
96	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
97	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₇	—	2	1	no	—
99	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
103	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
105	C₁₇×C₄⋊Q₈	—	2	1	no	—
106	C₁₇×C₄⋊Q₈	—	2	2	no	—
107	C₁₇×C₄⋊Q₈	—	2	1	no	—
108	C₁₇×C₄⋊Q₈	—	2	1	no	—
109	C₁₇×C₄⋊Q₈	—	2	1	no	—
110	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₇×#126	—	2	2	no	—
117	C₁₇×#126	—	2	2	no	—
118	C₁₇×#126	—	2	4	no	—
119	C₁₇×#126	—	2	4	no	—
120	C₁₇×#126	—	2	2	no	—
121	C₁₇×#125	—	2	2	no	—
122	C₁₇×#125	—	2	2	no	—
123	C₁₇×#125	—	2	4	no	—
124	C₁₇×#125	—	2	4	no	—
125	C₁₇×#125	—	2	1	no	—
126	C₁₇×#125	—	2	1	no	—
127	C₁₇×#125	—	2	2	no	—
128	C₁₇×#125	C₂³	1	2	yes	—
129	C₁₇×#125	C₂³	1	4	yes	—
130	C₁₇×#124	—	2	2	no	—
131	C₁₇×#124	—	2	2	no	—
132	C₁₇×#124	C₂³	1	2	yes	—
133	C₁₇×#123	—	2	2	no	—
134	C₁₇×#123	—	2	4	no	—
135	C₁₇×#123	—	2	2	no	—
136	C₁₇×#123	—	2	2	no	—
137	C₁₇×C₂²⋊Q₈	—	2	1	no	—
138	C₁₇×C₂²⋊Q₈	—	2	2	no	—
139	C₁₇×C₂²⋊Q₈	—	2	2	no	—
140	C₁₇×C₂²⋊Q₈	—	2	1	no	—
141	C₁₇×C₂²⋊Q₈	—	2	1	no	—
142	C₁₇×C₂²⋊Q₈	—	2	2	no	—
143	C₁₇×C₂²⋊Q₈	—	2	1	no	—
144	C₁₇×C₂²⋊Q₈	—	2	2	no	—
145	C₁₇×C₂²⋊Q₈	—	2	2	no	—
146	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₇×#121	—	2	2	no	—
151	C₁₇×#121	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₇	—	2	1	no	—
153	C₄×Q₈×C₁₇	—	2	2	no	—
154	C₄×Q₈×C₁₇	—	2	2	no	—
155	C₄×Q₈×C₁₇	—	2	2	no	—
156	C₄×Q₈×C₁₇	—	2	2	no	—
157	C₄×Q₈×C₁₇	—	2	1	no	—
158	C₄×Q₈×C₁₇	—	2	2	no	—
159	C₄×Q₈×C₁₇	—	2	2	no	—
160	C₄×Q₈×C₁₇	—	2	2	no	—
161	C₄×Q₈×C₁₇	—	2	1	no	—
162	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
169	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₁₇	—	2	1	no	—
172	C₄×D₄×C₁₇	—	2	2	no	—
173	C₄×D₄×C₁₇	—	2	1	no	—
174	C₄×D₄×C₁₇	—	2	1	no	—
175	C₄×D₄×C₁₇	—	2	2	no	—
176	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
177	C₄×D₄×C₁₇	D₄	1	2	yes	—
178	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₇	C₂³	1	2	yes	—
182	C₁₇×#117	—	2	1	no	—
183	C₁₇×#117	—	2	1	no	—
184	C₁₇×#117	—	2	2	no	—
185	C₁₇×#117	—	2	1	no	—
186	C₁₇×#117	—	2	2	no	—
187	C₁₇×#117	—	2	4	no	—
188	C₁₇×#117	—	2	1	no	—
189	C₁₇×#117	—	2	2	no	—
190	C₁₇×#117	D₄	1	1	yes	characteristic
191	C₁₇×#117	D₄	1	2	yes	—
192	C₁₇×#117	C₂³	1	1	yes	characteristic
193	C₁₇×#117	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
196	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₇	—	2	2	no	—
199	C₂×C₄²×C₁₇	—	2	1	no	—
200	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
202	C₁₇×#107	C₂³	1	2	yes	—
203	C₁₇×#107	C₂³	1	4	yes	—
204	C₁₇×#107	C₂³	1	4	yes	—
205	C₁₇×#107	C₂³	1	4	yes	—
206	C₁₇×#106	C₂³	1	4	yes	—
207	C₁₇×#106	C₂³	1	4	yes	—
208	C₁₇×#106	C₂³	1	2	yes	—
209	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₇×#103	C₂³	1	4	yes	—
215	C₁₇×#103	C₂³	1	2	yes	—
216	C₁₇×#103	C₂³	1	4	yes	—
