Subgroups — C₁₇×#62131 #16919875

Order 4352.

1736 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3482	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3344	C₂	1	4	yes	maximal, complemented
6	C₁₇×#3335	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3316	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3299	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3248	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3239	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3113	C₂	1	2	yes	maximal, complemented
14	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#475	C₂	1	2	yes	maximal, complemented
17	C₁₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₇	C₂²	1	2	yes	—
19	C₁₇×#557	—	2	1	no	—
20	C₁₇×#557	C₂²	1	1	yes	characteristic
21	C₁₇×#556	—	2	1	no	—
22	C₁₇×#556	C₂²	1	1	yes	characteristic
23	C₁₇×#554	C₂²	1	2	yes	—
24	C₁₇×#554	C₂²	1	4	yes	—
25	C₁₇×#552	—	2	2	no	—
26	C₁₇×#552	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₇	—	2	1	no	—
28	D₄×Q₈×C₁₇	—	2	2	no	—
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×#544	—	2	2	no	—
34	C₁₇×#544	—	2	1	no	—
35	C₁₇×#533	—	2	1	no	—
36	C₁₇×#533	C₂²	1	1	yes	characteristic
37	C₁₇×#533	C₂²	1	2	yes	—
38	C₁₇×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
41	C₁₇×#529	—	2	2	no	—
42	C₁₇×#529	C₂²	1	2	yes	—
43	C₁₇×#520	—	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×#501	C₂²	1	4	yes	—
49	C₁₇×#498	C₂²	1	2	yes	—
50	C₁₇×#489	C₂²	1	4	yes	—
51	C₁₇×#487	C₂²	1	2	yes	—
52	C₁₇×#485	C₂²	1	2	yes	—
53	C₁₇×#484	C₂²	1	4	yes	—
54	C₁₇×#483	C₂²	1	4	yes	—
55	C₁₇×#483	C₂²	1	4	yes	—
56	C₁₇×#481	C₂²	1	4	yes	—
57	C₁₇×#479	C₂²	1	4	yes	—
58	C₁₇×#477	C₂²	1	2	yes	—
59	C₁₇×#476	C₂²	1	2	yes	—
60	C₁₇×#475	C₂²	1	2	yes	—
61	C₁₇×#475	C₂²	1	2	yes	—
62	C₁₇×#475	C₂²	1	2	yes	—
63	C₁₇×#475	C₂²	1	2	yes	—
64	C₁₇×#475	C₂²	1	4	yes	—
65	C₁₇×#475	C₂²	1	1	yes	characteristic
66	C₁₇×#475	C₂²	1	2	yes	—
67	C₁₇×#475	C₂²	1	4	yes	—
68	C₁₇×#474	C₂²	1	1	yes	characteristic
69	C₁₇×#474	C₂²	1	2	yes	—
70	C₁₇×#470	C₂²	1	4	yes	—
71	C₁₇×#467	C₂²	1	4	yes	—
72	C₁₇×#465	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	C₁₇×#446	C₂²	1	2	yes	—
81	C₁₇×#441	C₂²	1	4	yes	—
82	C₁₇×#441	C₂²	1	4	yes	—
83	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
85	C₁₇×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₁₇	C₂²	1	2	yes	—
87	C₁₇×#432	C₂²	1	2	yes	—
88	C₁₇×#431	C₂²	1	1	yes	characteristic
89	C₁₇×#428	C₂²	1	2	yes	—
90	C₂×C₁₇×#106	C₂²	1	4	yes	—
91	C₁₇×#423	C₂²	1	1	yes	characteristic
92	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
93	C₁₇×#417	C₂²	1	2	yes	—
94	C₂×C₁₇×#103	C₂²	1	4	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	2	no	—
99	C₂²×Q₈×C₁₇	—	2	1	no	—
100	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