217	C₁₇×#103	C₂³	1	4	yes	—
218	C₁₇×#103	C₂³	1	2	yes	—
219	C₁₇×#103	C₂³	1	4	yes	—
220	C₁₇×#103	C₂³	1	2	yes	—
221	C₁₇×#103	C₂³	1	4	yes	—
222	C₁₇×#102	C₂³	1	4	yes	—
223	C₁₇×#102	C₂³	1	2	yes	—
224	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₄×C₈×C₁₇	C₂³	1	4	yes	—
227	C₄×C₈×C₁₇	C₂³	1	2	yes	—
228	#41×C₁₇	—	2	2	no	—
229	#41×C₁₇	—	4	2	no	—
230	#41×C₁₇	—	4	1	no	—
231	#41×C₁₇	—	4	4	no	—
232	C₂×Q₈×C₁₇	—	2	1	no	—
233	C₂×Q₈×C₁₇	—	2	2	no	—
234	C₂×Q₈×C₁₇	—	2	2	no	—
235	C₂×Q₈×C₁₇	—	2	1	no	—
236	C₂×Q₈×C₁₇	—	2	2	no	—
237	C₂×Q₈×C₁₇	—	2	4	no	—
238	C₂×Q₈×C₁₇	—	4	2	no	—
239	C₂×Q₈×C₁₇	—	4	4	no	—
240	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₁₇	—	2	2	no	—
245	C₂×D₄×C₁₇	—	2	1	no	—
246	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₇	—	2	2	no	—
250	C₂²×C₄×C₁₇	—	2	2	no	—
251	C₂²×C₄×C₁₇	—	2	2	no	—
252	C₂²×C₄×C₁₇	—	2	1	no	—
253	C₂²×C₄×C₁₇	—	2	1	no	—
254	C₂²×C₄×C₁₇	—	2	1	no	—
255	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
261	Q₁₆×C₁₇	—	2	4	no	—
262	Q₁₆×C₁₇	—	4	4	no	—
263	SD₁₆×C₁₇	—	4	2	no	—
264	M₁₆×C₁₇	—	4	4	no	—
265	M₁₆×C₁₇	—	4	2	no	—
266	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
268	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₁₇	—	2	1	no	—
270	C₄⋊C₄×C₁₇	—	2	1	no	—
271	C₄⋊C₄×C₁₇	—	2	1	no	—
272	C₄⋊C₄×C₁₇	—	2	1	no	—
273	C₄⋊C₄×C₁₇	—	2	1	no	—
274	C₄⋊C₄×C₁₇	—	2	2	no	—
275	C₄⋊C₄×C₁₇	—	2	2	no	—
276	C₄⋊C₄×C₁₇	—	2	4	no	—
277	C₄⋊C₄×C₁₇	—	2	4	no	—
278	C₄⋊C₄×C₁₇	—	2	2	no	—
279	C₄⋊C₄×C₁₇	—	2	2	no	—
280	C₄⋊C₄×C₁₇	—	2	2	no	—
281	C₄⋊C₄×C₁₇	—	2	2	no	—
282	C₄⋊C₄×C₁₇	—	2	1	no	—
283	C₄⋊C₄×C₁₇	—	2	4	no	—
284	C₄⋊C₄×C₁₇	—	2	2	no	—
285	C₄⋊C₄×C₁₇	—	2	2	no	—
286	C₄⋊C₄×C₁₇	—	2	2	no	—
287	C₄⋊C₄×C₁₇	—	2	4	no	—
288	C₄⋊C₄×C₁₇	—	2	1	no	—
289	C₄⋊C₄×C₁₇	—	2	2	no	—
290	C₄⋊C₄×C₁₇	—	2	2	no	—
291	C₄⋊C₄×C₁₇	—	2	2	no	—
292	C₄⋊C₄×C₁₇	—	2	2	no	—
293	C₄⋊C₄×C₁₇	—	2	1	no	—
294	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₁₇	—	2	4	no	—
304	C₂²⋊C₄×C₁₇	—	2	2	no	—
305	C₂²⋊C₄×C₁₇	—	2	2	no	—
306	C₂²⋊C₄×C₁₇	—	2	4	no	—
307	C₂²⋊C₄×C₁₇	—	2	2	no	—
308	C₂²⋊C₄×C₁₇	—	2	1	no	—
309	C₂²⋊C₄×C₁₇	—	2	2	no	—
310	C₂²⋊C₄×C₁₇	—	2	2	no	—
311	C₂²⋊C₄×C₁₇	—	2	1	no	—
312	C₂²⋊C₄×C₁₇	—	2	1	no	—
313	C₂²⋊C₄×C₁₇	—	2	2	no	—
314	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
317	C₄²×C₁₇	—	2	2	no	—
318	C₄²×C₁₇	—	2	2	no	—
319	C₄²×C₁₇	—	2	1	no	—
320	C₄²×C₁₇	—	2	4	no	—
321	C₄²×C₁₇	—	2	4	no	—
322	C₄²×C₁₇	—	2	2	no	—
323	C₄²×C₁₇	—	2	1	no	—
324	C₄²×C₁₇	—	2	1	no	—
325	C₄²×C₁₇	—	2	2	no	—
326	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₁₇	C₂×D₄	1	2	yes	—
328	C₄²×C₁₇	C₂×D₄	1	2	yes	—
329	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₇	C₂⁴	1	2	yes	—
331	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
332	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
333	#62146	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₁₇	—	2	1	no	—
335	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
336	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₁₇	—	2	2	no	—
338	Q₈×C₁₇	—	2	1	no	—
339	Q₈×C₁₇	—	2	2	no	—
340	Q₈×C₁₇	—	2	2	no	—
341	Q₈×C₁₇	—	2	2	no	—
342	Q₈×C₁₇	—	2	2	no	—
343	Q₈×C₁₇	—	4	4	no	—
344	Q₈×C₁₇	—	4	4	no	—
345	Q₈×C₁₇	—	4	4	no	—
346	Q₈×C₁₇	—	4	2	no	—
347	Q₈×C₁₇	—	4	2	no	—
348	Q₈×C₁₇	2₋¹⁺⁴	1	2	yes	—
349	D₄×C₁₇	—	2	2	no	—
350	D₄×C₁₇	—	2	1	no	—
351	D₄×C₁₇	—	2	1	no	—
352	D₄×C₁₇	—	4	2	no	—
353	D₄×C₁₇	—	4	2	no	—
354	D₄×C₁₇	—	4	4	no	—
355	C₂×C₄×C₁₇	—	2	1	no	—
356	C₂×C₄×C₁₇	—	2	2	no	—
357	C₂×C₄×C₁₇	—	2	4	no	—
358	C₂×C₄×C₁₇	—	2	2	no	—
359	C₂×C₄×C₁₇	—	2	2	no	—
360	C₂×C₄×C₁₇	—	2	1	no	—
361	C₂×C₄×C₁₇	—	2	2	no	—
362	C₂×C₄×C₁₇	—	2	1	no	—
363	C₂×C₄×C₁₇	—	2	1	no	—
364	C₂×C₄×C₁₇	—	2	2	no	—
365	C₂×C₄×C₁₇	—	2	2	no	—
366	C₂×C₄×C₁₇	—	2	1	no	—
367	C₂×C₄×C₁₇	—	2	2	no	—
368	C₂×C₄×C₁₇	—	2	2	no	—
369	C₂×C₄×C₁₇	—	2	4	no	—
370	C₂×C₄×C₁₇	—	4	2	no	—
371	C₂×C₄×C₁₇	—	4	2	no	—
372	C₂×C₄×C₁₇	—	4	4	no	—
373	C₂×C₄×C₁₇	—	4	4	no	—
374	C₂×C₄×C₁₇	—	4	4	no	—
375	C₂×C₄×C₁₇	—	4	2	no	—
376	C₂×C₄×C₁₇	—	4	2	no	—
377	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
386	C₈×C₁₇	—	2	2	no	—
387	C₈×C₁₇	—	2	2	no	—
388	C₈×C₁₇	—	2	4	no	—
389	#3509	C₂×C₁₇	1	1	yes	characteristic, complemented
390	#3482	C₂×C₁₇	1	1	yes	characteristic
391	#3383	C₂×C₁₇	1	2	yes	complemented
392	#3364	C₂×C₁₇	1	2	yes	complemented
393	#3353	C₂×C₁₇	1	2	yes	complemented
394	#3352	C₂×C₁₇	1	4	yes	complemented
395	#3328	C₂×C₁₇	1	2	yes	complemented
396	#3327	C₂×C₁₇	1	4	yes	complemented
397	#3255	C₂×C₁₇	1	1	yes	characteristic, complemented
398	#3252	C₂×C₁₇	1	2	yes	complemented
399	#3233	C₂×C₁₇	1	2	yes	complemented
400	#3230	C₂×C₁₇	1	1	yes	characteristic, complemented
401	#3107	C₂×C₁₇	1	1	yes	characteristic, complemented
402	#3104	C₂×C₁₇	1	2	yes	complemented
403	#3079	C₂×C₁₇	1	1	yes	characteristic, complemented
404	#3078	C₂×C₁₇	1	2	yes	complemented
405	#2991	C₂×C₁₇	1	1	yes	characteristic, complemented
406	C₂²×C₁₇	—	2	2	no	—
407	C₂²×C₁₇	—	2	1	no	—
408	C₂²×C₁₇	—	2	1	no	—
409	C₂²×C₁₇	—	2	2	no	—
410	C₂²×C₁₇	—	2	2	no	—
411	C₂²×C₁₇	—	2	1	no	—
412	C₂²×C₁₇	—	4	1	no	—
413	C₂²×C₁₇	—	4	1	no	—
414	C₂²×C₁₇	—	4	1	no	—
415	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₁₇	—	2	1	no	—
417	C₄×C₁₇	—	2	2	no	—
418	C₄×C₁₇	—	2	2	no	—
419	C₄×C₁₇	—	2	1	no	—
420	C₄×C₁₇	—	2	2	no	—
421	C₄×C₁₇	—	2	2	no	—
422	C₄×C₁₇	—	2	1	no	—
423	C₄×C₁₇	—	4	2	no	—
424	C₄×C₁₇	—	4	2	no	—
425	C₄×C₁₇	—	4	1	no	—
426	C₄×C₁₇	—	4	2	no	—
427	C₄×C₁₇	—	4	4	no	—
428	C₄×C₁₇	—	4	1	no	—
429	C₄×C₁₇	—	4	2	no	—
430	C₄×C₁₇	#575	1	2	yes	—
431	C₄×C₁₇	#578	1	2	yes	—
432	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₄×C₁₇	#585	1	1	yes	characteristic
434	#557	—	2	1	no	—
435	#557	C₂²×C₁₇	1	2	yes	—
436	#557	C₂²×C₁₇	1	1	yes	characteristic
437	#556	—	2	1	no	—
438	#556	—	2	1	no	—