106	C₁₇×C₄⋊Q₈	—	2	1	no	—
107	C₁₇×C₄⋊Q₈	—	2	1	no	—
108	C₁₇×C₄⋊Q₈	—	2	4	no	—
109	C₁₇×C₄⋊Q₈	—	2	2	no	—
110	C₁₇×C₄⋊Q₈	—	2	1	no	—
111	C₁₇×C₄⋊Q₈	—	2	2	no	—
112	C₁₇×C₄⋊Q₈	—	2	1	no	—
113	C₁₇×C₄⋊Q₈	—	2	2	no	—
114	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₇×#126	—	2	2	no	—
122	C₁₇×#126	—	2	2	no	—
123	C₁₇×#126	—	2	2	no	—
124	C₁₇×#125	—	2	2	no	—
125	C₁₇×#125	—	2	2	no	—
126	C₁₇×#125	—	2	4	no	—
127	C₁₇×#125	—	2	2	no	—
128	C₁₇×#125	—	2	1	no	—
129	C₁₇×#125	—	2	2	no	—
130	C₁₇×#125	—	2	1	no	—
131	C₁₇×#125	C₂³	1	2	yes	—
132	C₁₇×#124	—	2	2	no	—
133	C₁₇×#124	C₂³	1	2	yes	—
134	C₁₇×#123	—	2	2	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	1	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	2	no	—
144	C₁₇×C₂²⋊Q₈	—	2	4	no	—
145	C₁₇×C₂²⋊Q₈	—	2	4	no	—
146	C₁₇×C₂²⋊Q₈	—	2	4	no	—
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×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₇×#121	—	2	2	no	—
152	C₁₇×#121	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₇	—	2	2	no	—
154	C₄×Q₈×C₁₇	—	2	1	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	1	no	—
159	C₄×Q₈×C₁₇	—	2	2	no	—
160	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
163	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₇	—	2	1	no	—
170	C₄×D₄×C₁₇	—	2	4	no	—
171	C₄×D₄×C₁₇	—	2	2	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	2	no	—
184	C₁₇×#117	—	2	1	no	—
185	C₁₇×#117	—	2	1	no	—
186	C₁₇×#117	—	2	2	no	—
187	C₁₇×#117	—	2	1	no	—
188	C₁₇×#117	—	2	2	no	—
189	C₁₇×#117	D₄	1	2	yes	—
190	C₁₇×#117	D₄	1	1	yes	characteristic
191	C₁₇×#117	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
193	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
194	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	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×#106	C₂³	1	4	yes	—
205	C₁₇×#106	C₂³	1	4	yes	—
206	C₁₇×#106	C₂³	1	4	yes	—
207	C₁₇×#106	C₂³	1	2	yes	—
208	C₁₇×#106	C₂³	1	4	yes	—
209	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₇×#103	C₂³	1	2	yes	—
215	C₁₇×#103	C₂³	1	4	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	2	yes	—
220	C₁₇×#103	C₂³	1	4	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	2	yes	—
225	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₇×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₇	C₂³	1	2	yes	—
228	#41×C₁₇	—	2	4	no	—
229	#41×C₁₇	—	2	2	no	—
230	#41×C₁₇	—	4	1	no	—
231	#41×C₁₇	—	4	4	no	—
232	C₂×Q₈×C₁₇	—	2	2	no	—
233	C₂×Q₈×C₁₇	—	2	1	no	—
234	C₂×Q₈×C₁₇	—	2	2	no	—
235	C₂×Q₈×C₁₇	—	2	1	no	—
236	C₂×Q₈×C₁₇	—	2	4	no	—
237	C₂×Q₈×C₁₇	—	2	2	no	—
238	C₂×Q₈×C₁₇	—	2	4	no	—
239	C₂×Q₈×C₁₇	—	4	2	no	—
240	C₂×Q₈×C₁₇	—	8	4	no	—
241	C₂×Q₈×C₁₇	—	8	2	no	—
242	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₇	—	2	2	no	—
247	C₂×D₄×C₁₇	—	2	1	no	—
248	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₇	—	2	2	no	—
252	C₂²×C₄×C₁₇	—	2	2	no	—
253	C₂²×C₄×C₁₇	—	2	2	no	—
254	C₂²×C₄×C₁₇	—	2	4	no	—
255	C₂²×C₄×C₁₇	—	2	1	no	—
256	C₂²×C₄×C₁₇	—	2	1	no	—
257	C₂²×C₄×C₁₇	—	2	1	no	—
258	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
264	Q₁₆×C₁₇	—	2	4	no	—
265	Q₁₆×C₁₇	—	4	4	no	—
266	SD₁₆×C₁₇	—	4	2	no	—
267	M₁₆×C₁₇	—	4	2	no	—
268	C₂×C₈×C₁₇	—	4	4	no	—
269	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
270	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
271	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₁₇	—	2	4	no	—
273	C₄⋊C₄×C₁₇	—	2	2	no	—
274	C₄⋊C₄×C₁₇	—	2	1	no	—
275	C₄⋊C₄×C₁₇	—	2	2	no	—
276	C₄⋊C₄×C₁₇	—	2	4	no	—
277	C₄⋊C₄×C₁₇	—	2	2	no	—
278	C₄⋊C₄×C₁₇	—	2	4	no	—
279	C₄⋊C₄×C₁₇	—	2	1	no	—
280	C₄⋊C₄×C₁₇	—	2	1	no	—
281	C₄⋊C₄×C₁₇	—	2	1	no	—
282	C₄⋊C₄×C₁₇	—	2	2	no	—
283	C₄⋊C₄×C₁₇	—	2	2	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	2	no	—
288	C₄⋊C₄×C₁₇	—	2	1	no	—
289	C₄⋊C₄×C₁₇	—	2	2	no	—
290	C₄⋊C₄×C₁₇	—	2	1	no	—
291	C₄⋊C₄×C₁₇	—	2	2	no	—
292	C₄⋊C₄×C₁₇	—	2	1	no	—
293	C₄⋊C₄×C₁₇	—	2	2	no	—
294	C₄⋊C₄×C₁₇	—	2	4	no	—
295	C₄⋊C₄×C₁₇	—	2	2	no	—
296	C₄⋊C₄×C₁₇	—	2	1	no	—
297	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
306	C₂²⋊C₄×C₁₇	—	2	2	no	—
307	C₂²⋊C₄×C₁₇	—	2	4	no	—
308	C₂²⋊C₄×C₁₇	—	2	2	no	—
309	C₂²⋊C₄×C₁₇	—	2	2	no	—
310	C₂²⋊C₄×C₁₇	—	2	1	no	—
311	C₂²⋊C₄×C₁₇	—	2	2	no	—
312	C₂²⋊C₄×C₁₇	—	2	2	no	—
313	C₂²⋊C₄×C₁₇	—	2	1	no	—
314	C₂²⋊C₄×C₁₇	—	2	1	no	—
315	C₂²⋊C₄×C₁₇	—	2	2	no	—
316	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
317	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
318	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
319	C₄²×C₁₇	—	2	2	no	—
320	C₄²×C₁₇	—	2	1	no	—
321	C₄²×C₁₇	—	2	4	no	—
322	C₄²×C₁₇	—	2	2	no	—
323	C₄²×C₁₇	—	2	2	no	—
324	C₄²×C₁₇	—	2	1	no	—
325	C₄²×C₁₇	—	2	1	no	—
326	C₄²×C₁₇	—	2	2	no	—
327	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₁₇	C₂×D₄	1	2	yes	—
329	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₇	C₂×D₄	1	2	yes	—
331	C₄²×C₁₇	C₂⁴	1	2	yes	—
332	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
334	#62131	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₁₇	—	2	1	no	—
336	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
337	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
338	Q₈×C₁₇	—	2	2	no	—
339	Q₈×C₁₇	—	2	1	no	—
340	Q₈×C₁₇	—	2	2	no	—
341	Q₈×C₁₇	—	2	2	no	—
342	Q₈×C₁₇	—	2	2	no	—
343	Q₈×C₁₇	—	2	2	no	—
344	Q₈×C₁₇	—	4	4	no	—
345	Q₈×C₁₇	—	4	2	no	—
346	Q₈×C₁₇	—	4	2	no	—
347	Q₈×C₁₇	—	4	4	no	—
348	Q₈×C₁₇	—	8	4	no	—
349	Q₈×C₁₇	—	8	2	no	—
350	Q₈×C₁₇	2₋¹⁺⁴	1	2	yes	—
351	D₄×C₁₇	—	2	4	no	—
352	D₄×C₁₇	—	2	1	no	—
353	D₄×C₁₇	—	2	1	no	—
354	D₄×C₁₇	—	4	2	no	—
355	D₄×C₁₇	—	4	4	no	—
356	D₄×C₁₇	#137	1	4	yes	—
357	C₂×C₄×C₁₇	—	2	4	no	—