439	#556	C₂²×C₁₇	1	1	yes	characteristic
440	#556	C₂²×C₁₇	1	2	yes	—
441	#552	—	2	2	no	—
442	#552	—	2	2	no	—
443	#552	C₂²×C₁₇	1	2	yes	—
444	#552	C₂²×C₁₇	1	4	yes	—
445	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
446	#548	C₂²×C₁₇	1	2	yes	—
447	#547	—	2	1	no	—
448	#547	C₂²×C₁₇	1	1	yes	characteristic
449	#541	—	2	2	no	—
450	#536	—	2	1	no	—
451	#533	—	2	1	no	—
452	#533	C₂²×C₁₇	1	2	yes	—
453	#533	C₂²×C₁₇	1	1	yes	characteristic
454	#533	C₂²×C₁₇	1	1	yes	characteristic
455	#533	C₂²×C₁₇	1	2	yes	—
456	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
457	#529	—	2	2	no	—
458	#529	C₂²×C₁₇	1	2	yes	—
459	#519	—	2	1	no	—
460	C₄×#41	—	2	1	no	—
461	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
462	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
463	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
464	#500	C₂²×C₁₇	1	2	yes	—
465	#499	C₂²×C₁₇	1	4	yes	—
466	#488	C₂²×C₁₇	1	4	yes	—
467	#487	C₂²×C₁₇	1	2	yes	—
468	#485	C₂²×C₁₇	1	4	yes	—
469	#485	C₂²×C₁₇	1	2	yes	—
470	#484	C₂²×C₁₇	1	4	yes	—
471	#484	C₂²×C₁₇	1	4	yes	—
472	#482	C₂²×C₁₇	1	4	yes	—
473	#479	C₂²×C₁₇	1	4	yes	—
474	#479	C₂²×C₁₇	1	4	yes	—
475	#479	C₂²×C₁₇	1	4	yes	—
476	#477	C₂²×C₁₇	1	2	yes	—
477	#477	C₂²×C₁₇	1	2	yes	—
478	#477	C₂²×C₁₇	1	2	yes	—
479	#476	C₂²×C₁₇	1	2	yes	—
480	#475	C₂²×C₁₇	1	2	yes	—
481	#475	C₂²×C₁₇	1	1	yes	characteristic
482	#475	C₂²×C₁₇	1	2	yes	—
483	#475	C₂²×C₁₇	1	2	yes	—
484	#474	C₂²×C₁₇	1	2	yes	—
485	#474	C₂²×C₁₇	1	1	yes	characteristic
486	#470	C₂²×C₁₇	1	4	yes	—
487	#470	C₂²×C₁₇	1	4	yes	—
488	#468	C₂²×C₁₇	1	4	yes	—
489	#464	C₂²×C₁₇	1	4	yes	—
490	#462	C₂²×C₁₇	1	2	yes	—
491	#462	C₂²×C₁₇	1	1	yes	characteristic
492	#462	C₂²×C₁₇	1	2	yes	—
493	#461	C₂²×C₁₇	1	1	yes	characteristic
494	#452	C₂²×C₁₇	1	2	yes	—
495	#451	C₂²×C₁₇	1	4	yes	—
496	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
497	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
498	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
499	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
500	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
501	#436	C₂²×C₁₇	1	2	yes	—
502	#436	C₂²×C₁₇	1	4	yes	—
503	#431	C₂²×C₁₇	1	2	yes	—
504	#431	C₂²×C₁₇	1	1	yes	characteristic
505	#428	C₂²×C₁₇	1	4	yes	—
506	#428	C₂²×C₁₇	1	2	yes	—
507	#423	C₂²×C₁₇	1	2	yes	—
508	#423	C₂²×C₁₇	1	1	yes	characteristic
509	#419	C₂²×C₁₇	1	4	yes	—
510	#417	C₂²×C₁₇	1	2	yes	—
511	C₂×C₁₇	—	4	2	no	—
512	C₂×C₁₇	—	4	1	no	—
513	C₂×C₁₇	—	8	1	no	—
514	C₂×C₁₇	#3489	1	1	yes	characteristic
515	C₂×C₁₇	C₂×#575	1	1	yes	characteristic
516	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
517	C₂×#41	—	2	1	no	—
518	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
519	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
522	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
523	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