358	C₂×C₄×C₁₇	—	2	1	no	—
359	C₂×C₄×C₁₇	—	2	2	no	—
360	C₂×C₄×C₁₇	—	2	4	no	—
361	C₂×C₄×C₁₇	—	2	2	no	—
362	C₂×C₄×C₁₇	—	2	2	no	—
363	C₂×C₄×C₁₇	—	2	1	no	—
364	C₂×C₄×C₁₇	—	2	2	no	—
365	C₂×C₄×C₁₇	—	2	1	no	—
366	C₂×C₄×C₁₇	—	2	1	no	—
367	C₂×C₄×C₁₇	—	2	2	no	—
368	C₂×C₄×C₁₇	—	2	1	no	—
369	C₂×C₄×C₁₇	—	2	2	no	—
370	C₂×C₄×C₁₇	—	2	2	no	—
371	C₂×C₄×C₁₇	—	2	4	no	—
372	C₂×C₄×C₁₇	—	2	2	no	—
373	C₂×C₄×C₁₇	—	4	2	no	—
374	C₂×C₄×C₁₇	—	4	4	no	—
375	C₂×C₄×C₁₇	—	4	4	no	—
376	C₂×C₄×C₁₇	—	4	2	no	—
377	C₂×C₄×C₁₇	—	4	2	no	—
378	C₂×C₄×C₁₇	—	8	4	no	—
379	C₂×C₄×C₁₇	—	8	2	no	—
380	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
389	C₈×C₁₇	—	2	2	no	—
390	C₈×C₁₇	—	2	2	no	—
391	C₈×C₁₇	—	2	4	no	—
392	#3503	C₂×C₁₇	1	1	yes	characteristic, complemented
393	#3482	C₂×C₁₇	1	1	yes	characteristic
394	#3387	C₂×C₁₇	1	2	yes	complemented
395	#3369	C₂×C₁₇	1	2	yes	complemented
396	#3344	C₂×C₁₇	1	4	yes	complemented
397	#3335	C₂×C₁₇	1	2	yes	complemented
398	#3316	C₂×C₁₇	1	4	yes	complemented
399	#3299	C₂×C₁₇	1	2	yes	complemented
400	#3255	C₂×C₁₇	1	1	yes	characteristic, complemented
401	#3248	C₂×C₁₇	1	2	yes	complemented
402	#3239	C₂×C₁₇	1	2	yes	complemented
403	#3229	C₂×C₁₇	1	1	yes	characteristic, complemented
404	#3113	C₂×C₁₇	1	2	yes	complemented
405	#3107	C₂×C₁₇	1	1	yes	characteristic, complemented
406	#3079	C₂×C₁₇	1	1	yes	characteristic, complemented
407	C₂×#475	C₂×C₁₇	1	2	yes	complemented
408	#2990	C₂×C₁₇	1	1	yes	characteristic, complemented
409	C₂²×C₁₇	—	2	2	no	—
410	C₂²×C₁₇	—	2	2	no	—
411	C₂²×C₁₇	—	2	1	no	—
412	C₂²×C₁₇	—	2	1	no	—
413	C₂²×C₁₇	—	2	1	no	—
414	C₂²×C₁₇	—	4	1	no	—
415	C₂²×C₁₇	—	4	1	no	—
416	C₂²×C₁₇	—	4	1	no	—
417	C₂²×C₁₇	C₂×#137	1	4	yes	—
418	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
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	—	2	2	no	—
424	C₄×C₁₇	—	2	2	no	—
425	C₄×C₁₇	—	2	1	no	—
426	C₄×C₁₇	—	4	2	no	—
427	C₄×C₁₇	—	4	2	no	—
428	C₄×C₁₇	—	4	1	no	—
429	C₄×C₁₇	—	4	2	no	—
430	C₄×C₁₇	—	4	1	no	—
431	C₄×C₁₇	—	4	2	no	—
432	C₄×C₁₇	—	4	4	no	—
433	C₄×C₁₇	C₂×#137	1	2	yes	—
434	C₄×C₁₇	#577	1	2	yes	—
435	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
436	C₄×C₁₇	#585	1	1	yes	characteristic
437	Q₈²	C₂²×C₁₇	1	2	yes	—
438	#557	—	2	1	no	—
439	#557	C₂²×C₁₇	1	1	yes	characteristic
440	#556	—	2	1	no	—
441	#556	C₂²×C₁₇	1	1	yes	characteristic
442	#554	C₂²×C₁₇	1	2	yes	—
443	#554	C₂²×C₁₇	1	4	yes	—
444	#552	—	2	2	no	—
445	#552	C₂²×C₁₇	1	2	yes	—
446	D₄×Q₈	—	2	1	no	—
447	D₄×Q₈	—	2	2	no	—
448	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
449	#548	C₂²×C₁₇	1	2	yes	—
450	#547	—	2	1	no	—
451	#547	C₂²×C₁₇	1	1	yes	characteristic
452	#544	—	2	2	no	—
453	#544	—	2	1	no	—
454	#533	—	2	1	no	—
455	#533	C₂²×C₁₇	1	1	yes	characteristic
456	#533	C₂²×C₁₇	1	2	yes	—
457	#533	C₂²×C₁₇	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
459	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
460	#529	—	2	2	no	—
461	#529	C₂²×C₁₇	1	2	yes	—
462	#520	—	2	1	no	—
463	C₄×#41	—	2	1	no	—
464	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
465	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
467	#501	C₂²×C₁₇	1	4	yes	—
468	#498	C₂²×C₁₇	1	2	yes	—
469	#489	C₂²×C₁₇	1	4	yes	—
470	#487	C₂²×C₁₇	1	2	yes	—
471	#485	C₂²×C₁₇	1	2	yes	—
472	#484	C₂²×C₁₇	1	4	yes	—
473	#483	C₂²×C₁₇	1	4	yes	—
474	#483	C₂²×C₁₇	1	4	yes	—
475	#481	C₂²×C₁₇	1	4	yes	—
476	#479	C₂²×C₁₇	1	4	yes	—
477	#477	C₂²×C₁₇	1	2	yes	—
478	#476	C₂²×C₁₇	1	2	yes	—
479	#475	C₂²×C₁₇	1	1	yes	characteristic
480	#475	C₂²×C₁₇	1	2	yes	—
481	#475	C₂²×C₁₇	1	4	yes	—
482	#475	C₂²×C₁₇	1	4	yes	—
483	#475	C₂²×C₁₇	1	2	yes	—
484	#475	C₂²×C₁₇	1	2	yes	—
485	#475	C₂²×C₁₇	1	2	yes	—
486	#475	C₂²×C₁₇	1	2	yes	—
487	#474	C₂²×C₁₇	1	2	yes	—
488	#474	C₂²×C₁₇	1	1	yes	characteristic
489	#470	C₂²×C₁₇	1	4	yes	—
490	#467	C₂²×C₁₇	1	4	yes	—
491	#465	C₂²×C₁₇	1	4	yes	—
492	#464	C₂²×C₁₇	1	4	yes	—
493	#462	C₂²×C₁₇	1	1	yes	characteristic
494	#462	C₂²×C₁₇	1	2	yes	—
495	#462	C₂²×C₁₇	1	2	yes	—
496	#461	C₂²×C₁₇	1	1	yes	characteristic
497	#452	C₂²×C₁₇	1	2	yes	—
498	#451	C₂²×C₁₇	1	4	yes	—
499	#446	C₂²×C₁₇	1	2	yes	—
500	#441	C₂²×C₁₇	1	4	yes	—
501	#441	C₂²×C₁₇	1	4	yes	—
502	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
503	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
504	#435	C₂²×C₁₇	1	4	yes	—
505	C₈×D₄	C₂²×C₁₇	1	2	yes	—
506	#432	C₂²×C₁₇	1	2	yes	—
507	#431	C₂²×C₁₇	1	1	yes	characteristic
508	#428	C₂²×C₁₇	1	2	yes	—
509	C₂×#106	C₂²×C₁₇	1	4	yes	—
510	#423	C₂²×C₁₇	1	1	yes	characteristic
511	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
512	#417	C₂²×C₁₇	1	2	yes	—
513	C₂×#103	C₂²×C₁₇	1	4	yes	—
514	C₂×C₁₇	—	2	4	no	—
515	C₂×C₁₇	—	4	1	no	—
516	C₂×C₁₇	—	8	1	no	—
517	C₂×C₁₇	#3489	1	1	yes	characteristic
518	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
519	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
520	C₂×#41	—	2	1	no	—
521	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
522	C₂×#41	C₂³×C₁₇	1	1	yes	characteristic
523	C₂²×Q₈	—	2	2	no	—
524	C₂²×Q₈	—	2	1	no	—
525	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
526	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
527	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
528	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
529	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
530	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	4	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
544	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	4	no	—
552	#125	—	2	2	no	—
553	#125	—	2	1	no	—
554	#125	—	2	2	no	—
555	#125	—	2	1	no	—