525	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
526	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	4	no	—
541	#126	—	2	4	no	—
542	#126	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	—	2	4	no	—
546	#125	—	2	4	no	—
547	#125	—	2	1	no	—
548	#125	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	C₂³×C₁₇	1	2	yes	—
551	#125	C₂³×C₁₇	1	4	yes	—
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	C₂³×C₁₇	1	2	yes	—
555	#123	—	2	2	no	—
556	#123	—	2	4	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
569	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
570	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
572	#121	—	2	2	no	—
573	#121	C₂³×C₁₇	1	2	yes	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
587	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
591	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
599	C₄×D₄	D₄×C₁₇	1	2	yes	—
600	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₇	1	2	yes	—
604	#117	—	2	1	no	—
605	#117	—	2	1	no	—
606	#117	—	2	2	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	4	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	D₄×C₁₇	1	1	yes	characteristic
613	#117	D₄×C₁₇	1	2	yes	—
614	#117	C₂³×C₁₇	1	1	yes	characteristic
615	#117	C₂³×C₁₇	1	4	yes	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
620	C₂×C₄²	—	2	2	no	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
624	#107	C₂³×C₁₇	1	4	yes	—
625	#107	C₂³×C₁₇	1	4	yes	—
626	#107	C₂³×C₁₇	1	2	yes	—
627	#107	C₂³×C₁₇	1	4	yes	—
628	#106	C₂³×C₁₇	1	2	yes	—
629	#106	C₂³×C₁₇	1	4	yes	—
630	#106	C₂³×C₁₇	1	4	yes	—
631	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
632	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
633	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
634	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
635	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
636	#103	C₂³×C₁₇	1	4	yes	—
637	#103	C₂³×C₁₇	1	2	yes	—
638	#103	C₂³×C₁₇	1	4	yes	—
639	#103	C₂³×C₁₇	1	4	yes	—
640	#103	C₂³×C₁₇	1	2	yes	—
641	#103	C₂³×C₁₇	1	4	yes	—
642	#103	C₂³×C₁₇	1	2	yes	—
643	#103	C₂³×C₁₇	1	4	yes	—
644	#102	C₂³×C₁₇	1	4	yes	—
645	#102	C₂³×C₁₇	1	2	yes	—
646	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
647	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
648	C₄×C₈	C₂³×C₁₇	1	2	yes	—
649	C₄×C₈	C₂³×C₁₇	1	4	yes	—
650	C₁₇	#62146	1	1	yes	characteristic, direct product factor, Sylow
651	#41	—	2	2	no	—
652	#41	—	4	2	no	—
653	#41	—	4	1	no	—
654	#41	—	4	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	4	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
670	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
671	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
684	Q₁₆	—	2	4	no	—
685	Q₁₆	—	4	4	no	—
686	SD₁₆	—	4	2	no	—
687	M₁₆	—	4	4	no	—
688	M₁₆	—	4	2	no	—
689	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
690	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
691	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
720	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
723	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
738	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
739	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₁₇	1	2	yes	—
752	C₄²	C₂×D₄×C₁₇	1	2	yes	—
753	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
754	C₄²	C₂⁴×C₁₇	1	2	yes	—
755	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
756	C₂³	—	2	1	no	—
757	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
758	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	4	4	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	Q₈	—	4	2	no	—
770	Q₈	C₁₇×2₋¹⁺⁴	1	2	yes	—
771	D₄	—	2	2	no	—
772	D₄	—	2	1	no	—
773	D₄	—	2	1	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
807	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	4	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	4	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	C₁₇×#575	1	2	yes	—
836	C₄	C₁₇×#578	1	2	yes	—
837	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
838	C₄	C₁₇×#585	1	1	yes	characteristic
839	C₂	—	4	2	no	—
840	C₂	—	4	1	no	—
841	C₂	—	8	1	no	—
842	C₂	C₁₇×#3489	1	1	yes	characteristic
843	C₂	C₂×C₁₇×#575	1	1	yes	characteristic
844	C₂	C₂×C₁₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3509	C₂	semidirect
3. C₁₇×#3383	C₂	semidirect
4. C₁₇×#3364	C₂	semidirect
5. C₁₇×#3353	C₂	semidirect
6. C₁₇×#3352	C₂	semidirect
7. C₁₇×#3328	C₂	semidirect
8. C₁₇×#3327	C₂	semidirect
9. C₁₇×#3255	C₂	semidirect
10. C₁₇×#3252	C₂	semidirect
11. C₁₇×#3233	C₂	semidirect
12. C₁₇×#3230	C₂	semidirect
13. C₁₇×#3107	C₂	semidirect
14. C₁₇×#3104	C₂	semidirect
15. C₁₇×#3079	C₂	semidirect
16. C₁₇×#3078	C₂	semidirect
17. C₁₇×#2991	C₂	semidirect
333. #62146	C₁₇	direct (N × H)
389. #3509	C₂×C₁₇	semidirect
391. #3383	C₂×C₁₇	semidirect
392. #3364	C₂×C₁₇	semidirect
393. #3353	C₂×C₁₇	semidirect
394. #3352	C₂×C₁₇	semidirect
395. #3328	C₂×C₁₇	semidirect
396. #3327	C₂×C₁₇	semidirect
397. #3255	C₂×C₁₇	semidirect
398. #3252	C₂×C₁₇	semidirect
399. #3233	C₂×C₁₇	semidirect
400. #3230	C₂×C₁₇	semidirect
401. #3107	C₂×C₁₇	semidirect
402. #3104	C₂×C₁₇	semidirect
403. #3079	C₂×C₁₇	semidirect
404. #3078	C₂×C₁₇	semidirect
405. #2991	C₂×C₁₇	semidirect
650. C₁₇	#62146	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3509	2
C₁₇×#3482	2
C₁₇×#3383	2
C₁₇×#3364	2
C₁₇×#3353	2
C₁₇×#3352	2
C₁₇×#3328	2
C₁₇×#3327	2
C₁₇×#3255	2
C₁₇×#3252	2
C₁₇×#3233	2
C₁₇×#3230	2
C₁₇×#3107	2
C₁₇×#3104	2
C₁₇×#3079	2
C₁₇×#3078	2
C₁₇×#2991	2
#62146	17

Subgroups — C17×#62146 #16919890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62146 #16919890