556	#125	C₂³×C₁₇	1	2	yes	—
557	#124	—	2	2	no	—
558	#124	C₂³×C₁₇	1	2	yes	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	#123	—	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	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
575	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
576	#121	—	2	2	no	—
577	#121	C₂³×C₁₇	1	2	yes	—
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	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
589	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
590	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
593	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
602	C₄×D₄	D₄×C₁₇	1	2	yes	—
603	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₁₇	1	2	yes	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	D₄×C₁₇	1	2	yes	—
615	#117	D₄×C₁₇	1	1	yes	characteristic
616	#117	C₂³×C₁₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
623	C₂×C₄²	—	2	2	no	—
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
627	#107	C₂³×C₁₇	1	4	yes	—
628	#107	C₂³×C₁₇	1	2	yes	—
629	#106	C₂³×C₁₇	1	2	yes	—
630	#106	C₂³×C₁₇	1	4	yes	—
631	#106	C₂³×C₁₇	1	4	yes	—
632	#106	C₂³×C₁₇	1	4	yes	—
633	#106	C₂³×C₁₇	1	4	yes	—
634	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
635	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
636	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
637	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
639	#103	C₂³×C₁₇	1	2	yes	—
640	#103	C₂³×C₁₇	1	4	yes	—
641	#103	C₂³×C₁₇	1	4	yes	—
642	#103	C₂³×C₁₇	1	4	yes	—
643	#103	C₂³×C₁₇	1	2	yes	—
644	#103	C₂³×C₁₇	1	2	yes	—
645	#103	C₂³×C₁₇	1	4	yes	—
646	#103	C₂³×C₁₇	1	4	yes	—
647	#102	C₂³×C₁₇	1	4	yes	—
648	#102	C₂³×C₁₇	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
651	#97	C₂³×C₁₇	1	4	yes	—
652	C₄×C₈	C₂³×C₁₇	1	2	yes	—
653	C₁₇	#62131	1	1	yes	characteristic, direct product factor, Sylow
654	#41	—	2	4	no	—
655	#41	—	2	2	no	—
656	#41	—	4	1	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	4	2	no	—
666	C₂×Q₈	—	8	4	no	—
667	C₂×Q₈	—	8	2	no	—
668	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
669	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
675	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
676	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
690	Q₁₆	—	2	4	no	—
691	Q₁₆	—	4	4	no	—
692	SD₁₆	—	4	2	no	—
693	M₁₆	—	4	2	no	—
694	C₂×C₈	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
696	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
697	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
730	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
743	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	2	no	—
753	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₁₇	1	2	yes	—
756	C₄²	C₂×D₄×C₁₇	1	2	yes	—
757	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
758	C₄²	C₂⁴×C₁₇	1	2	yes	—
759	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
760	C₂³	—	2	1	no	—
761	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
762	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	2	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	8	4	no	—
774	Q₈	—	8	2	no	—
775	Q₈	C₁₇×2₋¹⁺⁴	1	2	yes	—
776	D₄	—	2	4	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	1	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	C₁₇×#137	1	4	yes	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	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	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	—	8	2	no	—
805	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
814	C₈	—	2	2	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	4	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	C₂×C₁₇×#137	1	4	yes	—
826	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	4	no	—
841	C₄	C₂×C₁₇×#137	1	2	yes	—
842	C₄	C₁₇×#577	1	2	yes	—
843	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
844	C₄	C₁₇×#585	1	1	yes	characteristic
845	C₂	—	2	4	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	1	no	—
848	C₂	C₁₇×#3489	1	1	yes	characteristic
849	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
850	C₂	C₂×C₁₇×#577	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×#3503	C₂	semidirect
3. C₁₇×#3387	C₂	semidirect
4. C₁₇×#3369	C₂	semidirect
5. C₁₇×#3344	C₂	semidirect
6. C₁₇×#3335	C₂	semidirect
7. C₁₇×#3316	C₂	semidirect
8. C₁₇×#3299	C₂	semidirect
9. C₁₇×#3255	C₂	semidirect
10. C₁₇×#3248	C₂	semidirect
11. C₁₇×#3239	C₂	semidirect
12. C₁₇×#3229	C₂	semidirect
13. C₁₇×#3113	C₂	semidirect
14. C₁₇×#3107	C₂	semidirect
15. C₁₇×#3079	C₂	semidirect
16. C₂×C₁₇×#475	C₂	semidirect
17. C₁₇×#2990	C₂	semidirect
334. #62131	C₁₇	direct (N × H)
392. #3503	C₂×C₁₇	semidirect
394. #3387	C₂×C₁₇	semidirect
395. #3369	C₂×C₁₇	semidirect
396. #3344	C₂×C₁₇	semidirect
397. #3335	C₂×C₁₇	semidirect
398. #3316	C₂×C₁₇	semidirect
399. #3299	C₂×C₁₇	semidirect
400. #3255	C₂×C₁₇	semidirect
401. #3248	C₂×C₁₇	semidirect
402. #3239	C₂×C₁₇	semidirect
403. #3229	C₂×C₁₇	semidirect
404. #3113	C₂×C₁₇	semidirect
405. #3107	C₂×C₁₇	semidirect
406. #3079	C₂×C₁₇	semidirect
407. C₂×#475	C₂×C₁₇	semidirect
408. #2990	C₂×C₁₇	semidirect
653. C₁₇	#62131	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×#3503	2
C₁₇×#3482	2
C₁₇×#3387	2
C₁₇×#3369	2
C₁₇×#3344	2
C₁₇×#3335	2
C₁₇×#3316	2
C₁₇×#3299	2
C₁₇×#3255	2
C₁₇×#3248	2
C₁₇×#3239	2
C₁₇×#3229	2
C₁₇×#3113	2
C₁₇×#3107	2
C₁₇×#3079	2
C₂×C₁₇×#475	2
C₁₇×#2990	2
#62131	17

Subgroups — C17×#62131 #16919875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62131 #16919875